Lyapunov-Based Distributed MPC Schemes: Sequential and Iterative Approaches
In this chapter, we focus on two distributed MPC (DMPC) schemes for the control of large-scale nonlinear systems in which several distinct sets of manipulated inputs are used to regulate the system. In the first scheme, the distributed controllers use a one-directional communication strategy, are evaluated in sequence and each controller is evaluated once at each sampling time; in the second scheme, the distributed controllers utilize a bi-directional communication strategy, are evaluated in parallel and iterate to improve closed-loop performance. In the design of the distributed controllers, Lyapunov-based model predictive control techniques are used. To ensure the stability of the closed-loop system, each model predictive controller in both schemes incorporates a stability constraint which is based on a suitable Lyapunov-based controller. We review the properties of the two DMPC schemes from stability, performance, computational complexity points of view. Subsequently, we briefly discuss the applications of the DMPC schemes to chemical processes and renewable energy generation systems.
KeywordsModel Predictive Control Stability Constraint Model Predictive Controller Input Trajectory Energy Generation System
- 1.F. Allgöwer, H. Chen, Nonlinear model predictive control schemes with guaranteed stability, in NATO ASI on Nonlinear Model Based Process Control, ed. by R. Berber, C. Kravaris (Kluwer Academic Publishers, Dordrecht, 1998), pp. 465–494Google Scholar
- 5.S.L.D. Kothare, M. Morari, Contractive model predictive control for constrained nonlinear systems. IEEE Trans. Autom. Control 45(6), 1053–1071 (2000)Google Scholar
- 7.J. Liu, X. Chen, D. Muñoz de la Peña, P.D. Christofides, Sequential and iterative architectures for distributed model predictive control of nonlinear process systems. AIChE J. 56(8), 2137–2149 (2010)Google Scholar
- 13.D. Nes̆ić, A. Teel, P. Kokotovic, Sufficient conditions for stabilization of sampled-data nonlinear systems via discrete time approximations. Syst. Control Lett. 38(4–5), 259–270 (1999)Google Scholar
- 15.W. Qi, J. Liu, P.D. Christofides, Distributed supervisory predictive control of distributed wind and solar energy generation systems. IEEE Trans. Control Syst. Technol. 21, 504–512 (2013) (in press)Google Scholar