@incollection{eprints1257,
           pages = {1227 --1232},
           month = {December},
            year = {2011},
           title = {Synthesis of low-complexity stabilizing piecewise affine controllers: a control-Lyapunov function approach},
          author = {Liang  Lu and W.P.M.H. Heemels and Alberto Bemporad},
       publisher = {IEEE},
            note = {This work was partially supported by the European Commission through project MOBY-DIC ?Model-based synthesis of digital electronic circuits for embedded control? (FP7-INFSO-ICT-248858).},
       booktitle = {Proceedings of the 50th IEEE Conference on Decision and Control and European Control Conference (CDC-ECC)},
        keywords = {PWA control Lyapunov function approach; automatic refinement procedure; constrained linear system; constraint satisfaction; large scale system; local linear programming feasibility problems; low complexity stabilizing piecewise affine controller synthesis; low memory requirements; model predictive controllers; multiparametric optimization techniques; piecewise afflne state feedback controllers; Lyapunov methods; affine transforms; computational complexity; constraint satisfaction problems; large-scale systems; linear programming; linear systems; piecewise constant techniques; predictive control; stability; state feedback;},
             url = {http://eprints.imtlucca.it/1257/},
        abstract = {Explicit model predictive controllers computed exactly by multi-parametric optimization techniques often lead to piecewise affine (PWA) state feedback controllers with highly complex and irregular partitionings of the feasible set. In many cases complexity prohibits the implementation of the resulting MPC control law for fast or large-scale system. This paper presents a new approach to synthesize low-complexity PWA controllers on regular partitionings that enhance fast on-line implementation with low memory requirements. Based on a PWA control-Lyapunov function, which can be obtained as the optimal cost for a constrained linear system corresponding to a stabilizing MPC setup, the synthesis procedure for the low-complexity control law boils down to local linear programming (LP) feasibility problems, which guarantee stability, constraint satisfaction, and certain performance requirements. Initially, the PWA controllers are computed on a fixed regular partitioning. However, we also present an automatic refinement procedure to refine the partitioning where necessary in order to satisfy the design specifications. A numerical example show the effectiveness of the novel approach.}
}