The robust model predictive control based on mixed H₂/H_∞ approach with separated performance formulations and its ISpS analysis

ABSTRACT

In practical applications, systems are always influenced by parameter uncertainties and external disturbance. Both the H₂ performance and the H_∞ performance are important for the real applications. For a constrained system, the previous designs of mixed H₂/H_∞ robust model predictive control (RMPC) optimise one performance with the other performance requirement as a constraint. But the two performances cannot be optimised at the same time. In this paper, an improved design of mixed H₂/H_∞ RMPC for polytopic uncertain systems with external disturbances is proposed to optimise them simultaneously. In the proposed design, the original uncertain system is decomposed into two subsystems by the additive character of linear systems. Two different Lyapunov functions are used to separately formulate the two performance indices for the two subsystems. Then, the proposed RMPC is designed to optimise both the two performances by the weighting method with the satisfaction of the H_∞ performance requirement. Meanwhile, to make the design more practical, a simplified design is also developed. The recursive feasible conditions of the proposed RMPC are discussed and the closed-loop input state practical stable is proven. The numerical examples reflect the enlarged feasible region and the improved performance of the proposed design.

KEYWORDS:

• Robust model predictive control
• mixed H₂/H_∞
• separated formulation

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

National Science Foundation of China [grant number 61374110, 61333009, 61473317, 61521063, 61590924, 61573239].