Optimal in the Mean Control of Deterministic Switchable Systems Given Discrete Inexact Measurements

Abstract

We consider the problem of the optimal-in-the-mean control of a switchable system whose continuous change of state is described by differential equations, whereas instantaneous discrete changes of the state (switches) are described by recurrent equations. Discrete changes in the control process simulate the operation of an automaton (with a memory) that switches modes of the continuous motion of a control plant. Switching moments and their number are not set in advance. The quality of the control is characterized by a functional that takes into account the cost of each switch. The state of the control plant is not known exactly; however, this state is refined as a result of discrete inexact measurements. Therefore, in addition to the problem of the optimal control, the problem of the optimal-in-the-mean control of bundles of trajectories is also studied. Sufficient conditions for the optimality of control are obtained; based on them, algorithms for constructing the suboptimal control of bundles of trajectories of switchable systems given discrete inexact measurements are proposed. The use of the algorithms is demonstrated by academic examples.