International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지

Input Constrained Robust Model Predictive Control with Enlarged Stabilizable Region

  • Lee, Young-Il (Dept. of Control and Instrumentation, Seoul National University of Technology)
  • Published : 2005.09.01
Download PDF
⟨ Previous Next ⟩

Abstract

The dual-mode strategy has been adopted in many constrained MPC (Model Predictive Control) methods. The size of stabilizable regions of states of MPC methods depends on the size of underlying feasible and positively invariant sets and the number of control moves. The results, however, may perhaps be conservative because the definition of positive invariance does not allow temporal departure of states from the set. In this paper, a concept of periodic invariance is introduced in which states are allowed to leave a set temporarily but return into the set in finite time steps. The periodic invariance can be defined with respect to sets of different state feedback gains. These facts make it possible for the periodically invariant sets to be considerably larger than ordinary invariant sets. The periodic invariance can be defined for systems with polyhedral model uncertainties. We derive a MPC method based on these periodically invariant sets. Some numerical examples are given to show that the use of periodic invariance yields considerably larger stabilizable sets than the case of using ordinary invariance.

Keywords

References

  1. Y. I. Lee and B. Kouvaritakis, 'Robust receding horizon predictive control for systems with uncertain dynamics and input saturation,' Automatica, vol. 36, pp. 1497-1504, 2000 https://doi.org/10.1016/S0005-1098(00)00064-9
  2. Y. I. Lee and B. Kouvaritakis, 'A linear programming approach to constrained robust predictive control,' IEEE Trans. on Automatic Control, vol. 45, no. 9, pp. 1765-1770, 2000 https://doi.org/10.1109/9.880645
  3. Y. I. Lee, 'Receding horizon control for input constrained linear parameter varying systems,' IEE Proceedings-Control Theory and Application, vol. 151, no. 5, pp. 547-553, September 2004
  4. M. V. Kothare, V. Balakrishnan, and M. Morari, 'Robust constrained model predictive control using linear matrix inequalities,' Automatica, vol. 32, no. 10, pp. 1361-1379, 1996 https://doi.org/10.1016/0005-1098(96)00063-5
  5. Y. Lu and Y. Arkun, 'A scheduling quasiminmax MPC for LPV systems,' Proc. of American Control Conference, pp. 2272-2276, 1999
  6. S. Boyd, L. EI Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in Systems and Control Theory, SIAM, Philadelphia, 1994