(393e) Distributed Model Predictive Control of Two-Time-Scale Nonlinear Systems

Distributed model predictive control (DMPC) schemes are of particular interest for the process industries because of their ability to handle input and state constraints, to coordinate control actions of different controllers, and to overcome the increasing computational complexity of centralized MPC. In a DMPC architecture, the manipulated inputs are computed by solving more than one control (optimization) problems in separate processors in a coordinated fashion. With respect to available results in this direction, several DMPC methods have been proposed in the literature. In our previous works [1,2], two different DMPC architectures, namely, a sequential DMPC architecture and an iterative DMPC architecture, were designed for nonlinear systems via Lyapunov model predictive control techniques. In these works, we considered fully coupled nonlinear systems that are not characterized by two-time-scale behavior. In the design of DMPC, specific system dynamic properties, two-time-scale dynamics for example, may be taken advantage of to simplify the design of distributed MPC controllers; therefore, the computational complexities of the distributed MPC optimization problems may be further reduced.

In this work, we consider the design of a DMPC scheme for nonlinear systems whose dynamics can be described by nonlinear two-time-scale systems. Specifically, we assume that the dynamics of a nonlinear system involve coupled fast and slow dynamics and are described by singularly perturbed systems in standard form. In the design of the DMPC, some of the distributed controllers are used to manipulate control inputs associated with fast system dynamics and some of the distributed controllers are used to manipulated control inputs associated with the slow system dynamics. In the design of the distributed controllers associated with the fast subsystem, where the slow states remain fixed; we employ explicit control techniques because fast calculation of the control action is required; on the other hand in the design of the distributed controllers associated with the slow subsystem, we utilize sequential and iterative schemes. This approach to controller design can significantly reduce the computational complexities of the MPC optimization problems associated with the full two-time-scale nonlinear system. Sufficient conditions under which the state of the closed-loop system is ultimately bounded in an invariant region containing the origin are derived. The theoretical results are demonstrated through a nonlinear chemical process example.

[1] J. Liu, D. Munoz de la Pena, and P. Christofides, ?Distributed model predictive control of nonlinear process systems,? AIChE Journal, vol. 55, pp. 1171?1184, 2009.

[2] J. Liu, X. Chen, D. Munoz de la Pena, and P. Christofides, ?Sequential and iterative architectures for distributed model predictive control of nonlinear process systems,? AIChE Journal, in press.