抄録
In this paper, sufficient conditions for the stochastic controllability of nonlinear distributed parameter systems are established by the stochastic Lyapunov-like functional method.
First, nonlinear distributed parameter systems subjected to random excitations are described by the stochastic evolution equation in L2-space.
Secondly, the stochastic controllability concept is defined in the sense of the L2-norm, and a theorem is proved to give sufficient conditions for stochastic controllability. Since the conditions are stated implicitly in terms of a stochastic Lyapunov-like functional, it is necessary, from the practical point of view, to construct the functional from system parameters. For this purose, a distributed parameter system with an additive control signal and subjected to noise disturbance depending linearly on the system state is considered. Controllability conditions are obtained which contain Kalman's condition as a special case.
The remainder of this paper is devoted to developing comparative discussions of the controllability conditions obtained here with those for linear deterministic distributed parameter systems.
