Distributed Lyapunov-Based Model Predictive Control with Safety-Based Constraints

Control system designs must ensure process safety. In [1], a control design was proposed that includes explicit constraints on process safety to shrink the region of process operation when required to a smaller region (safety region) around the operating steady-state when a safety logic unit indicates that certain regions of state-space away from the steady-state may lead to process safety concerns due to process disturbances or actuator faults. The safety-based controller design was developed with a centralized model predictive control (MPC) structure; thus, computation time limitations within a sampling period may reduce the effectiveness of such a controller design for promoting process safety. An alternative MPC architecture that is intended to improve the computation time of the MPC algorithm is a distributed model predictive control (DMPC) architecture [2]-[3]. This MPC architecture has been investigated for computation time benefits since it can reduce the number of decision variables in each of the distributed optimization problems and may be able to terminate the optimization problems before the optimal solution is found while maintaining feasibility and closed-loop stability of the controller [4]-[5].

In this work, we propose the integration of a distributed model predictive control architecture with Lyapunov-based model predictive control (LMPC) and Lyapunov-based economic model predictive control (LEMPC) formulated with safety-based constraints. We consider both iterative and sequential distributed control architectures, and the partitioning of inputs between the various optimization problems in the distributed structure based on their impact on process safety. In addition, we investigate the conditions required for guaranteed feasibility and closed-loop stability of the algorithm, and discuss the termination of the algorithm and computation time benefits. Through a chemical process example, we demonstrate the proposed controller design and the effects of the control architecture on process safety considerations, and compare the time required to reach the safety level set and the computation time of the algorithm with that which can be achieved under a centralized safety-based model predictive control scheme.

[1] Albalawi F, Alanqar A, Durand H, Christofides PD. A feedback control framework for safe and economically-optimal operation of nonlinear processes. AIChE Journal. 2016; in press.

[2] Christofides PD, Liu J, Muñoz de la Peña D. Networked and Distributed Predictive Control: Methods and Nonlinear Process Network Applications. London, England: Springer, 2011.

[3] Scattolini R. Architectures for distributed and hierarchical model predictive control- A review. Journal of Process Control. 2009;19:723-731.

[4] Anderson TL, Ellis M, Christofides PD. Distributed economic model predictive control of a catalytic reactor: Evaluation of sequential and iterative architectures. In: Proceedings of the IFAC International Symposium on Advanced Control of Chemical Processes. Whistler, Canada, 2015;26-31.

[5] Venkat AN, Hiskens IA, Rawlings JB, Wright SJ. Distributed MPC strategies with application to power system automatic generation control. IEEE Transactions on Control Systems Technology. 2008;16:1192-1206.