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  • Articles  (47)
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  • Optimal control  (47)
  • Springer  (47)
  • 2020-2022
  • 1995-1999  (47)
  • Mathematics  (47)
  • 1
    Electronic Resource
    Electronic Resource
    A Technique for Stochastic Control Problems with Unbounded Control Set (1999)
    Springer
    Journal of theoretical probability 12 (1999), S. 255-270 
    Details
    ISSN: 1572-9230
    Keywords: Optimal control ; stochastic differential equations ; convergence in law ; unbounded control set ; suboptimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We describe a change of time technique for stochastic control problems with unbounded control set. We demonstrate the technique on a class of maximization problems that do not have optimal controls. Given such a problem, we introduce an extended problem which has the same value function as the original problem and for which there exist optimal controls that are expressible in simple terms. This device yields a natural sequence of suboptimal controls for the original problem. By this we mean a sequence of controls for which the payoff functions approach the value function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1021761030407
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  • 2
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    Optimal budgetary and monetary policies under uncertainty: A stochastic control approach (1995)
    Springer
    Annals of operations research 58 (1995), S. 379-402 
    Details
    ISSN: 1572-9338
    Keywords: Optimal control ; stochastic control ; dynamic systems ; economics ; public-sector applications ; optimization ; budgetary policies ; monetary policy
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract In this paper, we determine optimal budgetary and monetary policies for Austria using a small macroeconometric model. We use a Keynesian model of the Austrian economy, called FINPOL1, estimated by ordinary least squares, which relates the main objective variables of Austrian economic policies, such as the growth rate of real gross domestic product, the rate of unemployment, the rate of inflation, the balance of payments, and the ratio of the federal budget deficit to GDP, to fiscal and monetary policy instruments, namely expenditures and revenues of the federal budget and money supply. Optimal fiscal and monetary policies are calculated for the model under a quadratic objective function using the algorithm OPTCON for the optimum control of nonlinear stochastic dynamic systems. Several control experiments are performed in order to assess the influence of different kinds of uncertainty on optimal budgetary and monetary policies. Apart from deterministic optimization runs, different assumptions about parameter uncertainties are introduced; the results of these different stochastic optimum control experiments are compared and interpreted.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02038862
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  • 3
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    Sensitivity, controllability, and necessary conditions of optimal control problems governed by integral equations (1995)
    Springer
    Applied mathematics & optimization 32 (1995), S. 73-97 
    Details
    ISSN: 1432-0606
    Keywords: Optimal control ; State constraint ; Volterra integral equation ; Necessary conditions ; Controllability ; Sensitivity ; Value function ; Proximal normal analysis ; Proximal analysis ; 49J22 ; 49K22 ; 93B05 ; 93B06 ; 93B35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Infinite-dimensional perturbations in all constraints of an optimal control problem governed by a Volterra integral equation with the presence of a state constraint are considered. These perturbations give rise to a value function, whose analysis through the proximal normal technique provides sensitivity, controllability, and even necessary conditions for the basic problem. Actually all information about the value function is contained in Clarke's normal cone of its epigraph, which can be characterized by the proximal normal formula.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01189904
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  • 4
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    Value function and optimality condition for semilinear control problems. II: Parabolic case (1996)
    Springer
    Applied mathematics & optimization 33 (1996), S. 1-33 
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    ISSN: 1432-0606
    Keywords: Optimal control ; Value function ; Analytic semigroups ; Semiconcave functions ; Distributed parameter systems ; 49K20 ; 49L20 ; 47B44 ; 49J52
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we continue to study properties of the value function and of optimal solutions of a semilinear Mayer problem in infinite dimensions. Applications concern systems governed by a state equation of parabolic type. In particular, the issues of the joint Lipschitz continuity and semiconcavity of the value function are treated in order to investigate the differentiability of the value function along optimal trajectories.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01187960
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  • 5
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    The optimal control approach to generalized multiprocessor scheduling (1996)
    Springer
    Algorithmica 15 (1996), S. 17-49 
    Details
    ISSN: 1432-0541
    Keywords: Scheduling ; Multiprocessor scheduling ; Parallel algorithms ; NP-completeness ; Theoretical computer science ; Operations research ; Optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract In this paper we present several new results in the theory of homogeneous multiprocessor scheduling. We start with some assumptions about the behavior of tasks, with associated precedence constraints, as processor power is applied. We assume that as more processors are applied to a task, the time taken to compute it decreases, yielding some speedup. Because of communication, synchronization, and task scheduling overhead, this speedup increases less than linearly with the number of processors applied. We also assume that the number of processors which can be assigned to a task is a continuous variable, with a view to exploiting continuous mathematics. The optimal scheduling problem is to determine the number of processors assigned to each task, and task sequencing, to minimize the finishing time. These assumptions allow us to recast the optimal scheduling problem in a form which can be addressed by optimal control theory. Various theorems can be proven which characterize the optimal scheduling solution. Most importantly, for the special case where the speedup function of each task isp α , wherep is the amount of processing power applied to the task, we can directly solve our equations for the optimal solution. In this case, for task graphs formed from parallel and series connections, the solution can be derived by inspection. The solution can also be shown to be shortest path from the initial to the final state, as measured by anl 1/α distance metric, subject to obstacle constraints imposed by the precedence constraints.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01942605
