scholarly journals Numerical computation of optimal control problems with unknown final time

1974 ◽  
Vol 45 (2) ◽  
pp. 274-284 ◽  
Author(s):  
G.M Aly ◽  
W.C Chan
Keyword(s):  
Optimal Control ◽  
Numerical Computation ◽  
Optimal Control Problems ◽  
Control Problems ◽  
Final Time

Improved Gradient-Type Algorithms for Zero Terminal Gradient Optimal Control Problems

1987 ◽  
Vol 109 (4) ◽  
pp. 355-362
Author(s):  
Chung-Feng Kuo ◽  
Chen-Yuan Kuo
Keyword(s):  
Optimal Control ◽  
Rate Of Convergence ◽  
Optimal Control Problems ◽  
Control Variable ◽  
Transformation Method ◽  
Control Problems ◽  
Final Time ◽  
Time Problem ◽  
Gradient Type ◽  
Improved Algorithm

Difficulties often arise when we apply the gradient type algorithms employing penalty functions to optimal control problems with variable final time. There is another class of optimal control problems for which the necessary conditions for optimality require a zero gradient at the final time. This causes the gradient-type algorithms, in their standard forms, to become incapable of changing the terminal value of the control variable at each iteration and the rate of convergence is adversely affected. In this paper, we first apply a new transformation method developed by Polak [19] which transforms the variable final time problem into a fixed final time problem. Second, an improved gradient-type algorithm is developed to overcome the zero terminal gradient problem. It is shown that, by applying this transformation and improved algorithm to four examples, not only the variable final time and zero terminal gradient problems are solved and the control vector updated in the correct direction but the rate of convergence of the improved algorithm is faster than that of the traditional gradient-type algorithms.

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.

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