%0 Conference Paper
%A Lazar, Mircea
%A Heemels, W.P.M.H.
%A Bemporad, Alberto
%A Weiland, Siep
%B Assessment and Future Directions of Nonlinear Model Predictive Control
%C Freudenstadt-Lauterbad, Germany
%D 2005
%F eprints:530
%K Non-smooth systems; Hybrid systems; Model predictive control; Lyapunov stability; Robust stability
%T On the stability and robustness of non-smooth nonlinear MPC
%U http://eprints.imtlucca.it/530/
%X This paper considers discrete-time nonlinear, possibly discontinuous, systems in closed-loop with Model Predictive  Controllers (MPC). The aim of the paper is to provide a priori sufficient conditions for asymptotic stability in  the Lyapunov sense and robust stability, while allowing for both the system dynamics and the value function of the MPC cost (the usual candidate Lyapunov function in MPC) to be discontinuous functions of the state. The motivation for this work lies in the recent development of MPC for hybrid systems, which are inherently discontinuous and nonlinear systems. As an application of the general theory, it is shown that Lyapunov stability is achieved in hybrid MPC. For a particular class of piecewise affine systems, a modified MPC set-up is proposed, which is proven to be robust to small additive disturbances via an input-to-state stability argument.