Robust Quadratic Optimal Control of Linear Systems with Ellipsoid-Set Learning

Despite the celebrated success of linear quadratic Gaussian control (LQG) for stochastic systems, LQG approaches are inefficient in handling systems with non-Gaussian noises. This paper is concerned with linear quadratic control of discrete-time systems with bounded noises and unobservable system states. We describe such noises and system states by ellipsoidal sets, enabling the establishment of boundaries for those uncertainties in the control. Further, we learn and update the ellipsoidal sets for the system states by an ellipsoidal set-membership filter. With the learned ellipsoidal sets, we derive a robust state-feedback optimal control law by solving a rendered semidefinite programming problem. Simulation results demonstrate the enhanced control performance by the proposed method.