On the Existence of a Lipschitz Feedback Control in a Control Problem with State Constraints
- 1 Downloads
We consider a nonlinear control system with state constraints given as a solution set for a finite system of nonlinear inequalities. The problem of constructing a feedback control that ensures the viability of trajectories of the closed system in a small neighborhood of the boundary of the state constraints is studied. Under some assumptions, the existence of a feedback control in the form of a Lipschitz function of the state of the system is proved.
Keywordsstate constraints feedback control viability problem invariance.
Unable to display preview. Download preview PDF.
- 2.A. B. Kurzhanski and T. F. Filippova, “On the theory of trajectory tubes—A mathematical formalism for uncertain dynamics, viability and control,” in Advances in Nonlinear Dynamics and Control: A Report from Russia, Ed. by A. B. Kurzhanski (Birkhäuser, Boston, 1993), Ser. Progress in Systems and Control Theory 17, pp. 122–188.CrossRefGoogle Scholar
- 4.F. L. Chernousko, State Estimation for Dynamic Systems (Nauka, Moscow, 1988; CRC, Boca Raton, 1994).Google Scholar
- 7.M. Gusev, “On reachability analysis for nonlinear control systems with state constraints,” in Proceedings of the 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Madrid, Spain, 2014 (AIMS, Springfield, MO, 2015), pp. 579–587.Google Scholar
- 8.M. I. Gusev, “Application of penalty function method to computation of reachable sets for control systems with state constraints, AIP Conf. Proc. 1773, paper 050003 (2016).Google Scholar