TR2014-121

Stabilizing Dynamic Controllers for Hybrid Systems: A Hybrid Control Lyapunov Function Approach


    •  Di Cairano, S.; Lazar, M.; Heemels, W.P.M.H.; Bemporad, A., "Stabilizing Dynamic Controllers for Hybrid Systems: A Hybrid Control Lyapunov Function Approach", IEEE Transactions on Automatic Control, May 2014.
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      • @article{DiCairano2014may,
      • author = {{Di Cairano}, S. and Lazar, M. and Heemels, W.P.M.H. and Bemporad, A.},
      • title = {Stabilizing Dynamic Controllers for Hybrid Systems: A Hybrid Control Lyapunov Function Approach},
      • journal = {IEEE Transactions on Automatic Control},
      • year = 2014,
      • month = may,
      • url = {http://www.merl.com/publications/TR2014-121}
      • }
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  • Research Areas:

    Advanced Control Systems, Mechatronics


This paper proposes a dynamic controller structure and a systematic design procedure for stabilizing discrete-time hybrid systems. The proposed approach is based on the concept of control Lyapunov functions (CLFs), which, when available, can be used to design a stabilizing state-feedback control law. In general, the construction of a CLF for hybrid dynamical systems involving both continuous and discrete states is extremely complicated, especially in the presence of non-trivial discrete dynamics. Therefore, we introduce the novel concept of a hybrid control Lyapunov function, which allows the compositional design of a discrete and a continuous part of the CLF, and we formally prove that the existence of a hybrid CLF guarantees the existence of a classical CLF. A constructive procedure is provided to synthesize a hybrid CLF, by expanding the dynamics of the hybrid system with a specific controller dynamics. We show that this synthesis procedure leads to a dynamic controller that can be implemented by a receding horizon control strategy, and that the associated optimization problem is numerically tractable for a fairly general class of hybrid systems, useful in real world applications. Compared to classical hybrid receding horizon control algorithms, the proposed approach typically requires a shorter prediction horizon to guarantee asymptotic stability of the closed-loop system, which yields a reduction of the computational burden, as illustrated through two examples.