An Algorithm for Computing Boundary Points of Reachable Sets of Control Systems Under Integral Constraints

Abstract

In this paper we consider a reachability problem for a nonlinear affine-control system with integral constraints, which assumed to be quadratic in control variables. Under controllability assumptions it was proved in [8] that any admissible control that steers the control system to the boundary of its reachable set is a local solution to an optimal control problem with an integral cost functional and terminal constraints. This leads to the Pontriagyn maximum principle for boundary trajectories. We propose here a numerical algorithm for computing the reachable set boundary based on the maximum principle and provide some numerical examples.

State estimation for bilinear impulsive control systems under uncertainties

“…Among them we mention here [Kurzhanski and Valyi, 1997;Kurzhanski and Varaiya, 2014;Mazurenko, 2012;Schweppe, 1973;Walter and Pronzato, 1997]. For models with linear dynamics under such setmembership uncertainty there are several constructive approaches which allow to find effective estimates of reachable sets of control systems under uncertainty [Gusev, 2017;Chernousko, 1996;Filippova, 2010;Kurzhanski and Valyi, 1997;Kurzhanski and Varaiya, 2014;Polyak and etc., 2004].…”