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  • Articles  (11)
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  • optimal control
  • Springer  (10)
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  • Mathematics  (11)
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  • Articles  (11)
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  • Springer  (10)
  • Wiley-Blackwell  (1)
  • American Geophysical Union
  • American Institute of Physics (AIP)
  • American Physical Society
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  • 2005-2009
  • 2000-2004
  • 1995-1999  (11)
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  • 1
    Electronic Resource
    Electronic Resource
    On the existence of optimal controls for nonlinear infinite dimensional systems (1998)
    Springer
    Czechoslovak mathematical journal 48 (1998), S. 291-312 
    Details
    ISSN: 1572-9141
    Keywords: evolution triple ; optimal control ; monotone operator ; hemicontinuous operator ; parabolic system ; property (Q)
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We consider nonlinear systems with a priori feedback. We establish the existence of admissible pairs and then we show that the Lagrange optimal control problem admits an optimal pair. As application we work out in detail two examples of optimal control problems for nonlinear parabolic partial differential equations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022889404413
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  • 2
    Electronic Resource
    Electronic Resource
    Scheduling Under Common Due Date, A Single Resource and Precedence Constraints—A Dynamic Approach (1998)
    Springer
    Discrete event dynamic systems 8 (1998), S. 353-364 
    Details
    ISSN: 1573-7594
    Keywords: scheduling ; optimal control ; time-decomposition methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper discusses dynamic methods for solving a class of multi-project scheduling problems in which rates of job performances are controllable and resources such as money, energy or manpower per time unit, are renewable and continuously divisible. The objective is to complete the projects as close to the common due date as possible. Two different ways of imposing sequential precedence relations between project jobs are explored by formulating two dynamic models and studying their relationships on the optimal solution. Efficient time-decomposition algorithms for finding either globally optimal schedules or lower bound guided near-optimal solutions are suggested and computationally tested.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008345132480
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  • 3
    Electronic Resource
    Electronic Resource
    Modeling, Analysis, and Optimal Control of a Class of Hybrid Systems (1998)
    Springer
    Discrete event dynamic systems 8 (1998), S. 175-201 
    Details
    ISSN: 1573-7594
    Keywords: hybrid systems ; optimal control ; calculus of variations ; manufacturing systems ; queueing systems ; nonsmooth optimization ; two point boundary value problems
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract We propose a modeling framework for a class of hybrid systems which arise in many manufacturing environments and study related optimal control problems. In this framework, discrete entities have a state characterized by a temporal component whose evolution is described by event-driven dynamics, and a physical component whose evolution is described by time-driven dynamics. As a first step towards developing an optimal control theory for such hybrid systems, we formulate a problem consisting of a single-stage manufacturing process and use calculus of variations techniques to obtain structural properties and an explicit algorithm for deriving optimal policies.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008237701804
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  • 4
    Electronic Resource
    Electronic Resource
    Optimal Production Planning in a Multi-Product Stochastic Manufacturing System with Long-Run Average Cost (1998)
    Springer
    Discrete event dynamic systems 8 (1998), S. 37-54 
    Details
    ISSN: 1573-7594
    Keywords: Production planning ; stochastic dynamic programming ; vanishing discount approach ; optimal control ; long-run average cost
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper is concerned with the problem of production planning in a flexible manufacturing system consisting of a single or parallel failure-prone machines producing a number of different products. The objective is to choose the rates of production of the various products over time in order to meet their demands at the minimum long-run average cost of production and surplus. The analysis proceeds with a study of the corresponding problem with a discounted cost. It is shown using the vanishing discount approach for the average cost problem that the Hamilton-Jacobi-Bellman equation in terms of directional derivatives has a solution consisting of the minimal average cost and the so-called potential function. The result helps in establishing a verification theorem, and in specifying an optimal control policy in terms of the potential function. The results settle a hitherto open problem as well as generalize known results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008256409920
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  • 5
    Electronic Resource
    Electronic Resource
    Approximate Solutions to the Time-Invariant Hamilton–Jacobi–Bellman Equation (1998)
    Springer
    Journal of optimization theory and applications 96 (1998), S. 589-626 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear control ; optimal control ; Hamilton–Jacobi–Bellman equation ; feedback synthesis ; successive approximation ; Galerkin approximation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we develop a new method to approximate the solution to the Hamilton–Jacobi–Bellman (HJB) equation which arises in optimal control when the plant is modeled by nonlinear dynamics. The approximation is comprised of two steps. First, successive approximation is used to reduce the HJB equation to a sequence of linear partial differential equations. These equations are then approximated via the Galerkin spectral method. The resulting algorithm has several important advantages over previously reported methods. Namely, the resulting control is in feedback form and its associated region of attraction is well defined. In addition, all computations are performed off-line and the control can be made arbitrarily close to optimal. Accordingly, this paper presents a new tool for designing nonlinear control systems that adhere to a prescribed integral performance criterion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022664528457
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  • 6
    Electronic Resource
    Electronic Resource
    Robust Stabilization for a Class of Uncertain Nonlinear Systems with Time-Varying Delay: Razumikhin-Type Approach (1998)
