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Stabilizing dynamic controllers for hybrid systems: a hybrid control Lyapunov function approach

Di Cairano, Stefano and Heemels, W.P.M.H. and Lazar, Mircea and Bemporad, Alberto Stabilizing dynamic controllers for hybrid systems: a hybrid control Lyapunov function approach. IEEE Transactions on Automatic Control , 59 (10). 2629 -2643. ISSN 0018-9286 (2014)

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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.

Item Type: Article
Identification Number: 10.1109/TAC.2014.2324111
Uncontrolled Keywords: Asymptotic stability; Closed loop systems; Lyapunov methods; Optimal control; Optimization; Systematics
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
T Technology > TL Motor vehicles. Aeronautics. Astronautics
Research Area: Computer Science and Applications
Depositing User: Ms T. Iannizzi
Date Deposited: 16 Jul 2014 12:09
Last Modified: 03 Dec 2014 13:05
URI: http://eprints.imtlucca.it/id/eprint/2260

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