Event‐triggered MPC design for distributed systems toward global performance

Abstract

Summary This paper studies the coordination control problem of stabilizing large‐scale dynamically coupled systems via a novel event‐triggered distributed model predictive control (DMPC) approach. In order to achieve global performance, certain constraints relevant to the triggering instant are imposed on the DMPC optimization problem, and triggering mechanisms are designed by taking into account coupling influences. Specifically, the triggering conditions derived from the feasibility and stability analysis are based on the local subsystem state and the information received from its neighbors. Based on these triggering mechanisms, the event‐triggered DMPC algorithm is built, and a dual‐mode strategy is adopted. As a result, the controllers solve the optimization problem and coordinate with each other asynchronously, which reduces the amount of communication and lowers the frequency of controller updates while achieving global performance. The recursive feasibility of the proposed event‐triggered DMPC algorithm is proved, and sufficient parameter conditions about the prediction horizon and the triggering threshold are established. It shows that the system state can be gradually driven into the terminal set under the proposed strategy. Finally, an academic example and a realistic simulation problem to the water level of a 4‐tank system are provided to verify the effectiveness of the proposed algorithm.

Robust model predictive control for polytopic uncertain systems with state saturation nonlinearities under Round‐Robin protocol

“…Figure 2 depicts the trajectory of the states for the open-loop system and the closed-loop system, which verifies that the addressed system with the state saturation nonlinearities is stable under the proposed state-feedback RMPC algorithm. From Figure 2, it is easily seen that the trajectory of the states for the open-loop system and the closed-loop system can reach 1 at k = 2 due to the state saturation condition (3). Figure 3 shows the trajectories of the states and the control input of the closed-loop system.…”

“…In the past few decades, model predictive control (MPC), known as receding horizon control, has received particular research attention because of its great potential in handling the optimization problems including input, state/output constraints. So far, an MPC strategy has been extensively applied into various industries and a rich body of the results has been reported in the literature . Note that the aforementioned MPC strategies for nominal systems might be invalid for systems with parameter uncertainties.…”

“…So far, an MPC strategy has been extensively applied into various industries and a rich body of the results has been reported in the literature. [1][2][3][4][5] Note that the aforementioned MPC strategies [6][7][8][9] for nominal systems might be invalid for systems with parameter uncertainties. It is, therefore, vitally important to develop some new MPC strategies to guarantee the system robustness against the parameter uncertainties, which readily gives rise to the robust MPC (RMPC).…”

Hierarchically coordinated economic MPC plantwide control of mixed continuous‐batch units in process industries with application to a beet sugar plant

“…Recent contributions, for example, deal with hybrid models 24 and event-triggered schemes. 25 In the works of Maestre et al 26 and Alvarado et al, 27 different algorithms are compared as applied to nontrivial benchmarks.…”

“…The energy balance to the product inside the chamber is given by means of (25), where h syp , h seed , and h mc are, respectively, the specific enthalpies (J/kg) of the streams of feed liquor, of the seed and of the resulting massecuite. The relationship between temperatures and enthalpies for these technical streams is tabulated for the given purity, brix, and crystal content.…”