This paper deals with the approximate controllability for the semilinear retarded control system. We will also derive the equivalent relation between controllability and stabilizability of the solution for the corresponding linear control system.
This paper investigates the time optimal control problem to a target set for semilinear control systems involving time delays or memories when a principal operator is unbounded by the construction of a fundamental solution and an easy consequence of the definition of real interpolation spaces. A convergence theorem of time optimal controls for the given semilinear retarded system to a point target set is also given.
Abstract. This paper deals with the regularity properties for a class of semilinear integrodifferential functional differential equations. It is shown the relation between the reachable set of the semilinear system and that of its corresponding linear system. We also show that the Lipschitz continuity and the uniform boundedness of the nonlinear term can be considerably weakened. Finally, a simple example to which our main result can be applied is given.
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