Regulators with noise in the dynamic component unit (Q1287251)

The authors consider the control of a linear stochastic system \[ dx= A(t)x(t)dt+ B(t)u(t)dt+ d\xi,\quad t\in [0,T] \] by the observations \[ dy= C(t)x(t)dt+ d\eta. \] Here \(\xi\) and \(\eta\) are independent Wiener processes. A regulator with a feedback and with a dynamic component (filter) is constructed for this system. It is supposed that a random Wiener noise \(\nu\) of known intensity acts in the dynamic component unit of the regulator. The problem of construction of an optimal regulator which minimizes the special functional \(J(u)\) along the trajectories of the system is solved. The influence of the additional noise \(\nu\) on the quality of the control is considered; the control is determined by the separation principle. The equations for the parameters of the optimal regulator are obtained. Dynamic systems with constant coefficients are investigated in detail; the stability of stationary regulators is studied and the comparison of regulators is presented.