Approximate calculation of reachable sets for linear control systems with different control constraints

Abstract

The paper considers the problem of approximate construction of reachability sets for a linear control system, when the control action is constrained simultaneously by geometric and several integral constraints. A variant of the transition from a continuous to a discrete system is proposed by uniformly dividing the time interval and replacing the controls at the step of dividing them with their mean values. The convergence of the reachability set of the approximating system to the reachability set of the original system in the Hausdorff metric is proved as the discretization step tends to zero, and an estimate is obtained for the rate of convergence. An algorithm for constructing the boundary of reachable sets based on solving a family of conic programming problems is proposed. Numerical simulation has been carried out.