Traversing Target Points Under Lack of Information: A Game-Theoretical Approach

Abstract

A dynamical object controlled under conditions of unknown disturbances or counteractions is considered. The goal is to bring the object to given target points at given times regardless of the disturbance actions. To solve this problem, the quality index is introduced that evaluates the distance between the object and target points at the indicated times, and a zero-sum differential game is considered in which the control actions minimize this quality index while the disturbance actions maximize it. The initial problem is reduced to calculating the game value and constructing a saddle point of the game. The corresponding resolving procedure is proposed that is based on the upper convex hulls method. An example is considered. Results of numerical simulations are presented. © 2018