Lyapunov-based economic model predictive control of nonlinear systems

Abstract

Abstract-In this work, we focus on a class of general nonlinear systems and design a model predictive control (MPC) scheme which is capable of optimizing closed-loop performance with respect to general economic considerations taken into account in the construction of the cost function. Specifically, in the proposed design, the MPC optimizes a cost function which is related directly to certain economic considerations and is not necessarily dependent on a steady-state - unlike the conventional MPC designs. The proposed MPC is designed via Lyapunov-based techniques and has two different operation modes. The first operation mode corresponds to the periods in which the cost function should be optimized (e.g., normal production periods); and in this operation mode, the MPC maintains the closed-loop system state within a pre-defined stability region and optimizes the cost function to its maximum extent. The second operation mode corresponds to operation in which the system is driven by the MPC to an appropriate steady-state. In the MPC design, suitable constraints are incorporated to guarantee that the closed-loop system state is always bounded in the pre-defined stability region and is ultimately bounded in a small region containing the origin. The theoretical results are illustrated through a chemical process example.