Multi-objective nonlinear model predictive control through switching cost functions and its applications to chemical processes

This paper proposes a switching multi-objective model predictive control (MOMPC) algorithm for constrained nonlinear continuous-time process systems. Different cost functions to be minimized in MPC are switched to satisfy different performance criteria imposed at different sampling times. In order to ensure recursive feasibility of the switching MOMPC and stability of the resulted closed-loop system, the dual-mode control method is used to design the switching MOMPC controller. In this method, a local control law with some free-parameters is constructed using the control Lyapunov function technique to enlarge the terminal state set of MOMPC. The correction term is computed if the states are out of the terminal set and the free-parameters of the local control law are computed if the states are in the terminal set. The recursive feasibility of the MOMPC and stability of the resulted closed-loop system are established in the presence of constraints and arbitrary switches between cost functions. Finally, implementation of the switching MOMPC controller is demonstrated with a chemical process example for the continuous stirred tank reactor.

Graphic abstractThe blue ellipse denotes the terminal state set of the switching multi-objective NMPC controller of a CSTR process, red ‘○’ denotes the operating steady-state point of the CSTR process, and black solid lines denote the state-phase trajectories of the CSTR process controlled by the proposed NMPC, starting from six initial states (a)–(f). By taking into account arbitrarily changing economic factors of reactant materials and energy, the CSTR system with the proposed NMPC controller can asymptotically converge to the operating steady-state point while satisfying the constraint on species concentration CA and reactor temperature TR.Figure optionsDownload as PowerPoint slide