Optimal Stochastic Control in the Interception Problem of a Randomly Tacking Vehicle

Andrey A. Galyaev, Pavel V. Lysenko and Evgeny Y. Rubinovich
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Andrey A. Galyaev: Institute of Control Sciences of RAS, 117997 Moscow, Russia
Pavel V. Lysenko: Institute of Control Sciences of RAS, 117997 Moscow, Russia
Evgeny Y. Rubinovich: Institute of Control Sciences of RAS, 117997 Moscow, Russia

Mathematics, 2021, vol. 9, issue 19, 1-15

Abstract: This article considers the mathematical aspects of the problem of the optimal interception of a mobile search vehicle moving along random tacks on a given route and searching for a target, which travels parallel to this route. Interception begins when the probability of the target being detected by the search vehicle exceeds a certain threshold value. Interception was carried out by a controlled vehicle (defender) protecting the target. An analytical estimation of this detection probability is proposed. The interception problem was formulated as an optimal stochastic control problem, which was transformed to a deterministic optimization problem. As a result, the optimal control law of the defender was found, and the optimal interception time was estimated. The deterministic problem is a simplified version of the problem whose optimal solution provides a suboptimal solution to the stochastic problem. The obtained control law was compared with classic guidance methods. All the results were obtained analytically and validated with a computer simulation.

Keywords: optimal stochastic control; path planning; 2D random search; interception (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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