Distributed model predictive control with saturated inputs by a saturation‐dependent Lyapunov function

• Published in: Optimal control applications & methods Vol. 38; no. 3; pp. 336 - 354
• Main Authors: Zhang, L., Xie, W., Wang, J.
• Format: Journal Article
• Language: English
• Published: Glasgow Wiley Subscription Services, Inc 01.05.2017
• Subjects: Actuators; Controllers; distributed model predictive control; Invariants; Iterative algorithms; Iterative methods; Liapunov functions; Linear matrix inequalities; Optimization; parameter dependent; polytopic uncertain; Predictive control; Robust control; saturated inputs; Saturation; saturation dependent; Subsystems
• ISSN: 0143-2087; 1099-1514
• DOI: 10.1002/oca.2258

Summary In this paper, distributed model predictive control (MPC) problems are considered for input‐saturated polytopic uncertain systems by a saturation‐dependent Lyapunov function approach. The actuator saturation is processed by the transformation into the linear convex combination form. By the decomposition of the control input, distributed MPC controllers are designed in parallel for each subsystems. The Lyapunov Function we select is saturation dependent, which is less conservative than the general Lyapunov Function approach. An invariant set condition is provided and min–max distributed MPC is proposed based on the invariant set. The robust distributed MPC controllers are determined by solving a linear matrix inequality (LMI) optimization problem. To reduce the conservatism, we present a robust distributed MPC algorithm, which is not only saturation dependent but also parameter dependent. A Jacobi iterative algorithm is developed to coordinate the distributed MPC controllers. A simulation example with multi‐subsystem is carried out to demonstrate the effectiveness of the proposed distributed MPC algorithms. Copyright © 2016 John Wiley & Sons, Ltd.