Existence of optimal controls on hybrid time domains. (February 2019)

• Record Type: Journal Article
• Authors: Goebel, Rafal
• Is Part Of: Nonlinear analysis. Volume 31(2019)
• Page Start: 153
• Page End: 165
• Publication Date: 2019-02
• Subjects: Optimal control -- Hybrid control system -- Existence of optimal solutions -- Hybrid time domain; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2018.07.005
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: Hybrid control systems are considered, combining continuous-time dynamics and discrete-time dynamics, and modeled by differential equations or inclusions, by difference equations or inclusions, and by constraints on the resulting dynamics. Solutions are defined on hybrid time domains. Finite-horizon and infinite-horizon optimal control problems for such control systems are considered. Existence of optimal open-loop controls is shown. The assumptions used include, essentially, the existence for the (non-hybrid) continuous-time case; the existence for the (non-hybrid) discrete-time case; mild conditions on the endpoint penalties; and closedness and boundedness, in the finite-horizon case, of the set of admissible hybrid time domains. Examples involving switching systems and hybrid automata are included.