On robustness of constrained non-linear H_∞ predictive controllers with disturbances

Abstract

This article considers the robustness problem of H _∞ model predictive controllers for constrained non-linear discrete-time systems subject to disturbances, which are dependent on the system state and input. The notions of input-to-state stability and finite L ₂-gain of non-linear systems are introduced and exploited to investigate the robustness properties of this predictive controller under the state and input constraints and the disturbance. Moreover, this robustness of the controller is extended to the case of suboptimality of the solution. With its feasibility at initial time, the feasibility of the online optimisation problem is guaranteed for all times in the presence of disturbances and constraints. Finally, an example is employed to illustrate the proposed results.

Keywords:

• non-linear model predictive control
• input-to-state stability
• finite L ₂-gain
• non-linear H _∞ control
• suboptimal control

Acknowledgments

This work is supported by Natural Science Foundation of China under Grant 60674029 and the Specialised Research Fund for Doctoral Program of Higher Education of China under Grant 20050358044.