TWO-POINT BOUNDARY PROBLEM SOLUTION BY NON-GRADIENT RANDOM SEARCH METHOD
Abstract
The numerical solution of two-point boundary problem when determining optimal control of dynamical system by means of Pontryagin’s maximum principle is considered. The initial conditions of conjugate set of equations are determined by use of non-gradient random search method.
The non-gradient random search method based on application of stochastic procedures for range of problems solving, including the deterministic ones. When solving the task of optimal control estimation of dynamical system by means of Pontryagin’s maximum principle the initial conditions of conjugate set of equations must be determined, provided that dynamical system’s variables values meet the known terminal conditions Y(tk).
The problem’s solution lie in random selection of vector of initial conditions in some actual range, numerical integration of basic and conjugate systems and subsequent processing of findings. Statistic processing gives the mean and RMS estimations of initial conditions values, providing terminal conditions values hit in some domain Q0 relative to Y(tk) point. For the purpose of ensuring of representative sampling for mean and RMS values estimation the adaptive recurrent search procedure with stepby-step domain Q0 contraction is introduced. The initial conditions of conjugate set of equations on the next search stage are determined on a base of sample estimates of distribution’s parameters.
The example problem solution for thirst-order control object is given. The findings confirm the possibility of proposed approach utilization for optimal control synthesis of dynamical system by means of Pontryagin’s maximum principle.
About the Author
V. A. Malkin
Military Academy of the Republic of Belarus
Belarus
Belarus
Professor, PhD in Engineering
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Review
For citations:
Malkin V.A. TWO-POINT BOUNDARY PROBLEM SOLUTION BY NON-GRADIENT RANDOM SEARCH METHOD. «System analysis and applied information science». 2016;(1):29-34. (In Russ.)
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