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  • 6
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    Provably good approximation algorithms for optimal kinodynamic planning: Robots with decoupled dynamics bounds (1995)
    Springer
    Algorithmica 14 (1995), S. 443-479 
    Details
    ISSN: 1432-0541
    Keywords: Robot motion planning ; Optimal control ; Polynomial-timeɛ-approximation algorithm ; Time-optimal trajectory ; Shortest path ; Kinodynamics ; Polyhedral obstacles
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract We consider the following problem: given a robot system, find a minimal-time trajectory that goes from a start state to a goal state while avoiding obstacles by a speed-dependent safety margin and respecting dynamics bounds. In [1] we developed a provably good approximation algorithm for the minimum-time trajectory problem for a robot system with decoupled dynamics bounds (e.g., a point robot in ℝ3). This algorithm differs from previous work in three ways. It is possible (1) to bound the goodness of the approximation by an error termɛ; (2) to bound the computational complexity of our algorithm polynomially; and (3) to express the complexity as a polynomial function of the error term. Hence, given the geometric obstacles, dynamics bounds, and the error termɛ, the algorithm returns a solution that isɛ-close to optimal and requires only a polynomial (in (1/ɛ)) amount of time. We extend the results of [1] in two ways. First, we modify it to halve the exponent in the polynomial bounds from 6d to 3d, so that the new algorithm isO(c d N 1/ɛ)3d ), whereN is the geometric complexity of the obstacles andc is a robot-dependent constant. Second, the new algorithm finds a trajectory that matches the optimal in time with anɛ factor sacrificed in the obstacle-avoidance safety margin. Similar results hold for polyhedral Cartesian manipulators in polyhedral environments. The new results indicate that an implementation of the algorithm could be reasonable, and a preliminary implementation has been done for the planar case.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586636
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  • 7
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    Provably good approximation algorithms for optimal kinodynamic planning for Cartesian robots and open-chain manipulators (1995)
    Springer
    Algorithmica 14 (1995), S. 480-530 
    Details
    ISSN: 1432-0541
    Keywords: Robot motion planning ; Optimal control ; Polynomial-timeɛ-approximation algorithm ; Time-optimal trajectory ; Full dynamics ; Shortest path ; Kinodynamics ; Polyhedral obstacles
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Inoptimal kinodynamic planning, given a robot system, we must find a minimal-time trajectory that goes from a start state to a goal state while avoiding obstacles by a speed-dependent safety margin and respecting dynamics bounds. With Canny and Reif [1], we approached this problem from anɛ-approximation standpoint and introduced a provably good approximation algorithm for optimal kinodynamic planning for a robot obeying particle dynamics. If a solution exists, this algorithm returns a trajectoryɛ-close to optimal in time polynomial in both (1/ɛ) and the geometric complexity. We extend [1] and [2] tod-link three-dimensional robots with full rigid-body dynamics amidst obstacles. Specifically, we describe polynomial-time approximation algorithms for Cartesian robots obeyingL 2 dynamic bounds and for open-kinematic-chain manipulators with revolute and prismatic joints. The latter class includes many industrial manipulators. The correctness and complexity of these algorithms rely on new trajectory tracking lemmas for robots with coupled dynamics bounds.
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    URL: http://dx.doi.org/10.1007/BF01586637
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  • 8
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    On unbounded solutions of Bellman's equation associated with optimal switching control problems with state constraints (1995)
    Springer
    Applied mathematics & optimization 31 (1995), S. 1-17 
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    ISSN: 1432-0606
    Keywords: Bellman equation ; Hamilton-Jacobi equation ; Quasi-variational inequality ; Viscosity solution ; Unbounded solutions ; Optimal switching ; Optimal control ; State constraints ; Production engineering ; 49C05 ; 49C20 ; 49B10 ; 49A36
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study a quasi-variational inequality system with unbounded solutions. It represents the Bellman equation associated with an optimal switching control problem with state constraints arising from production engineering. We show that the optimal cost is the unique viscosity solution of the system.
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    URL: http://dx.doi.org/10.1007/BF01182554
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  • 9
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    Constrained retarded nonlinear optimal control problems in Banach state space (1996)
    Springer
    Applied mathematics & optimization 34 (1996), S. 191-230 
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    ISSN: 1432-0606
    Keywords: Optimal control ; Retarded systems ; Control in infinite-dimensional state space ; Primary 49K25 ; Secondary 34K35
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Necessary conditions are proved for the optimal control of solutions of ordinary and retarded differential equations in a Banach state space, with mixed and pure state restrictions. The treatment includes the possibility of point targets. A generalization of earlier results for finite-dimensional or Hilbert state spaces is obtained.
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    URL: http://dx.doi.org/10.1007/BF01182624
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  • 10
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    Boundary optimal control of MHD flows (1995)
    Springer
    Applied mathematics & optimization 32 (1995), S. 143-162 
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    ISSN: 1432-0606
    Keywords: Optimal control ; Magnetohydrodynamics ; Electrically conducting fluid ; Primary 49J20 ; 49K20 ; Secondary 35Q35 ; 49M05 ; 76W05 ; 93C10 ; 93C20
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with some optimal control problems associated with the equations of steady-state, incompressible magnetohydrodynamics. These problems have direct applications to nuclear reactor technology, magnetic propulsion devices, and design of electromagnetic pumps. These problems are first put into an appropriate mathematical formulation. Then the existence of optimal solutions is proved. The use of Lagrange multiplier techniques is justified and an optimality system of equations is derived. The theory is applied to an example.
