(295c) Noniterative Distributed Model Predictive Control through Multiparametric Programming

In a distributed control system architecture, an array of controllers control the different subsystems of an interacting process system and exchange information with each other to improve the peofrmance of the overall control system. The information exchange is realized through intermediate iterations or solving multiple optimization problems at each time step [1]. The performance of a cooperative distributed model predictive control (CDMPC) system converges to that of its centralized counterpart with increase in the number of intermediate iterations [2]. Typically, iterations are terminated before convergence to save computational costs or to respond within the control time period, hence preventing the system from achieving the best possible control performance. Researchers have been focusing on reducing the time of execution of each intermediate iteration [3, 4], improving the rate of convergence, or reduce the number of intermediate interations to obtain the solution [5].

This work differs from the aforementioned approaches as the proposed novel methods completely eliminate the need to perform intermediate iterations, by taking advantage of multiparametric programming, a method for optimization under uncertainity (mpCDMPC). The iterations are replaced by simultaneous solutions of the offline-generated affine functions of the parameter space. In the distributed case, along with the system states, set points, and pervious control inputs, the control inputs of other subsystem controllers are also regarded as parameters. The proposed mpCDMPC algorithms are evaluated by numerical simulations on random plants with different number of subsystems. Being noniterative, the methods reduce communication between subsystems, thereby also improving cyber security while significantly reducing the online computational time.

REFERENCES

[1] P. D. Christofides, R. Scattolini, D. M. de la Pena, J. Liu, Distributed model predictive control: A tutorial review and future research directions, Computers & Chemical Engineering 51 (2013) 21–41.

[2] B. T. Stewart, A. N. Venkat, J. B. Rawlings, S. J. Wright, G. Pannocchia, Cooperative distributed model predictive control, Systems & Control Letters 59 (2010) 460–469.

[3] R. S. Saini, I. Pappas, S. Avraamidou, H. S. Ganesh, Noncooperative distributed model predictive control: A multiparametric programming approach, Industrial & Engineering Chemistry Research (2023).

[4] A. Bemporad, M. Morari, V. Dua, E. N. Pistikopoulos, The explicit linear quadratic regulator for constrained systems, Automatica 38 (2002) 3–20.

[5] J. Wang, Y. Yang, An improved iterative solution for cooperative distributed mpc, Automatica 140 (2022) 110155.