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

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.

Optimal Maneuvering for Autonomous Vehicle Self-Localization

“…The act of determining an optimal path is also found in applications such as missile guidance, for example in scenarios of target interception [ 34 , 35 ]. In these applications, it is often assumed that the onboard sensor suite is capable of detecting the target perfectly [ 34 , 35 ].…”

“…The act of determining an optimal path is also found in applications such as missile guidance, for example in scenarios of target interception [ 34 , 35 ]. In these applications, it is often assumed that the onboard sensor suite is capable of detecting the target perfectly [ 34 , 35 ]. Because the target state is assumed to be perfectly known, the path planning can be determined using optimal control theory, for example, using Pontryagin’s maximum principle [ 33 , 34 ].…”

“…In these applications, it is often assumed that the onboard sensor suite is capable of detecting the target perfectly [ 34 , 35 ]. Because the target state is assumed to be perfectly known, the path planning can be determined using optimal control theory, for example, using Pontryagin’s maximum principle [ 33 , 34 ]. Pontryagin’s maximum principle has also been used to determine an optimal path for AOA tracking, however, under the assumption that the UAV’s coordinates are known exactly [ 33 ].…”