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    URL: http://dx.doi.org/10.1007/BF01185228
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  • 11
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    Generalized sentinels defined via least squares (1995)
    Springer
    Applied mathematics & optimization 31 (1995), S. 189-218 
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    ISSN: 1432-0606
    Keywords: Least squares ; Sentinels ; Optimal control ; Regularization ; Duality ; 93A30 ; 49K27
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We address the problem of monitoring a linear functional (c, x)Eof an unknown vectorx of a Hilbert spaceE, the available data being the observationz, in a Hilbert spaceF, of a vectorAx depending linearly onx through some known operatorAεℒ(E; F). WhenE=E 1×E 2,c=(c 1 0), andA is injective and defined through the solution of a partial differential equation, Lions ([6]–[8]) introduced sentinelssεF such that (s, Ax)Fis sensitive to x1 εE 1 but insensitive to x2 ε E2. In this paper we prove the existence, in the general case, of (i) a generalized sentinel (s, σ) ε ℱ ×E, where ℱ ⊃F withF dense in 80, such that for anya priori guess x0 ofx, we have 〈s, Ax〉ℱℱ + (σ, x0)E=(c, x)E, where x is the least-squares estimate ofx closest tox 0, and (ii) a family of regularized sentinels (s n , σ n ) ε F×E which converge to (s, σ). Generalized sentinels unify the least-squares approach (by construction !) and the sentinel approach (whenA is injective), and provide a general framework for the construction of “sentinels with special sensitivity” in the sense of Lions [8]).
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    URL: http://dx.doi.org/10.1007/BF01182788
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  • 12
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    An SQP method for optimal control of weakly singular Hammerstein integral equations (1996)
    Springer
    Applied mathematics & optimization 33 (1996), S. 227-252 
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    ISSN: 1432-0606
    Keywords: Lagrange-Newton method ; Sequential quadratic programming ; Optimal control ; Weakly singular Hammerstein integral equations ; Control constraints ; 49M05 ; 49K22
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate local convergence of an SQP method for nonlinear optimal control of weakly singular Hammerstein integral equations. Sufficient conditions for local quadratic convergence of the method are discussed.
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    URL: http://dx.doi.org/10.1007/BF01204703
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  • 13
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    Optimal control of the chemotherapy of HIV (1997)
    Springer
    Journal of mathematical biology 35 (1997), S. 775-792 
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    ISSN: 1432-1416
    Keywords: Key words: Chemotherapy ; HIV ; Optimal control ; Ordinary differential equation system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract.  Using an existing ordinary differential equation model which describes the interaction of the immune system with the human immunodeficiency virus (HIV), we introduce chemotherapy in an early treatment setting through a dynamic treatment and then solve for an optimal chemotherapy strategy. The control represents the percentage of effect the chemotherapy has on the viral production. Using an objective function based on a combination of maximizing benefit based on T cell counts and minimizing the systemic cost of chemotherapy (based on high drug dose/strength), we solve for the optimal control in the optimality system composed of four ordinary differential equations and four adjoint ordinary differential equations.
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    URL: http://dx.doi.org/10.1007/s002850050076
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  • 14
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    Optimal control for a tandem network of queues with blocking (1997)
    Springer
    Acta mathematicae applicatae sinica 13 (1997), S. 425-437 
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    ISSN: 1618-3932
    Keywords: Optimal control ; tandem queueing system
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider a two-station tandem queue with no intermediate buffer. Jobs at the first station may be blocked when the following station is occupied by another job. The objective is to control the arrival and departure processes, subject to some capacity limits, so that an expected discounted profit function is maximized. We prove that the optimal control policy is of a threshold type, and the characterization of the threshold is provided.
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    URL: http://dx.doi.org/10.1007/BF02009552
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  • 15
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    Neural network controller for a multivariable model of submarine dynamics (1998)
    Springer
    Neural computing & applications 7 (1998), S. 295-308 
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    ISSN: 1433-3058
    Keywords: Adaptive ; Backpropagation ; Multivariable ; Neural networks ; Optimal control ; Submarine
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract Recently, there have been many attempts to use neural networks as a feedback controller. However, most of the reported cases seek to control Single-Input Single-Output (SISO) systems using some sort of adaptive strategy. In this paper, we demonstrate that neural networks can be used for the control of complex multivariable, rather than simply SISO, systems. A modified direct control scheme using a neural network architecture is used with backpropagation as the adaptive algorithm. The proposed algorithm is designed for Multi-Input Multi-Output (MIMO) systems, and is similar to that proposed by Saerens and Soquet [1] and Goldenthal and Farrell [2] for (SISO) systems, and differs only in the form of the gradient approximation. As an example of the application of this approach, we investigate the control of the dynamics of a submarine vehicle with four inputs and four outputs, in which the differential stern, bow and rudder control surfaces are dynamically coordinated to cause the submarine to follow commanded changes in roll, yaw rate, depth rate and pitch attitude. Results obtained using this scheme are compared with those obtained using optimal linear quadratic control.
