@incollection{eprints572,
          author = {Alberto Bemporad and Francesco Borrelli and Manfred Morari},
       publisher = {IEEE},
         journal = {Proc. 39th IEEE Conf. on Decision and Control},
       booktitle = {Decision and Control Conference},
         address = {Sydney, Australia December, 2000},
           pages = {1810--1815},
          volume = {2},
            year = {2000},
           title = {Optimal controllers for hybrid systems: stability and piecewise linear explicit form},
        keywords = {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},
        abstract = {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},
             url = {http://eprints.imtlucca.it/572/}
}