TY  - CHAP
CY  - Sydney, Australia December, 2000
Y1  - 2000///
SP  - 1810
A1  - Bemporad, Alberto
A1  - Borrelli, Francesco
A1  - Morari, Manfred
PB  - IEEE
UR  - http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=912125&isnumber=19689
TI  - Optimal controllers for hybrid systems: stability and piecewise linear explicit form
AV  - none
KW  - closed-loop stability; heat exchange system; hybrid systems; input trajectories; linear function evaluation; mixed logical dynamical framework; model predictive controller; multiparametric mixed-integer linear program; piecewise affine systems; piecewise linear optimal controllers; stabilizing controller; tracking error; weighted 1/?-norm; closed loop systems; control system synthesis; discrete time systems; heat exchangers; integer programming; linear programming; optimal control; predictive control; stability
N2  - 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 framework, or, equivalently, as piecewise affine systems. A stabilizing controller is obtained by designing a model predictive controller, 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 online solution if the sampling-time is too small for the available computation power. Rather than solving the MILP online, we propose a different approach where all the computation is moved off line, by solving a multiparametric MILP. As the resulting control law is piecewise affine, online computation is drastically reduced to a simple linear function evaluation. An example of piecewise linear optimal control of a heat exchange system shows the potential of the method
M1  - 2
SN  - 0-7803-6638-7 
EP  - 1815
T2  - Decision and Control Conference
ID  - eprints572
ER  -