Robust Quadratic Optimal Control for Discrete-Time Linear Systems with Non-Stochastic Noises

In this paper, the quadratic optimal control problem is investigated for the discrete-time linear systems with process and measurement noises which belong to specified ellipsoidal sets. As the noises are non-stochastic, the traditional Kalman filtering and Dynamic Bellman Equation are not applicable for the proposed control problem. To obtain the optimal control, we firstly converted the multi-step quadratic global optimal control problem to multiple one-step quadratic local approximate optimal control problems. For each one-step quadratic optimal control problem, considering that the system states are not fully available, the set-membership filtering is applied to estimate the true state feasible set. Then based on robust optimization, a robust state feedback control strategy can be obtained by solving a certain semidefinite programming (SDP) problem. The method can not only achieve the optimal control, but also estimate the system states more accurately. Finally, the simulation results verify the effectiveness of the proposed algorithm.