Controllability, Stability And Its Optimal Control Of A Class Nonlinear Distributed Parameter System

In this paper, we study a class of nonlinear distributed parameter as follows:The initial condition Q(x,Q) = Q0(x) x e Q , At first we transform it an abstract evolution equation:Using the theory of semigroups of operators, we find the mild solution of system (1) and the solution is unique ?Considering corresponding linear system:we follow the sufficient and necessary conditions of system (2) from the controllability of system (3) ?So the sufficient and necessary conditions of system (2) is obtained?We discuss the stability conditions of system (1) On the base of its controllability ?At last we study the necessary conditions of optimal control problem on the system, and applying to variation theory we acquire the adjoint equation which the admission dual-controls are satisfied<,...