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  • Articles  (12)
  • Articles: DFG German National Licenses  (12)
  • Optimal control  (12)
  • 2010-2014
  • 1980-1984  (12)
  • 1950-1954
  • 1980  (12)
  • Mathematics  (12)
  • History
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  • Articles  (12)
Source
  • Articles: DFG German National Licenses  (12)
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  • 2010-2014
  • 1980-1984  (12)
  • 1950-1954
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  • Mathematics  (12)
  • History
  • 1
    Electronic Resource
    Electronic Resource
    Near-optimum design of nonstationary linear systems with state and control delays (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 73-88 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; suboptimal control ; time-delay systems ; linear systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A computationally efficient method based on a sensitivity approach is developed to obtain suboptimal control for nonstationary linear systems with multiple state and control delays and with quadratic cost. The proposed suboptimal control includes some truncated series whose terms are calculated in a recursive manner from nondelay system optimization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934590
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  • 2
    Electronic Resource
    Electronic Resource
    Suboptimal control of systems with multiple delays (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 621-633 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; time-delay systems ; linear systems ; multiple-delay systems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The application of Pontryagin's maximum principle to the optimization of linear systems with time delays results in a system of coupled two-point boundary-value problems involving both delay and advance terms. The exact solution of this system of TPBV problems is extremely difficult, if not impossible. In this paper, a fast-converging iterative approach is developed for obtaining the suboptimal control for nonstationary linear systems with multiple state and control delays and with quadratic cost. At each step of the proposed method, a linear nondelay system with an extra perturbing input must be optimized. The procedure can be extended for the optimization of nonlinear systems with multiple time-varying delays, provided that some of the nonlinearities satisfy the Lipschitz condition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01686725
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  • 3
    Electronic Resource
    Electronic Resource
    Solution of nonlinear optimal control problems in Hilbert spaces by means of linear programming techniques (1980)
    Springer
    Journal of optimization theory and applications 30 (1980), S. 643-661 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; measures ; Hilbert spaces ; linear programming ; approximation techniques
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Optimal control problems in Hilbert spaces are considered in a measure-theoretical framework. Instead of minimizing a functional defined on a class of admissible trajectory-control pairs, we minimize one defined on a set of measures; this set is defined by the boundary conditions and the differential equation of the problem. The new problem is an infinite-dimensionallinear programming problem; it is shown that it is possible to approximate its solution by that of a finite-dimensional linear program of sufficiently high dimensions, while this solution itself can be approximated by a trajectory-control pair. This pair may not be strictly admissible; if the dimensionality of the finite-dimensional linear program and the accuracy of the computations are high enough, the conditions of admissibility can be said to be satisfied up to any given accuracy. The value given by this pair to the functional measuring the performance criterion can be about equal to theglobal infimum associated with the classical problem, or it may be less than this number. It appears that this method may become a useful technique for the computation of optimal controls, provided the approximations involved are acceptable.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01686727
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  • 4
    Electronic Resource
    Electronic Resource
    Junction phenomena for optimal control with state-variable inequality constraints of third order (1980)
    Springer
    Journal of optimization theory and applications 31 (1980), S. 85-99 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; junction conditions ; calculus of variations ; inequality constraints
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract It is known that extremal arcs governed by inequality constraints of third order (constraint relations that must be differentiated three times to generate a control equation) cannot join an unconstrained arc, except in special cases. But a control problem is exhibited, for which every extremal includes a constrained arc of third order. The constrained arc joins the end of an infinite sequence of consecutive unconstrained arcs of finite total duration. Evidence (but not proof) is given that this phenomenon is typical, rather than exceptional. An analogous phenomenon is well known for optimal control problems with singular arcs of second order.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934790
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  • 5
    Electronic Resource
    Electronic Resource
    Existence and global asymptotic stability of optimal trajectories for a class of infinite-horizon, nonconvex systems (1980)
    Springer
    Journal of optimization theory and applications 31 (1980), S. 515-533 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; economic systems ; stability ; existence theory ; turnpike property
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Sufficient conditions for the existence of optimal trajectories and for the global asymptotic stability of these trajectories are given for a class of nonconvex and nonautonomous systems controlled over an infinite-time horizon. The concept ofG-supported trajectory is introduced. It is shown that, under some assumptions, aG-supported trajectory is overtaking and is globally asymptotically stable. The concept of overtaking trajectory has been previously defined as a notion of optimality on an infinite-time domain. For autonomous systems, under weaker conditions, one guarantees the existence of weakly overtaking trajectories. Finally, it is shown howG-supported trajectories can be obtained, and an application to the study of a pre-predator ecosystem optimally harvested is sketched.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934475
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  • 6
    Electronic Resource
    Electronic Resource
    On optimal control problems with state constraints (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 75-80 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; state constraints ; multipliers ; perturbation theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with necessary conditions for a general optimal control problem developed by Russak and Tan. It is shown that, in most cases, a further relation between the multipliers holds. This result is of interest in particular for the investigation of perturbations of the state constraint.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934843
