Optimal feedback control for a class of second-order evolution differential inclusions with Clarke’s subdifferential

Abstract

The goal of this paper is to study optimal feedback control for a class of non-autonomous second-order evolution inclusions with Clarke's subdifferential in a separable reflexive Banach space. We only assume that the second order evolution operator involved satisfies the strong continuity condition instead of the compactness, which was used in previous literature. By using the properties of multimaps and Clarke's subdifferential, we assume some sufficient conditions to ensure the existence of feasible pairs of the feedback control systems. Furthermore, we also prove the existence of optimal control pairs.

Study of Nonlinear Second-Order Differential Inclusion Driven by a Φ−Laplacian Operator Using the Lower and Upper Solutions Method

“…Te Φ − Laplacian operator under consideration applies to several areas such as nonlinear elasticity, non-Newtonian fuid theory, theory of capillary surfaces, and difusion of fows in porous media (see [14]). As for diferential inclusions, they arise in the mathematical modelling of certain problems in the control theory, optimisation, mathematical economics, sweeping process, stochastic analysis, and many other felds (see [15][16][17]). Finally, variational inequalities models many applied problems, such as diferential, Nash games electrical circuits with ideal diodes, dynamic trafc networks and hybrid engineering systems with variable structures, and Coulomb friction for contacting bodies (see [18]).…”