Discrete-Valued Model Predictive Control Using Sum-of-Absolute-Values Optimization

In this paper, we propose a new design method of discrete-valued model predictive control for continuous-time linear time-invariant systems based on sum-of-absolute-values (SOAV) optimization. The finite-horizon discrete-valued control design is formulated as an SOAV optimal control, which is an expansion of L-1 optimal control. It is known that under the normality assumption, the SOAV optimal control exists and takes values in a fixed finite alphabet set if the initial state lies in a subset of the reachable set. In this paper, we analyze the existence and discreteness property for systems that do not necessarily satisfy the normality assumption. Then, we extend the finite-horizon SOAV optimal control to infinite-horizon model predictive control (MPC). We give sufficient conditions for the recursive feasibility and the stability of the MPC-based feedback system in the presence of bounded noise. Simulation results show the effectiveness of the proposed method.