(409d) Cooperative, Distributed Model Predictive Control for Systems with Coupled Input Constraints

We consider a plant-wide control problem divided into several subsystems, each of which is controlled by a model predictive controller (MPC). The MPC systems employ two optimization layers. The steady-state target optimization layer calculates feasible steady states, accounting for disturbances in plant operating conditions. The subsystem dynamic controllers move the plant to these targets. Coupled constraints are constraints shared between subsystems within the plant. These constraints arise because of shared subsystem feeds or utilities and are usually represented as the off-diagonal blocks in the plant-wide constraint matrix. Distributed model predictive control, the control strategy considered here, decomposes the plant-wide control problem into a collection of subsystem problems while ensuring stability and optimality [1, 2]. Distributed control is viewed as more flexible and robust because the plant does not rely on a single centralized controller.

The distributed control problem can be viewed as an N-player game in which subsystems minimize their local objective [3]. In communication-based strategies [1], the subsystems iterate to a Nash equilibrium, which is sufficient for stability if the subsystems are weakly coupled dynamically. This strategy is inadequate, however, for the steady-state problem because typically the interactions between subsystems are strong. In this case a Nash equilibrium is not necessarily a stable operating point. Cooperative strategies, however, produce iterates that converge to the Pareto optimal point, a stable point for any strength interactions [2]. Cooperative model predictive control has been shown to work with both centralized and distributed steady-state target calculations but has so far assumed that the decomposed subsystems' constraints are uncoupled in the distributed target calculation. Introduction of coupled constraints into the cooperative steady-state target calculation produces suboptimal plant-wide steady states.

Most previous work for distributed target calculation with coupled constraints uses a coordinator [4]. The coordinator solves a dual problem for the Lagrange multipliers of the coupled constraints. Structurally, however, the coordinator is similar to the centralized target calculation. A completely distributed control system does not have a coordinator.

Using industrial examples, we illustrate how the coupled constraint problem arises. We show that while cooperative control with coupled constraints is suboptimal, it guarantees closed-loop stability for all stationary points of the steady-state target calculation. Finally, we show how performance can be improved using algorithms that account for the constraint coupling without the need for third-party coordination. These methods maintain the attractive stability and optimality properties of cooperative controller while preserving the distributed control topology in plants with coupled constraints.

REFERENCES

[1] Eduardo Camponogara, Dong Jia, Bruce H. Krogh, and Sarosh Talukdar. Distributed model predictive control. IEEE Ctl. Sys. Mag., pages 44–52, February 2002.

[2] Aswin N. Venkat, James B. Rawlings, and Stephen J. Wright. Stability and optimality of distributed, linear MPC. part 1: state feedback. Technical Report 2006–03, TWMCC, Department of Chemical and Biological Engineering, University of Wisconsin–Madison (Available at http://jbrwww.che.wisc.edu/tech-reports.html), October 2006.

[3] James B. Rawlings and Brett T. Stewart. Coordinating multiple optimization-based controllers: new opportunities and challenges. In DYCOPS, Cancun, Mexico, June 2007.

[4] R. Cheng, JF Forbes, and WS Yip. Price-driven coordination method for solving plant-wide MPC problems. J. Proc. Cont., 17(5):429–438, 2007.