eprintid: 2260
rev_number: 7
eprint_status: archive
userid: 6
dir: disk0/00/00/22/60
datestamp: 2014-07-16 12:09:17
lastmod: 2014-12-03 13:05:43
status_changed: 2014-07-16 12:09:17
type: article
metadata_visibility: show
creators_name: Di Cairano, Stefano
creators_name: Heemels, W.P.M.H.
creators_name: Lazar, Mircea
creators_name: Bemporad, Alberto
creators_id: 
creators_id: 
creators_id: 
creators_id: alberto.bemporad@imtlucca.it
title: Stabilizing dynamic controllers for hybrid systems: a hybrid control Lyapunov function approach

ispublished: pub
subjects: QA75
subjects: TL
divisions: CSA
full_text_status: none
keywords: Asymptotic stability; Closed loop systems; Lyapunov methods; Optimal control; Optimization; Systematics
abstract: 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.
date: 2014-09
date_type: published
publication: IEEE Transactions on Automatic Control 
volume: 59
number: 10
publisher: IEEE 
pagerange: 2629 -2643
id_number: doi:10.1109/TAC.2014.2324111
refereed: TRUE
issn: 0018-9286
official_url: http://dx.doi.org/10.1109/TAC.2014.2324111
citation:   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)