In this paper we develop a priori stabilization conditions for infinity norm based hybrid MPC in the terminal cost and constraint set fashion. Closed-loop stability is achieved using infinity norm inequalities that guarantee that the value function corresponding to the MPC cost is a Lyapunov function of the controlled system. We show that Lyapunov asymptotic stability can be achieved even though the MPC value function may be discontinuous. One of the advantages of this hybrid MPC scheme is that the terminal constraint set can be directly obtained as a sublevel set of the calculated terminal cost, which is also a local piecewise linear Lyapunov function. This yields a new method to obtain positively invariant sets for PWA systems.
|Title of host publication||Hybrid systems: computation and control : 8th international workshop, HSCC 2005, Zurich, Switzerland, March 9-11, 2005 ; proceedings|
|Editors||M. Morari, L. thiele|
|Place of Publication||Berlin|
|Publication status||Published - 2005|
|Name||Lecture Notes in Computer Science|
Lazar, M., Heemels, W. P. M. H., Weiland, S., Bemporad, A., & Pastravanu, O. (2005). Infinity norms as Lyapunov functions for model predictive control of constrained PWA systems. In M. Morari, & L. thiele (Eds.), Hybrid systems: computation and control : 8th international workshop, HSCC 2005, Zurich, Switzerland, March 9-11, 2005 ; proceedings (pp. 417-432). (Lecture Notes in Computer Science; Vol. 3414). Berlin: Springer. https://doi.org/10.1007/978-3-540-31954-2_27