Sufficient optimality conditions for controlling switched systems

Optimization of Switchable Systems’ Trajectories

“…) and there is no actual switching are excluded. The possible equality of successive moments in (1.1) means that the system performs instant multiple switchings [2,3].…”

“…The application of the dynamic programming method [28] is based on the concept of a value function (Hamilton-Jacobi-Bellman function), which is determined by the minimum value of the functional of the remaining losses. For the SS under consideration, the method for constructing sufficient conditions developed for a more general model of hybrid systems is used [3]. According to this method, the value function is constructed using auxiliary functions, the so-called generators of the value function [2][3][4].…”

“…In contrast to [7], the number of switchings and switching moments are not predetermined and are subject to optimization. In this case, multiple switchings at a fixed time instant are not excluded [2][3][4]. Similar models were previously considered in the class of logical-dynamical systems [8].…”

“…Switchable systems (SSs) serve as mathematical models of multimode automatic control systems for technological processes and moving objects [1][2][3][4]. The functioning of such systems is represented by continuous-discrete processes that have a heterogeneous description [4][5][6] and belong to hybrid systems (HSs).…”

“…The optimality conditions obtained for them turn out to be more constructive than in the general case [11,17]. To construct sufficient optimality conditions, the approach developed in [3] is applied with the use of auxiliary cost functions: the so-called generators and conditional cost functions. The derivation of the necessary conditions for optimality is traditional.…”