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    URL: http://dx.doi.org/10.1007/BF01428121
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  • 16
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    The linear quadratic optimal control problem for linear descriptor systems with variable coefficients (1997)
    Springer
    Mathematics of control, signals, and systems 10 (1997), S. 247-264 
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    ISSN: 1435-568X
    Keywords: Descriptor systems ; Differential algebraic equations ; Optimal control ; Strangeness index ; Riccati differential-algebraic equations ; Euler-Lagrange equations ; Linear feedback
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics , Technology
    Notes: Abstract We study linear quadratic optimal control problems for linear variable coefficient descriptor systems. Generalization from the case of standard control problems leads to several difficulties. We discuss a behavioral approach that solves some of these difficulties. Furthermore, an analysis of general rectangular systems is given and generalized Euler-Lagrange equations and Riccati differential algebraic equations are discussed.
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    URL: http://dx.doi.org/10.1007/BF01211506
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  • 17
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    Disturbance rejecting optimal regulation of hyperbolic systems (1995)
    Springer
    Mathematics of control, signals, and systems 8 (1995), S. 241-256 
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    ISSN: 1435-568X
    Keywords: Robust control ; H ∞ control ; Disturbance rejection ; Hyperbolic systems ; Optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology , Mathematics , Technology
    Notes: Abstract Optimal regulation of hyperbolic systems in the presence of unknown exogenous and initial disturbances is considered. Necessary conditions for determining the optimal control that tracks a desired trajectory in the presence of disturbances are developed. These necessary conditions have the form of a twopoint boundary-value problem along with certain equality and inequality conditions. The results also characterize the worst possible disturbances that are accommodated by the optimum controller without any serious performance degradation. Numerical results on the control of a vibrating beam are presented.
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    URL: http://dx.doi.org/10.1007/BF01211861
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  • 18
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    Optimal Control of Linear Time-Varying Systems via Haar Wavelets (1999)
    Springer
    Journal of optimization theory and applications 103 (1999), S. 641-655 
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    ISSN: 1573-2878
    Keywords: Optimal control ; Haar wavelets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper introduces the application of Haar wavelets to the optimal control synthesis for linear time-varying systems. Based upon some useful properties of Haar wavelets, a special product matrix, a related coefficient matrix, and an operational matrix of backward integration are proposed to solve the adjoint equation of optimization. The results obtained by the proposed Haar approach are almost the same as those obtained by the conventional Riccati method.
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    URL: http://dx.doi.org/10.1023/A:1021740209084
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  • 19
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    Boundaries of the receding horizon control for interconnected systems (1995)
    Springer
    Journal of optimization theory and applications 84 (1995), S. 251-271 
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    ISSN: 1573-2878
    Keywords: Optimal control ; decentralized control ; interconnected systems ; receding horizon control ; rolling horizon control ; predictive control ; quadratic optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In recent years, the finite-horizon quadratic minimization problem has become popular in process control, where the horizon is constantly rolled back. In this paper, this type of control, which is also called the receding horizon control, is considered for interconnected systems. First, the receding horizon control equations are formulated; then, some stability conditions depending on the interconnection norms and the horizon lengths are presented. For ∈-coupled systems, stability results similar to centralized systems are obtained. For interconnected systems which are not ∈-coupled, the existence of a horizon length and a corresponding stabilizing receding horizon control are derived. Finally, the performance of a locally computed receding horizon control for time-invariant and time-varying systems with different updating intervals is examined in an example.
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    URL: http://dx.doi.org/10.1007/BF02192114
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  • 20
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    Time-optimal extension and retraction of robots: Numerical analysis of the switching structure (1995)
    Springer
    Journal of optimization theory and applications 84 (1995), S. 589-616 
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    ISSN: 1573-2878
    Keywords: Optimal control ; robotics ; path planning ; maximum principle ; multi-point boundary value problems ; multiple shooting
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The problem of the time-optimal control of robot manipulators is of importance because of its potential for increasing the productivity of assembly lines. This work is part of a series of papers by the authors on this topic using direct and indirect methods of optimization. A cylindrical robot or a spherical polar robot constrained to the horizontal plane is considered, and optimal solutions for radial maneuvers are generated. Indirect methods are employed in order to establish the switching structure of the solutions. The results show that even such apparently simple maneuvers as extension or retraction of a robot with a prismatic joint can produce very complex optimal solutions. Time-optimal retraction can exhibit ten different switching structures with eight switching points and two singular arcs.
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    URL: http://dx.doi.org/10.1007/BF02191987
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    Second-order sufficient conditions for control problems with mixed control-state constraints (1995)
    Springer
    Journal of optimization theory and applications 86 (1995), S. 649-667 
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    ISSN: 1573-2878
    Keywords: Optimal control ; mixed control-state constraints ; Hamilton-Jacobi inequality ; second-order sufficient conditions ; parametric optimization ; Riccati equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract References 1–4 develop second-order sufficient conditions for local minima of optimal control problems with state and control constraints. These second-order conditions tighten the gap between necessary and sufficient conditions by evaluating a positive-definiteness criterion on the tangent space of the active constraints. The purpose of this paper is twofold. First, we extend the methods in Refs. 3, 4 and include general boundary conditions. Then, we relate the approach to the two-norm approach developed in Ref. 5. A direct sufficiency criterion is based on a quadratic function that satisfies a Hamilton-Jacobi inequality. A specific form of such a function is obtained by applying the second-order sufficient conditions to a parametric optimization problem. The resulting second-order positive-definiteness conditions can be verified by solving Riccati equations.