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  • 7
    Electronic Resource
    Electronic Resource
    A property of an autonomous minimax optimal control problem (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 81-87 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; minimax problems ; maximum principle ; Hamiltonian function
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract A control system $$\dot x = f\left( {x,u} \right)$$ ,u) with cost functional $$\mathop {ess \sup }\limits_{T0 \leqslant t \leqslant T1} G\left( {x\left( t \right),u\left( t \right)} \right)$$ is considered. For an optimal pair $$\left( {\bar x\left( \cdot \right),\bar u\left( \cdot \right)} \right)$$ ,ū(·)), there is a maximum principle of the form $$\eta \left( t \right)f\left( {\bar x\left( t \right),\bar u\left( t \right)} \right) = \mathop {\max }\limits_{u \in \Omega \left( t \right)} \eta \left( t \right)f\left( {\bar x\left( t \right),u} \right).$$ By means of this fact, it is shown that $$\eta \left( t \right)f\left( {\bar x\left( t \right),\bar u\left( t \right)} \right)$$ is equal to a constant almost everywhere.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934844
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  • 8
    Electronic Resource
    Electronic Resource
    An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 1 (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 211-246 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; control constraints ; terminal equality constraints ; exact penalty function ; convergence
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The presence of control constraints, because they are nondifferentiable in the space of control functions, makes it difficult to cope with terminal equality constraints in optimal control problems. Gradient-projection algorithms, for example, cannot be employed easily. These difficulties are overcome in this paper by employing an exact penalty function to handle the cost and terminal equality constraints and using the control constraints to define the space of permissible search directions in the search-direction subalgorithm. The search-direction subalgorithm is, therefore, more complex than the usual linear program employed in feasible-directions algorithms. The subalgorithm approximately solves a convex optimal control problem to determine the search direction; in the implementable version of the algorithm, the accuracy of the approximation is automatically increased to ensure convergence.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934725
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  • 9
    Electronic Resource
    Electronic Resource
    Sufficient conditions for asymptotic optimal control (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 307-325 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; asymptotic optimal control ; calculus of variations ; Lagrange problems ; global minima ; absolute minima ; necessary conditions ; sufficient conditions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract For a selected family of Lagrange-type control problems involving a nonnegative integral costJ T (y,u) over the interval [0,T], 0〈T〈∞, with system conditions consisting of differential inequalities and/or equalities, the following material is treated: (i) a resumé of relevant necessary conditions and sufficient conditions for a pair (y T ,u T ) to minimizeJ T (y,u); (ii) conditions sufficient for the convergence asT→∞ of minimizing pairs (y T ,u T ) over [0,T] to a limit pair (y ∞,u ∞) over the infinite-time interval [0, ∞); (iii) conditions sufficient for (y ∞,u ∞) to minimize the costJ ∞(y,u) over [0, ∞); and (iv) conditions sufficient for the optimal cost per unit timeJ T (y T ,u T )/T to have a limit asT→∞.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934555
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  • 10
    Electronic Resource
    Electronic Resource
    An exact penalty function algorithm for optimal control problems with control and terminal equality constraints, part 2 (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 345-364 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; control constraints ; terminal equality constraints ; exact penalty functions ; convergence ; relaxed control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In Part 1 of this paper, implementable and conceptual versions of an algorithm for optimal control problems with control constraints and terminal equality constraints were presented. It was shown that anyL ∞ accumulation points of control sequences generated by the algorithms satisfy necessary conditions of optimality. Since such accumulation points need not exist, it is shown in this paper that control sequences generated by the algorithms always have accumulation points in the sense of control measure, and these accumulation points satisfy optimality conditions for the corresponding relaxed control problem.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934557
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  • 11
    Electronic Resource
    Electronic Resource
    On the order of singular optimal control problems (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 479-489 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; singular control ; junction conditions ; singular control order
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In singular optimal control problems, the functional form of the optimal control function is usually determined by solving the algebraic equation which results by successively differentiating the switching function until the control appears explicitly. This process defines the order of the singular problem. Order-related results are developed for singular linear-quadratic problems and for a bilinear example which gives new insights into the relationship between singular problem order and singular are order.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934035
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  • 12
    Electronic Resource
    Electronic Resource
    On the general inverse problem of optimal control theory (1980)
    Springer
    Journal of optimization theory and applications 32 (1980), S. 491-497 
    Details
    ISSN: 1573-2878
    Keywords: Optimal control ; inverse problems ; dynamic programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The general inverse problem of optimal control is considered from a dynamic programming point of view. Necessary and sufficient conditions are developed which two integral criteria must satisfy if they are to yield the same optimal feedback law, the dynamics being fixed. Specializing to the linear-quadratic case, it is shown how the general results given here recapture previously obtained results for quadratic criteria with linear dynamics.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00934036
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