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.
Highlights
The optimal control law of the defender obtained here was compared with classic guidance methods, mentioned in the Introduction, such as the pursuit guidance method and parallel guidance, which is a specific case of the proportional navigation guidance method
The searched object had a mobile defender onboard, which can be used for the distraction and destruction of the search vehicle, if it presents a danger to the searched object in the sense of its detection
The feature of this problem is that the defender has lower dynamic capabilities in comparison to the searching vehicle being intercepted
Summary
Markov process with a given state vector and a given matrix of the transition intensities between these states Such a model allows us to describe the trajectory of the SV in the form of a linear stochastic differential equation, which makes it possible to obtain the equations of the evolution of the mathematical expectation and variance. These equations allow us to formulate the problem of SV interception by the controlled vehicle with the criterion of a predicted miss or with a given mathematical expectation of a miss at the final position of the SV [16,17,18,19,20,21].
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