Optimal switching for hybrid semilinear evolutions. (November 2016)

• Record Type: Journal Article
• Authors: Rüffler, Fabian; Hante, Falk M.
• Is Part Of: Nonlinear analysis. Volume 22(2016)
• Page Start: 215
• Page End: 227
• Publication Date: 2016-11
• Subjects: Hybrid dynamical system -- Optimal control -- Switching time gradient -- Mode insertion gradient -- Delay differential equation -- Partial differential equation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nahs.2016.05.001
• Languages: English
• ISSNs: 1751-570X

Abstract

Abstract: We consider the optimization of a dynamical system by switching at discrete time points between abstract evolution equations composed by nonlinearly perturbed strongly continuous semigroups, nonlinear state reset maps at mode transition times and Lagrange-type cost functions including switching costs. In particular, for a fixed sequence of modes, we derive necessary optimality conditions using an adjoint equation based representation for the gradient of the costs with respect to the switching times. For optimization with respect to the mode sequence, we discuss a mode-insertion gradient. The theory unifies and generalizes similar approaches for evolutions governed by ordinary and delay differential equations. More importantly, it also applies to systems governed by semilinear partial differential equations including switching the principle part. Examples from each of these system classes are discussed.