## Optimal controllers for hybrid systems: Stability and piecewise linear explicit form (2000)

Venue: | in Proceedings of the 39th IEEE Conference on Decision and Control |

Citations: | 25 - 7 self |

### BibTeX

@INPROCEEDINGS{Bemporad00optimalcontrollers,

author = {A. Bemporad and F. Borrelli and M. Morari},

title = {Optimal controllers for hybrid systems: Stability and piecewise linear explicit form},

booktitle = {in Proceedings of the 39th IEEE Conference on Decision and Control},

year = {2000},

pages = {1810--1815},

publisher = {IEEE}

}

### Years of Citing Articles

### OpenURL

### Abstract

In this paper we propose a procedure for synthesizing piecewise linear optimal controllers for hybrid systems and investigate conditions for closed-loop stability. Hybrid systems are modeled in discrete-time within the mixed logical dynamical (MLD) framework[8], or, equivalently [7], as piecewise affine (PWA) systems. A stabilizing controller is obtained by designing a model predictive controller (MPC), which is based on the minimization of a weighted 1/∞-norm of the tracking error and the input trajectories over a finite horizon. The control law is obtained by solving a mixed-integer linear program (MILP) which depends on the current state. Although efficient branch and bound algorithms exist to solve MILPs, these are known to be NP-hard problems, which may prevent their on-line solution if the sampling-time is too small for the available computation power. Rather than solving the MILP on line, in this paper we propose a different approach where all the computation is moved off line, by solving a multiparametric MILP (mp-MILP). As the resulting control law is piecewise affine, on-line computation is drastically reduced to a simple linear function evaluation. An example of piecewise linear optimal control of the heat exchange system [16] shows the potential of the method.