(515c) Distributed Model Predictive Control of Switched Nonlinear Systems

Due to changes in raw materials, energy sources, product specifications and market demands, control of switched nonlinear systems with scheduled mode transitions has received considerable attention. From a controller design standpoint, in order
to achieve closed-loop stability, transition situations should be carefully accounted for in the control problem formulation and solution. In order to achieve  scheduled mode transitions in an optimal setting and accomodate input/state constraints, model predictive control (MPC) framework can be employed. Motivated by these considerations, in previous work [1], we proposed a centralized Lyapunov-based MPC formulation for switched nonlinear systems with prescribed scheduled mode transitions.   In particular, to account for the switched nature of the closed–loop system, we incorporated constraints, based on hybrid control theory, in the model predictive control formulation that preserve online implementation and enable preserving stability of the switched system. However, the computational complexity of a centralized MPC  may significantly increase as the number of control inputs and states increases. Distributed MPC (DMPC)  takes advantage of cooperation and communication of distributed predictive controllers, which communicate over a shared network, to reduce the computational burden of a centralized MPC solution at the cost of slight  degradation of closed-loop performance.

In the present work, we extend the results in [3] in a distributed setting. We consider a nonlinear switched system consisting of several subsystems that follows a prescribed switching policy. A Lyapunov-based iterative DMPC scheme [2] is proposed with appropriate stability constraints to achieve  stability of the switched closed-loop system subject to process disturbances and tracking of the prescribed switching policy. In terms of DMPC feasibility, the stability constraints make sure that at the end of each switching interval, the closed-loop system state enters the stability region of the subsequent mode while there is a reduction in the Lyapunov function value of the new mode compared to value that the Lyapunov function attained  the last time that the closed-loop system had switched to that mode. The theoretical result are demonstrated with a chemical process example.

[1] Mhaskar, P., N. H. El-Farra and P. D. Christofides, ''Predictive Control of Switched Nonlinear Systems with Scheduled Mode Transitions,'' IEEE Transactions On Automatic Control, 50, 1670-1680, 2005.

[2] Liu, J., X. Chen, D. Muñoz de la Peña and P. D. Christofides, ''Sequential and Iterative Architectures for Distributed Model Predictive Control of Nonlinear Process Systems,'' AIChE Journal, 56, 2137-2149, 2010.