Performance and Stability for Combined Economic and Regulatory Control in MPC

We propose a dual-objective MPC formulation in which the dual objective is the convex combination of an economicand regulatory stage cost, using a specially formulated stateand input-dependent dynamic weight function. The purpose of the dynamic weight function is to promote increased economic performance while ensuring asymptotic stability for the economically optimal steady-state setpoint. First, sufficient conditions are derived for which the dual-objective MPC value function is a Lyapunov candidate function. Next, we propose a weight function which satisfies these conditions. We implement the combined economic and regulatory MPC, with proposed weight function, in an isothermal CSTR numerical case study, which illustrates how economics are emphasized during process transients, while retaining stability by emphasizing the regulatory cost close to the setpoint.