Chapter 4 - Fractional Control Systems

Abstract

In this chapter, we study optimal control, controllability, and topological structure of solution sets for fractional control systems. Section 4.1 concerns the fractional finite time delay evolution systems and optimal controls in infinite dimensional spaces. In Section 4.2, we study optimal feedback controls of a system governed by semilinear fractional evolution equations via a compact semigroup in Banach spaces. Section 4.3 is devoted to the investigation of controllability for a class of Sobolev-type semilinear fractional evolution systems in a separable Banach space. In Section 4.4, we discuss the approximate controllability of Sobolev-type fractional evolution systems with classical nonlocal conditions in Hilbert spaces. Section 4.5 deals with the topological structure of solution sets (compactness and Rδ-property) for control problems of semilinear fractional delay evolution equations.