Dynamic real-time optimization for nonlinear systems with Lyapunov stabilizing MPC. (June 2022) - MacKinnon, Lloyd; Ramesh, Praveen Sundaresan; Mhaskar, Prashant; Swartz, Christopher L.E.
Abstract: The present work addresses the problem of stabilizing dynamic real-time optimization and control of nonlinear systems. Dynamic real-time optimization (DRTO) is a framework for computing an optimal operating trajectory for a plant and providing corresponding set-points for an underlying control algorithm to track. This technique can be enhanced by directly modeling the underlying control algorithm (such as an MPC) in a closed-loop DRTO (CL-DRTO). This allows the CL-DRTO to predict both the controller and plant responses to set-point changes, improving performance of the overall system. Certain systems are additionally complicated by the existence of unstable steady states, which make control of the system substantially more difficult. A number of stabilizing MPC techniques have been developed in order to handle this, and a closed-loop DRTO formulation was recently proposed to handle linear systems. This work seeks to bring the improved performance of a CL-DRTO to stabilizing control systems by formulating a CL-DRTO which utilizes and explicitly models an underlying Lyapunov stabilizing MPC to achieve stabilization for nonlinear systems. The proposed formulation is compared to the previously developed formulation to demonstrate the improved closed-loop control and performance. Highlights: Novel Lyapunov-based stabilizing MPC for nonlinear plants affine in inputs. Lyapunov constraint formulated to yield a convex MPC problem. Dynamic RTO formulation that uses predicted response of convex Lyapunov-based MPC. Lyapunov MPC shows improved stabilizable region over linear terminal constraint MPC. Lyapunov MPC based DRTO shows improved economic performance for unstable plant.