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    URL: http://dx.doi.org/10.1007/BF02192163
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    Use of Augmented Lagrangian Methods for the Optimal Control of Obstacle Problems (1997)
    Springer
    Journal of optimization theory and applications 95 (1997), S. 101-126 
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    ISSN: 1573-2878
    Keywords: Optimal control ; Lagrange multipliers ; augmented Lagrangians ; variational inequalities
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We investigate optimal control problems governed by variational inequalities involving constraints on the control, and more precisely the example of the obstacle problem. In this paper, we discuss some augmented Lagrangian algorithms to compute the solution.
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    URL: http://dx.doi.org/10.1023/A:1022635428708
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    Optimal Control of a Chemical Vapor Deposition Reactor (1998)
    Springer
    Journal of optimization theory and applications 97 (1998), S. 623-644 
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    ISSN: 1573-2878
    Keywords: Optimal control ; bang-bang control ; free boundary problems ; parabolic equations ; homogenizations ; optimality conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We study a simple model of chemical vapor deposition on a silicon wafer. The control is the flux of chemical species, and the objective is to grow the semiconductor film so that its surface attains a prescribed profile as nearly as possible. The surface is spatially fast oscillating due to the small feature scale, and therefore the problem is formulated in terms of its homogenized approximation. We prove that the optimal control is bang-bang, and we use this information to develop a numerical scheme for computing the optimal control.
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    URL: http://dx.doi.org/10.1023/A:1022694210246
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    Tracking Demands in Optimal Control of Managerial Systems with Continuously-Divisible, Doubly Constrained Resources (1998)
    Springer
    Journal of global optimization 13 (1998), S. 43-59 
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    ISSN: 1573-2916
    Keywords: Resource constrained scheduling ; renewable and nonrenewable resources ; Optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper addresses problems of allocating continuously divisible resources among multiple production activities. The resources are allowed to be doubly constrained, so that both usage at every point of time and cumulative consumption over a planning horizon are limited as it is often the case in project and production scheduling. The objective is to track changing in time demands for the activities as closely as possible. We propose a general continuous-time model that states the problem in a form of the optimal control problem with non-linear speed-resource usage functions. With the aid of the maximum principle, properties of the solutions are derived to characterize optimal resource usage policies. On the basis of this analytical investigation, numerical scheduling methods are suggested and computationally studied.
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    URL: http://dx.doi.org/10.1023/A:1008256009222
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    Optimal control in light traffic Markov decision processes (1997)
    Springer
    Mathematical methods of operations research 45 (1997), S. 63-79 
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    ISSN: 1432-5217
    Keywords: Optimal control ; Markov decision processes ; light traffic ; discounted cost ; average cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Economics
    Notes: Abstract We consider Markov Decision Processes under light traffic conditions. We develop an algorithm to obtain asymptotically optimal policies for both the total discounted and the average cost criterion. This gives a general framework for several light traffic results in the literature. We illustrate the method by deriving the asymptotically optimal control of a simple ATM network.
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    URL: http://dx.doi.org/10.1007/BF01194248
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    An existence and uniqueness theorem for one optimal control problem (1995)
    Springer
    Periodica mathematica Hungarica 30 (1995), S. 61-65 
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    ISSN: 1588-2829
    Keywords: Primary 49J20 ; Secondary 65L10 ; Optimal control ; boundary value problem ; existence theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper we investigate the existence and uniqueness for an optimal control problem with processes described by a quasilinear parabolic equation with controls in coefficients and the right side of this equation.
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    URL: http://dx.doi.org/10.1007/BF01876926
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    Feasible Direction Algorithm for Optimal Control Problems with State and Control Constraints: Implementation (1999)
    Springer
    Journal of optimization theory and applications 101 (1999), S. 623-649 
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    ISSN: 1573-2878
    Keywords: Optimal control ; state-constrained problems ; numerical algorithms
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we describe the implementation aspects of an optimization algorithm for optimal control problems with control, state, and terminal constraints presented in our earlier paper. The important aspect of the implementation is that, in the direction-finding subproblems, it is necessary only to impose the state constraint at relatively few points in the time involved. This contributes significantly to the algorithmic efficiency. The algorithm is applied to solve several optimal control problems, including the problem of the abort landing of an aircraft in the presence of windshear.
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    URL: http://dx.doi.org/10.1023/A:1021742204850
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    Global State Space Approach for the Efficient Numerical Solution of State-Constrained Trajectory Optimization Problems (1999)
    Springer
    Journal of optimization theory and applications 103 (1999), S. 75-93 
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    ISSN: 1573-2878
    Keywords: Optimal control ; state inequality constraints ; global state space form ; differential-algebraic boundary-value problems ; minimal coordinates ; trajectory optimization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A new approach based on a global state space form is introduced for solving trajectory optimization problems with state inequality constraints via indirect methods. The use of minimal coordinates on a boundary arc of the state constraint eliminates severe problems, which occur for standard methods and are due to the appearance of differential-algebraic boundary-value problems. Together with a hybrid approach and a careful treatment of some interior-point conditions, we obtain an efficient and reliable solution method.
