Stability of Economically-Oriented NMPC with Periodic Constraint

Abstract In smart grid environment, it is economically attractive to manage the load with respect prices and demands that could change periodically. Thus it is desired to operate some plants and system applications in a cyclic fashion. Model predictive control (MPC) and nonlinear MPC (NMPC) are widely accepted advanced control tools in process industry, due to their advantages of easily handling constraints and multi-input-multi-output systems. Nevertheless, the objective of the majority of NMPC applications is to track a predefined set point. This work proposes an economically-oriented NMPC formulation with periodic constraints that directly deal with systems that exhibit cyclic steady state behavior. The periodic constraint ensures the system converges to a cyclic steady state. In addition, nominal stability of the proposed NMPC formulation is analyzed, where we introduce a transformed system with the origin as the steady state. Hence, a Lyapunov function can be established at the steady state for the transformed system that is asymptotically stable at the origin. Consequently, asymptotic stability of the original system at the cyclic steady state can be inferred from the stability of the transformed system.