    Springer
    Journal of optimization theory and applications 98 (1998), S. 161-173 
    Details
    ISSN: 1573-2878
    Keywords: Robust stabilization ; optimal control ; time-delay systems ; Razumikhin-type approach
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, using a Razumikhin-type approach, the stabilization of a class of uncertain nonlinear systems with time-varying delay is considered. The proposed controller is based on a specific optimal control problem. Global asymptotic stability is guaranteed for the proposed control if some algebraic condition is met. An example illustrates the use of the main result.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022645116123
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  • 7
    Electronic Resource
    Electronic Resource
    Optimal Control of Rigid Body Angular Velocity with Quadratic Cost (1998)
    Springer
    Journal of optimization theory and applications 96 (1998), S. 507-532 
    Details
    ISSN: 1573-2878
    Keywords: Rigid bodies ; Hamilton–Jacobi equation ; Riccati equation ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this paper, we consider the problem of obtaining optimal controllers which minimize a quadratic cost function for the rotational motion of a rigid body. We are not concerned with the attitude of the body and consider only the evolution of the angular velocity as described by the Euler equations. We obtain conditions which guarantee the existence of linear stabilizing optimal and suboptimal controllers. These controllers have a very simple structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022656326640
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  • 8
    Electronic Resource
    Electronic Resource
    Optimization of a Class of Nonlinear Dynamic Systems: New Efficient Method without Lagrange Multipliers (1998)
    Springer
    Journal of optimization theory and applications 97 (1998), S. 11-28 
    Details
    ISSN: 1573-2878
    Keywords: Optimization ; nonlinear dynamic systems ; transformations ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This paper deals with optimization of a class of nonlinear dynamic systems with n states and m control inputs commanded to move between two fixed states in a prescribed time. Using conventional procedures with Lagrange multipliers, it is well known that the optimal trajectory is the solution of a two-point boundary-value problem. In this paper, a new procedure for dynamic optimization is presented which relies on tools of feedback linearization to transform nonlinear dynamic systems into linear systems. In this new form, the states and controls can be written as higher derivatives of a subset of the states. Using this new form, it is possible to change constrained dynamic optimization problems into unconstrained problems. The necessary conditions for optimality are then solved efficiently using weighted residual methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022666831628
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  • 9
    Electronic Resource
    Electronic Resource
    Optimal Control of a Stochastic Assembly Production Line (1998)
    Springer
    Journal of optimization theory and applications 98 (1998), S. 681-700 
    Details
    ISSN: 1573-2878
    Keywords: Manufacturing systems ; bang–bang control ; dynamic programming ; optimal control
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The system under consideration comprises n workstations in parallel and one assembly workstation. The workstations are either reliable or unreliable and the product demand is random. The n different type parts are processed first in the parallel workstations and then are joined in the assembly workstation. By minimizing the expected discounted cost, it is shown that the optimal control policy is of the bang–bang type and can be described by a set of switching manifolds. The structural properties of the optimal policy, such as monotonicity and asymptotic behavior, are investigated. These structural properties are very useful to find the optimal policy in large-size systems. Three numerical examples are given to demonstrate the results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022632231356
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  • 10
    Electronic Resource
    Electronic Resource
    Optimal Control of a Ship for a Course-Changing Maneuver (1998)
    Springer
    Journal of optimization theory and applications 97 (1998), S. 281-297 
    Details
    ISSN: 1573-2878
    Keywords: Nonlinear ship steering dynamics ; optimal control ; saturation ; slew rate limitation ; sequential gradient-restoration algorithm
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract The steering control of a ship during a course-changing maneuver is formulated as a Bolza optimal control problem, which is solved via the sequential gradient-restoration algorithm (SGRA). Nonlinear differential equations describing the yaw dynamics of a steering ship are employed as the differential constraints, and both amplitude and slew rate limits on the rudder are imposed. Two performance indices are minimized: one measures the time integral of the squared course deviation between the actual ship course and a target course; the other measures the time integral of the absolute course deviation. Numerical results indicate that a smooth transition from the initial set course to the target course is achievable, with a trade-off between the speed of response and the amount of course angle overshoot.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1022674516570
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  • 11
    Electronic Resource
    Electronic Resource
    Solving boundary-value problems using hp-version finite elements in time (1998)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 43 (1998), S. 425-440 
    Details
    ISSN: 0029-5981
    Keywords: numerical methods ; time-marching ; dynamics ; optimal control ; boundary-value problems ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: An hp-version finite element method for one-dimensional boundary value problems is presented. The method is based on a similar approach developed by the authors for solution of optimal control problems. The primary applications for the methodology include two-point- and multi-point-boundary-value problems, for example, in the time domain. Results presented for a 7-state/3-phase missile problem show that the method is very efficient for time-marching applications. Furthermore, it easily solves time-domain problems with discontinuities in the system equations and/or in the states, where the time at which these jumps (i.e. ‘events’) take place is determined by equations that govern the states. An example involving friction with intermittent sticking is presented to illustrate the power of the method. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 9 Ill.
    Type of Medium: Electronic Resource
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