Stabilization of nonlinear sampled-data systems and economic model predictive control application

This work first presents a few results on stabilization of a general class of nonlinear sampled-data systems which are subsequently used in the design of a model predictive control (MPC) scheme that renders the origin of the nonlinear sampled-data system exponentially stable. Second, a novel two-layer economic model predictive control (EMPC) structure that addresses provable finite-time and infinite-time economic performance improvement of nonlinear systems in closed-loop with EMPC is presented. In the upper layer, a Lyapunov-based EMPC (LEMPC) scheme is formulated with performance constraints by taking advantage of an auxiliary (tracking) Lyapunov-based model predictive control (LMPC) problem solution. The auxiliary LMPC is designed using the results obtained on stabilization of nonlinear sampled-data systems. The lower layer LEMPC is formulated with a shorter prediction horizon and smaller sampling period than the upper layer LEMPC and involves explicit performance-based constraints computed by the upper layer LEMPC. In this manner, the two-layer architecture allows for provable finite-time and infinite-time performance guarantees over the auxiliary (tracking) LMPC and is a computationally efficient control scheme at the feedback control layer by effectively dividing dynamic optimization and control tasks in two layers. A chemical process network example is used to demonstrate the performance and stability properties of the two-layer LEMPC structure.