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    URL: http://dx.doi.org/10.1023/A:1021721316295
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    State Analysis and Optimal Control of Time-Varying Discrete Systems via Haar Wavelets (1999)
    Springer
    Journal of optimization theory and applications 103 (1999), S. 623-640 
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    ISSN: 1573-2878
    Keywords: Optimal control ; discrete systems ; Haar wavelets
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The state analysis and optimal control of time-varying discrete systems via Haar wavelets are the main tasks of this paper. First, we introduce the definition of discrete Haar wavelets. Then, a comparison between Haar wavelets and other orthogonal functions is given. Based upon some useful properties of the Haar wavelets, a special product matrix and a related coefficient matrix are proposed; also, a shift matrix and a summation matrix are derived. These matrices are very effective in solving our problems. The local property of the Haar wavelets is applied to shorten the calculation procedures.
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    URL: http://dx.doi.org/10.1023/A:1021788125013
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    Direct training method for a continuous-time nonlinear optimal feedback controller (1995)
    Springer
    Journal of optimization theory and applications 84 (1995), S. 509-528 
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    ISSN: 1573-2878
    Keywords: Optimal control ; nonlinear feedback control ; feedforward neural networks
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The solutions of most nonlinear optimal control problems are given in the form of open-loop optimal control which is computed from a given fixed initial condition. Optimal feedback control can in principle be obtained by solving the corresponding Hamilton-Jacobi-Bellman dynamic programming equation, though in general this is a difficult task. We propose a practical and effective alternative for constructing an approximate optimal feedback controller in the form of a feedforward neural network, and we justify this choice by several reasons. The controller is capable of approximately minimizing an arbitrary performance index for a nonlinear dynamical system for initial conditions arising from a nontrivial bounded subset of the state space. A direct training algorithm is proposed and several illustrative examples are given.
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    URL: http://dx.doi.org/10.1007/BF02191983
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    Marketable permits in a stochastic dynamic model of the firm (1996)
    Springer
    Journal of optimization theory and applications 89 (1996), S. 129-155 
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    ISSN: 1573-2878
    Keywords: Optimal control ; stochastic control ; Hamilton-Jacobi-Bellman equation ; environmental problems ; dynamics of the firm ; marketable permits
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This contribution attempts to determine the effects of environmental regulation on the growth of an individual firm. Here, it is assumed that the firm revenue is stochastic. The government tries to reduce pollution by creating a market on which the firm has to buy permits in order to be allowed to pollute the environment. Pollution is an inevitable byproduct of the firm production process, and in our model the firm is offered two ways to deal with it. The first is to buy marketable permits, and the second is to clean up pollution which can be achieved through investing in abatement capital stock. It turns out that the firm optimal trajectory consists of at most seven different policies. They can be depicted in a feedback diagram from which we can conclude that, provided that the firm never faces a shortage of cash, productive and abatement capital stocks ultimately reach their equilibrium levels where marginal revenue equals marginal costs.
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    URL: http://dx.doi.org/10.1007/BF02192645
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    Homogenization of Optimal Control Problems for Functional Differential Equations (1997)
    Springer
    Journal of optimization theory and applications 93 (1997), S. 103-119 
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    ISSN: 1573-2878
    Keywords: Optimal control ; variational convergence ; functional differential equations
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The paper deals with the variational convergence of a sequence of optimal control problems for functional differential state equations with deviating argument. Variational limit problems are found under various conditions of convergence of the input data. It is shown that, upon sufficiently weak assumptions on convergence of the argument deviations, the limit problem can assume a form different from that of the whole sequence. In particular, it can be either an optimal control problem for an integro-differential equation or a purely variational problem. Conditions are found under which the limit problem preserves the form of the original sequence.
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    URL: http://dx.doi.org/10.1023/A:1022649817825
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    New Algorithm for Computing LQ Suboptimal Output Feedback Gains of Decentralized Control Systems (1997)
    Springer
    Journal of optimization theory and applications 93 (1997), S. 597-607 
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    ISSN: 1573-2878
    Keywords: Optimal control ; gradient flows ; optimization ; decentralized systems ; performance index
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, the problem of computing the suboptimal output feedback gains of decentralized control systems is investigated. First, the problem is formulated. Then, the gradient matrices based on the index function are derived and a new algorithm is established based on some nice properties. This algorithm shows that a suboptimal gain can be computed by solving several ordinary differential equations (ODEs). In order to find an initial condition for the ODEs, an algorithm for finding a stabilizing output feedback gain is exploited, and the convergence of this algorithm is discussed. Finally, an example is given to illustrate the proposed algorithm.
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    URL: http://dx.doi.org/10.1023/A:1022647230641
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    On a Class of Optimal Control Problems with State Jumps (1998)
    Springer
    Journal of optimization theory and applications 98 (1998), S. 65-82 
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    ISSN: 1573-2878
    Keywords: Optimal control ; switching times ; state jumps ; transformations ; optimal parameter selection problem ; automatic differentiation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider a class of optimal control problems in which the dynamical system involves a finite number of switching times together with a state jump at each of these switching times. The locations of these switching times and a parameter vector representing the state jumps are taken as decision variables. We show that this class of optimal control problems is equivalent to a special class of optimal parameter selection problems. Gradient formulas for the cost functional and the constraint functional are derived. On this basis, a computational algorithm is proposed. For illustration, a numerical example is included.
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    URL: http://dx.doi.org/10.1023/A:1022684730236
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    Optimal Control for an Obstruction Problem (1999)
    Springer
    Journal of optimization theory and applications 100 (1999), S. 435-439 
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    ISSN: 1573-2878
    Keywords: Optimal control ; flow round obstacles ; Pontryagin principle ; discretization
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A question of flow around an obstacle leads to an optimal control problem. If an optimum path exists, then it is calculable from the Pontryagin principle. The optimum is verified to be reached, using a discretization of the problem.
