Finite-dimensional adaptive control method for stochastic distributed parameter systems

A method of model reference adaptive control (MRAC) for stochastic distributed parameter systems is developed for the case when the plant is disturbed by additive noise and the observation data are disturbed by sensing noises. First, a mathematical description of plant model is given. Secondly, by using the concept of command generator tracker, an MRAC problem is formulated and a finite-dimensional adaptive control law is proposed. Finally, by using the stochastic Lyapunov function approach, the stability theorem for the controlled system and the convergence theorem for the tracking error of output are derived. The tracking error bound is evaluated in terms of the covariances of system noise and observation noise