Predictive control of hybrid systems : input-to-state stability results for sub-optimal solutions

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This article presents a novel model predictive control (MPC) scheme that achieves input-to-state stabilization of constrained discontinuous nonlinear and hybrid systems. Input-to-state stability (ISS) is guaranteed when an optimal solution of the MPC optimization problem is attained. Special attention is paid to the effect that sub-optimal solutions have on ISS of the closed-loop system. This issue is of interest as firstly, the infimum of MPC optimization problems does not have to be attained and secondly, numerical solvers usually provide only sub-optimal solutions. An explicit relation is established between the deviation of the predictive control law from the optimum and the resulting deterioration of the ISS property of the closed-loop system. By imposing stronger conditions on the sub-optimal solutions, ISS can even be attained in this case.
Original languageEnglish
Pages (from-to)180-185
Number of pages6
Issue number1
Publication statusPublished - 2009


  • Discontinuous systems
  • Hybrid systems
  • Input-to-state stability
  • Model predictive control
  • Sub-optimality


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