Untitled

Kolmanovskii, V. B.; Королева, Н Ю; Kosareva, N. P.

doi:10.1023/a:1023601424901

Cited by 1 publication

(2 citation statements)

References 1 publication

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this section, the method of approximation of the problem of optimal programmed control of a dynamic system with random parameters by a deterministic optimal control problem described in [2] will be applied to the problem (1), ( 4) - (6).…”

Section: Approximation Of Stochastic Problem With the Deterministic O...mentioning

confidence: 99%

“…Note that a vast literature is devoted to the problems of optimal control of stochastic systems, only a small part of which relates to the study of programmed control. For example, various aspects of programmed control, first of all necessary optimality conditions, were considered in [3][4][5][6][7]. In the already mentioned paper [1], the existence of optimal programmed control in problems without phase constraints as well as in problems with rather general phase constraints of two different types was proved.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Optimal programmed control in energy minimisation problem

Khrychev

2023

E3S Web of Conf.

View full text Add to dashboard Cite

This paper is devoted to the construction of optimal programmed control of the motion of a material point in a medium with a random coefficient of resistance in a homogeneous field of gravity of the Earth. The control objective is to minimise the mathematical expectation of the total mechanical energy of the material point. The problem is solved by two methods proposed by the author in previous works. Both methods assume approximation of the initial stochastic problem by deterministic optimal control problems. In the first case, the transition to approximate deterministic problems is carried out by replacing the parameters representing continuous random variables by discrete-type random variables converging in distribution to the original continuous ones (the method of distribution discretisation). The meaning of such a replacement is that the resulting approximate problem can be considered no longer as a stochastic, but as a deterministic optimal control problem, and can be solved, accordingly, with the help of known standard methods. In the second case, the initial stochastic dynamic system as a result of averaging its equations is replaced first by an infinite system and then, after zeroing all moments of sufficiently high order, by a finite system of equations for mixed moments of the solution and a random parameter (method of moments). The control functions and the optimal values of the quality functional obtained by the two methods were found to be almost identical, and both methods showed good convergence.

show abstract

Section: Approximation Of Stochastic Problem With the Deterministic O...mentioning

confidence: 99%