The problem of time-optimal control with the search of the goal point

Abstract

A point-to-point optimal control problem is considered with the goal point belonging to a given domain of uncertainity. The aim of control is to find (observe) the goal point within the bounds of this domain and bring the controlled state vector to the goal point with minimal time. The goal point is considered to be known (observed) when it occurs in the informational set, moving with the state vector. The formulation of time-optimal minimax problem and its complete solution for two-dimensional case are given. Several examples and an application in robotic illustrate the approach. A possible visual interpretation of the promlem under consideration is to identify the informational domain with the movable light spot, which can be controlled in the dark space to search and find initially unknown goal point within the given uncertainity set. The problem was first stated in [1], developed in [2] and present paper. Other approaches to the related problems see in [3, 4].