On the Optimal Control Problem With Variable Terminal Point

1971 ◽  
Vol 93 (4) ◽  
pp. 218-220
Author(s):  
R. A. Niemann
Keyword(s):  
Optimal Control ◽  
Local Minimum ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Local Maximum ◽  
Transversality Condition ◽  
Performance Criterion ◽  
Terminal Point ◽  
Control Problems ◽  
The Given

The class of optimal control problems is considered in which the terminal point is constrained to lie on some surface in the state space. A computational algorithm is developed which solves the problem for a series of terminal points on the given surface and iterates until the transversality condition is satisfied. An example is considered in which there are several solutions which satisfy the transversality condition, some producing a local minimum of the performance criterion with respect to the variable terminal point and some a local maximum. A sufficient condition for a local minimum is derived.

On the Optimal Control Problem With Unrestricted Final Time

1969 ◽  
Vol 91 (2) ◽  
pp. 155-160 ◽  
Author(s):  
C. T. Leondes ◽  
R. A. Niemann
Keyword(s):  
Optimal Control ◽  
Local Minimum ◽  
Computational Algorithm ◽  
Local Maximum ◽  
Fixed Time ◽  
Performance Criterion ◽  
Necessary Condition ◽  
Sufficient Condition ◽  
Final Time ◽  
Numerical Examples

In problems of optimal control, the final time T may be fixed or it may be unrestricted. For the unrestricted final time case, an additional necessary condition that the Hamiltonian be zero is added to the conditions for optimality used for the fixed time case. In this paper, it will be shown that this necessary condition may lead to a local maximum of the performance criterion with respect to final times as well as a local minimum. This paper first develops a computational algorithm using only the H = 0 condition, and then develops a sufficient condition for a local minimum with respect to final time and a computational algorithm employing this condition. Numerical examples are given to illustrate all results.

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 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.

scholarly journals A computational method for free time optimal control problems, with application to maximizing the range of an aircraft-like projectile

1987 ◽  
Vol 28 (3) ◽  
pp. 393-413 ◽  
Author(s):  
K. L. Teo ◽  
G. Jepps ◽  
E. J. Moore ◽  
S. Hayes
Keyword(s):  
Optimal Control ◽  
Computational Algorithm ◽  
Optimal Control Problems ◽  
Computational Method ◽  
Control Problems ◽  
Control Parametrization ◽  
Final Time ◽  
Final State ◽  
Method Of Solution ◽  
Time Optimal

AbstractA class of non-standard optimal control problems is considered. The non-standard feature of these optimal control problems is that they are of neither fixed final time nor of fixed final state. A method of solution is devised which employs a computational algorithm based on control parametrization techniques. The method is applied to the problem of maximizing the range of an aircraft-like gliding projectile with angle of attack control.

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.

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