Synthesis of Optimal Control-Systems with a Change of the Models of Motion

Abstract

In this paper, the problem of synthesizing an optimal system controlled with switches is considered. The term switching is understood more broadly than in hybrid systems; i.e., there is a controlled change of the mathematical model of the controlled system at a switching moment: the equations of motion, the state space, and controls are changed. The quality of the control process is estimated by the functional that takes into account both the losses in the continuous motion of the system between switching moments and the cost of each switch. The number of switches and the switching moments themselves are not preassigned and are found during the process of optimization. The sufficient conditions for optimal control are obtained and their application is demonstrated by academic examples of group performance.