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    URL: http://dx.doi.org/10.1023/A:1021746622539
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    Dynamic Programming Method for Constrained Discrete-Time Optimal Control (1999)
    Springer
    Journal of optimization theory and applications 101 (1999), S. 259-283 
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    ISSN: 1573-2878
    Keywords: Optimal control ; dynamic programming ; interior-point methods ; sequential quadratic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A dynamic programming method is presented for solving constrained, discrete-time, optimal control problems. The method is based on an efficient algorithm for solving the subproblems of sequential quadratic programming. By using an interior-point method to accommodate inequality constraints, a modification of an existing algorithm for equality constrained problems can be used iteratively to solve the subproblems. Two test problems and two application problems are presented. The application examples include a rest-to-rest maneuver of a flexible structure and a constrained brachistochrone problem.
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    URL: http://dx.doi.org/10.1023/A:1021733425632
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    Optimal Control Problems via Exact Penalty Functions (1998)
    Springer
    Journal of global optimization 12 (1998), S. 215-223 
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    ISSN: 1573-2916
    Keywords: Optimal control ; Exact penalization ; Directional differentiability ; Subdifferentiability ; Necessary optimality conditions ; Nonsmooth analysis
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The nonsmoothness is viewed by many people as at least an undesirable (if not unavoidable) property. Our aim here is to show that recent developments in Nonsmooth Analysis (especially in Exact Penalization Theory) allow one to treat successfully even some quite ‘smooth’ problems by tools of Nonsmooth Analysis and Nondifferentiable Optimization. Our approach is illustrated by one Classical Control Problem of finding optimal parameters in a system described by ordinary differential equations.
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    URL: http://dx.doi.org/10.1023/A:1008257323671
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    On Global Optimality Conditions for Nonlinear Optimal Control Problems (1998)
    Springer
    Journal of global optimization 13 (1998), S. 109-122 
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    ISSN: 1573-2916
    Keywords: Optimal control ; Pontryagin maximum principle ; Global optimality
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Let a trajectory and control pair $$(\bar x{\text{, }}\bar u{\text{)}}$$ maximize globally the functional g(x(T)) in the basic optimal control problem. Then (evidently) any pair (x,u) from the level set of the functional g corresponding to the value g( $$\bar x$$ (T)) is also globally optimal and satisfies the Pontryagin maximum principle. It is shown that this necessary condition for global optimality of $$(\bar x{\text{, }}\bar u{\text{)}}$$ turns out to be a sufficient one under the additional assumption of nondegeneracy of the maximum principle for every pair (x,u) from the above-mentioned level set. In particular, if the pair $$(\bar x{\text{, }}\bar u{\text{)}}$$ satisfies the Pontryagin maximum principle which is nondegenerate in the sense that for the Hamiltonian H, we have along the pair $$(\bar x{\text{, }}\bar u{\text{)}}$$ $$\mathop {{\text{max}}}\limits_u {\text{ }}H$$ ≢ $$\mathop {{\text{min}}}\limits_u {\text{ }}H$$ on [0,T], and if there is no another pair (x,u) such that g(x(T))=g( $$\bar x$$ (T)), then $$(\bar x{\text{, }}\bar u{\text{)}}$$ is a global maximizer.
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    URL: http://dx.doi.org/10.1023/A:1008211429313
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    Time-Varying Linear-Quadratic Control (1999)
    Springer
    Journal of optimization theory and applications 100 (1999), S. 515-525 
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    ISSN: 1573-2878
    Keywords: Optimal control ; linear-quadratic control ; time-varying feedback
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper discusses the performance of controlled linear dynamic systems that use time-varying feedforward signals and time-varying linear-quadratic (LQ) feedback gains. Such a time-varying LQ controller can bring a dynamic system to a desired final state in roughly half the time required by a time-invariant LQ controller, since it pushes at both ends, i.e., it uses significant control effort near the end of the maneuver, as well as at the beginning, to meet the specified end conditions; there is no overshoot and no settling time. This requires a more complex controller and some care with the high gains near the final time. A MATLAB3 code is listed that synthesizes and simulates zero-order-hold time-varying LQ controllers. The precision landing of a helicopter using four controls is treated as an example.
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    URL: http://dx.doi.org/10.1023/A:1022682305644
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    Neighborhood Turnpike Theorem for Continuous-Time Optimization Models (1999)
    Springer
    Journal of optimization theory and applications 101 (1999), S. 651-676 
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    ISSN: 1573-2878
    Keywords: Optimal control ; dynamic models ; optimal growth ; turnpike theorems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A neighborhood turnpike theorem is proved for continuous-time, infinite-horizon optimization models with positive discounting. Our approach is a primal one and no differentiability assumption is made. The basic hypothesis is a condition of uniform concavity at the point defining the undiscounted steady state. The main novelty here is that we formulate the theorem by taking the undiscounted steady state as the turnpike.
