Relaxation in controlled systems described by fractional integro-differential equations with nonlocal control conditions. (English) Zbl 1311.93039
Summary: A control system described by fractional evolution integro-differential equations and fractional integral nonlocal control conditions is investigated. This posed system is subjected to mixed multivalued control constraints whose values are nonconvex closed sets. Along with the original system, we consider the system in which the constraints on the controls are the closed convex hulls of the original constraints. More precisely, existence results for the mentioned nonlocal control systems are proved. Furthermore, we study relations between the solution sets of both systems.
MSC:
93C15 | Control/observation systems governed by ordinary differential equations |
26A33 | Fractional derivatives and integrals |
45J05 | Integro-ordinary differential equations |
93C25 | Control/observation systems in abstract spaces |