Luenberger-Like Observer Design and Optimal State Estimation of Logical Control Networks With Stochastic Disturbances

State estimation is important for the synthesis of nonlinear systems with stochastic disturbances. This work devotes to tackling the optimal state estimation problem of logical control networks (LCNs) with stochastic disturbances. First, based on the algebraic form of LCNs with stochastic disturbances, an effective approach is proposed to design the Luenberger-like observer. Second, by resorting to the Luenberger-like observer, a new criterion is presented to obtain the optimal state estimator by minimizing the mean square error. Third, the optimal state estimator is applied to the finite-horizon output tracking problem of LCNs with stochastic disturbances. Finally, an illustrative example is given to show the feasibility of the obtained results.