Computation of Approximately Optimal Control Signals for Systems With Time Delays

1974 ◽  
Vol 96 (3) ◽  
pp. 269-276
Author(s):  
L. B. Horwitz
Keyword(s):  
Optimal Control ◽  
Time Delays ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Control Signal ◽  
Control Problems ◽  
Piecewise Constant ◽  
Switching Times ◽  
Control Signals ◽  
Approximate Nature

A computational algorithm is presented for a class of optimal control problems involving time delays. The approach is to restrict the control signal to a class of piecewise constant time functions with a prescribed number of switching times, compute the optimal member of this class, and then repeat with a larger number of switching times. By allowing the number of switching times to increase beyond bound a sequence of restricted optimal control signals is developed whose limit approaches the unrestricted optimal control signal. In practice the computations are terminated after a finite number of repeats, thus leading to the approximate nature of the solution. The results of two examples are included to illustrate the technique.

scholarly journals The control parameterization enhancing transform for constrained optimal control problems

1999 ◽  
Vol 40 (3) ◽  
pp. 314-335 ◽  
Author(s):  
K. L. Teo ◽  
L. S. Jennings ◽  
H. W. J. Lee ◽  
V. Rehbock
Keyword(s):  
Optimal Control ◽  
Optimal Control Problems ◽  
Piecewise Linear ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
Piecewise Constant ◽  
Control Parameterization ◽  
Switching Times ◽  
Control Functions ◽  
Decision Variables

AbstractConsider a general class of constrained optimal control problems in canonical form. Using the classical control parameterization technique, the time (planning) horizon is partitioned into several subintervals. The control functions are approximated by piecewise constant or piecewise linear functions with pre-fixed switching times. However, if the optimal control functions to be obtained are piecewise continuous, the accuracy of this approximation process greatly depends on how fine the partition is. On the other hand, the performance of any optimization algorithm used is limited by the number of decision variables of the problem. Thus, the time horizon cannot be partitioned into arbitrarily many subintervals to reach the desired accuracy. To overcome this difficulty, the switching points should also be taken as decision variables. This is the main motivation of the paper. A novel transform, to be referred to as the control parameterization enhancing transform, is introduced to convert approximate optimal control problems with variable switching times into equivalent standard optimal control problems involving piecewise constant or piecewise linear control functions with pre-fixed switching times. The transformed problems are essentially optimal parameter selection problems and hence are solvable by various existing algorithms. For illustration, two non-trivial numerical examples are solved using the proposed method.

scholarly journals Nonlinearly constrained optimal control problems

1992 ◽  
Vol 33 (4) ◽  
pp. 517-530 ◽  
Author(s):  
K. L. Teo ◽  
K. H. Wong
Keyword(s):  
Optimal Control ◽  
General Class ◽  
State Constraints ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Constrained Optimal Control ◽  
Continuous State ◽  
Constraint Transcription ◽  
Inequality Type

AbstractIn a paper by Teo and Jennings, a constraint transcription is used together with the concept of control parametrisation to devise a computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type. The aim of this paper is to extend the results to a more general class of constrained optimal control problems, where the problem is also subject to terminal equality state constraints. For illustration, a numerical example is included.

scholarly journals On a computational algorithm for a class of optimal control problems involving discrete time delayed arguments

1978 ◽  
Vol 20 (3) ◽  
pp. 315-343 ◽  
Author(s):  
J. M. Murray ◽  
K. L. Teo
Keyword(s):  
Decision Making ◽  
Optimal Control ◽  
Simple Model ◽  
Discrete Time ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Decision Making Problem ◽  
Delayed Arguments

AbstractIn this paper, a computational algorithm for solving a class of optimal control problems involving discrete time-delayed arguments is presented. By way of example, a simple model of a production firm is devised for which the algorithm is used to solve a decision-making problem.

scholarly journals Optimal control problems with time delays: Two case studies in biomedicine

2018 ◽  
Vol 15 (5) ◽  
pp. 1137-1154 ◽  
Author(s):  
Laurenz Göllmann ◽  
◽  
Helmut Maurer ◽  
Keyword(s):  
Optimal Control ◽  
Case Studies ◽  
Time Delays ◽  
Optimal Control Problems ◽  
Control Problems

scholarly journals A conditional gradient method for a class of time-lag optimal control problems

1984 ◽  
Vol 25 (4) ◽  
pp. 518-537 ◽  
Author(s):  
K. H. Wong ◽  
K. L. Teo
Keyword(s):  
Optimal Control ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Convergence Property ◽  
Time Lag ◽  
Control Problems ◽  
Bounded Control ◽  
Conditional Gradient Method ◽  
Gradient Technique ◽  
Delayed Arguments

AbstractIn this paper, we consider a class of optimal control problems with discrete time delayed arguments and bounded control region. A computational algorithm for solving this class of time lag optimal control problems is developed by means of the conditional gradient technique. The convergence property of the algorithm is also investigated.

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