Hang Gao

Fixed points and controllability in delay systems

Schaefers fixed point theorem is used to study the controllability in an infinite delay system . A compact map or homotopy is constructed enabling us to show that if there is an a priori bound on all possible solutions of the companion control system , then there exists a solution for . The a priori bound is established by means of a Liapunov functional or applying an integral inequality. Applications to integral control systems are given to illustrate the approach.

A Class of Nonlinear Degenerate Integrodifferential Control Systems

In this paper, we study the approximate controllability and noncontrollability for a class of nonlinear degenerate integrodifferential control systems. Based on the property of finite propagation for the disturbances, we prove noncontrollability. We also establish sufficient conditions for approximate controllability of the system in L2(\Omega) . Moreover, we prove the global existence and uniqueness of generalized solutions.

Boundary Controllability of a Pseudoparabolic Equation

We deal with the controllability problem for the pseudoparabolic equation by means of boundary controls. Due to the unusual spectrum of this kind of equations, we prove that the null controllability property is false. Furthermore, by the explicit solution, we show that the approximate controllability holds.