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    URL: http://dx.doi.org/10.1023/A:1021794221688
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    Gradient-flow approach for computing a nonlinear-quadratic optimal-output feedback gain matrix (1995)
    Springer
    Journal of optimization theory and applications 85 (1995), S. 75-96 
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    ISSN: 1573-2878
    Keywords: Optimal control ; infinite horizon ; nonlinear-quadratic regulator problem ; linear state feedback ; approximate problems ; gradient-flow based algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, an approach is proposed for solving a nonlinear-quadratic optimal regulator problem with linear static state feedback and infinite planning horizon. For such a problem, approximate problems are introduced and considered, which are obtained by combining a finite-horizon problem with an infinite-horizon linear problem in a certain way. A gradient-flow based algorithm is derived for these approximate problems. It is shown that an optimal solution to the original problem can be found as the limit of a sequence of solutions to the approximate problems. Several important properties are obtained. For illustration, two numerical examples are presented.
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    URL: http://dx.doi.org/10.1007/BF02192300
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    Shooting method for the numerical solution of optimal control problems with bounded state variables (1996)
    Springer
    Journal of optimization theory and applications 89 (1996), S. 351-372 
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    ISSN: 1573-2878
    Keywords: Optimal control ; bounded state ; inequality constraints
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abtract Various methods have been proposed for the numerical solution of optimal control problems with bounded state variables. In this paper, a new method is put forward and compared with two other methods, one of which makes use of adjoint variables whereas the other does not. Some conclusions are drawn on the usefulness of the three methods involved.
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    URL: http://dx.doi.org/10.1007/BF02192534
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    Pathways to hopf bifurcations in dynamic continuous-time optimization problems (1996)
    Springer
    Journal of optimization theory and applications 91 (1996), S. 299-320 
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    ISSN: 1573-2878
    Keywords: Optimal control ; limit cycles ; Hopf bifurcation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The purpose of this paper is to characterize pathways to Hopf bifurcation in continuous time, concave, two-dimensional optimal control models. It is shown that essentially two pathways exist: control-state interaction and growth. The knowledge of such pathways provides a criterion at the stage of modelling on the potential complexity of optimal trajectories.
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    URL: http://dx.doi.org/10.1007/BF02190098
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    An Optimal Control Problem for Flows with Discontinuities (1997)
    Springer
    Journal of optimization theory and applications 94 (1997), S. 273-309 
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    ISSN: 1573-2878
    Keywords: Optimal control ; Euler flow equations ; sequential quadratic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we study a design problem for a duct flow with a shock. The presence of the shock causes numerical difficulties. Good shock-capturing schemes with low continuity properties often cannot be combined successfully with efficient optimization methods requiring smooth functions. A remedy studied in this paper is to introduce the shock location as an explicit variable. This allows one to fit the shock and yields a problem with sufficiently smooth functions. We prove the existence of optimal solutions, Fréchet differentiability, and the existence of Lagrange multipliers. In the second part, we introduce and investigate the discrete problem and study the relations between the optimality conditions for the infinite-dimensional problem and the discretized one. This reveals important information for the numerical solution of the problem. Numerical examples are given to demonstrate the theoretical findings.
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    URL: http://dx.doi.org/10.1023/A:1022616327742
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    Properties of the Bellman Function in Time-Optimal Control Problems (1997)
    Springer
    Journal of optimization theory and applications 94 (1997), S. 155-168 
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    ISSN: 1573-2878
    Keywords: Optimal control ; Bellman function ; value function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, time-optimal control problems with closed terminal sets are considered. We give conditions which guarantee the Bellman function to be Hölder and Lipschitz continuous. We then prove that the condition for Lipschitz continuity is also necessary.
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    URL: http://dx.doi.org/10.1023/A:1022615921015
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    Efficient Sequential Quadratic Programming Implementations for Equality-Constrained Discrete-Time Optimal Control (1997)
    Springer
    Journal of optimization theory and applications 95 (1997), S. 323-346 
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    ISSN: 1573-2878
    Keywords: Optimal control ; sequential quadratic programming ; dynamic programming ; Newton method
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Efficient sequential quadratic programming (SQP) implementations are presented for equality-constrained, discrete-time, optimal control problems. The algorithm developed calculates the search direction for the equality-based variant of SQP and is applicable to problems with either fixed or free final time. Problem solutions are obtained by solving iteratively a series of constrained quadratic programs. The number of mathematical operations required for each iteration is proportional to the number of discrete times N. This is contrasted by conventional methods in which this number is proportional to N 3. The algorithm results in quadratic convergence of the iterates under the same conditions as those for SQP and simplifies to an existing dynamic programming approach when there are no constraints and the final time is fixed. A simple test problem and two application problems are presented. The application examples include a satellite dynamics problem and a set of brachistochrone problems involving viscous friction.
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    URL: http://dx.doi.org/10.1023/A:1022635205221
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    Near Optimization of Dynamic Systems by Decomposition and Aggregation (1998)
    Springer
    Journal of optimization theory and applications 99 (1998), S. 1-22 
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    ISSN: 1573-2878
    Keywords: Optimal control ; dynamical systems ; decomposition ; aggregation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the reduction of a class of optimal control problems to simpler problems by using decomposition and aggregation. Decomposition is shown to provide a good approximation when the system dynamics involve nearly decomposable matrices or variables with strong and weak interactions. Aggregation provides a good approximation if each of the decomposed matrices has one or more dominant eigenvalues. It is shown how one can construct nearly-optimal controls for the given system from the optimal solutions of the simpler reduced problems.
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    URL: http://dx.doi.org/10.1023/A:1021739925071
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