A novel linear matrix inequality‐based robust event‐triggered model predictive control for a class of discrete‐time linearsystems

• Published in: International journal of robust and nonlinear control Vol. 31; no. 9; pp. 4416 - 4435
• Main Authors: Hu, Yingjie, Ding, Fan, Peng, Kai, Herbert Ho‐Ching Iu, Zhang, Xinan
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.06.2021
• Subjects: Computational geometry; Constraints; Convexity; Linear matrix inequalities; Mathematical models; Optimization; Predictive control; Robustness (mathematics); Stability analysis
• ISSN: 1049-8923; 1099-1239
• DOI: 10.1002/rnc.5482

This paper studies a linear matrix inequality (LMI)‐based robust event‐triggered model predictive control (ET‐MPC) for a class of discrete linear time‐invariant systems subject to bounded disturbances. In the presented robust event‐triggered MPC, the event‐triggered mechanism is first set by the deviation between the optimal state and actual state. In addition, the Lyapunov‐based stability condition is employed in the constraints for simplifying parameters and enhancing the universality. Subsequently, a novel design framework that involves LMIs approach is developed. In such a framework, the Lyapunov weight matrix is predesigned by solving a convex optimization problem with LMIs and the infinite horizon MPC optimization problem is also transformed as LMIs such that the computational complexity is significantly reduced. To guarantee robust constraint satisfaction, a dual‐mode control strategy is adopted. In this way, the proposed robust ET‐MPC has the ability to deal with the constrained system. Furthermore, the theoretical analysis of the recursive feasibility and stability is provided. The numerical simulations and comparison studies demonstrate that the proposed robust ET‐MPC not only has satisfying control performance but also significantly reduces the computational burden.