(434h) Tractable Control-Theoretic Constraint Design for Lyapunov-Based Economic Model Predictive Control

Safety-critical guarantees for advanced control (e.g., guarantees regarding closed-loop stability) often rely heavily on assumed parameters or characteristics of nonlinear systems which may be difficult to verify in practice. An example of an advanced control methodology of interest is economic model predictive control (EMPC) [1], which is a control design that determines control actions which optimize a general economic cost function, subject to constraints, over a prediction horizon with predictions of the process state obtained from a dynamic process model. For certain formulations of this controller, methods have been developed which attempt to make the determination of certain aspects of the control-theoretic properties required for closed-loop stability proofs able to be determined algorithmically (e.g., by adding positive definite terms to the stage cost of an EMPC formulation in [2]). However, for other formulations of this controller (e.g., a Lyapunov-based formulation known as Lyapunov-based EMPC, or LEMPC [3]), systematic techniques for constructing aspects of the control laws (such as sampling period length or the size of bounded regions of operation which trigger different constraints of the control formulation) which guarantee the control-theoretic properties have not been developed for general nonlinear systems in the presence of disturbances.

In this work, we explore several methods for attempting to reduce the challenges with designing control-theoretic constraints in LEMPC and analyzing whether a process achieves closed-loop stability. The first method to be examined [4] explores an implementation strategy for LEMPC that trades off between an LEMPC and an explicit stabilizing control law to attempt to make it less likely that closed-loop stability guarantees would not be obtained for the controller when the size of a region of operation used in determining which constraints are activated in the control law is selected without rigorous determination a priori of whether it meets control-theoretic conditions. Another method to be explored seeks to determine the form of an auxiliary controller and of functions used in closed-loop stability proofs by searching for linear combinations of functions from a pre-specified but large set which cause control-theoretic conditions to hold (following concepts from [5]). Finally, we explore the benefits and limitations of approaches based on game-playing (e.g., [6]) for attempting to locate functions and parameters in the control law design which achieve closed-loop stability goals.

[1] M. Ellis, H. Durand, and P. D. Christofides. A tutorial review of economic model predictive control methods. Journal of Process Control, 24:1156–1178, 2014.

[2] J. B. Rawlings, D. Angeli, and C. N. Bates. Fundamentals of economic model predictive control. In Proceedings of the IEEE Conference on Decision and Control, pp. 3851-3861, Maui, Hawaii, 2012.

[3] M. Heidarinejad, J. Liu and P. D. Christofides. Economic model predictive control of nonlinear process systems using Lyapunov techniques, AIChE Journal, 58:855-870, 2012.

[4] H. Durand and D. Messina. Enhancing practical tractability of Lyapunov-based economic model predictive control. In Proceedings of the American Control Conference, in press, Denver, Colorado, 2020.

[5] S. L. Brunton, J. L. Proctor and J. N. Kutz. Discovering governing equations from data by sparse identification of nonlinear dynamical systems. PNAS, 113:3932-3937, 2016.

[6] D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. van den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis. “Mastering the game of Go with deep neural networks and tree search.” Nature, 529:484-489, 2016.