Sensitivity analysis of hybrid systems with state jumps with application to trajectory tracking

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

23 Citations (Scopus)
1 Downloads (Pure)

Abstract

This paper addresses the sensitivity analysis for hybrid systems with discontinuous (jumping) state trajectories. We consider state-triggered jumps in the state evolution, potentially accompanied by mode switching in the control vector field as well. For a given trajectory with state jumps, we show how to construct an approximation of a nearby perturbed trajectory corresponding to a small variation of the initial condition and input. A major complication in the construction of such an approximation is that, in general, the jump times corresponding to a nearby perturbed trajectory are not equal to those of the nominal one. The main contribution of this work is the development of a notion of error to clarify in which sense the approximate trajectory is, at each instant of time, a firstorder approximation of the perturbed trajectory. This notion of error naturally finds application in the (local) tracking problem of a time-varying reference trajectory of a hybrid system. To illustrate the possible use of this new error definition in the context of trajectory tracking, we outline how the standard linear trajectory tracking control for nonlinear systems -based on linear quadratic regulator (LQR) theory to compute the optimal feedback gain- could be generalized for hybrid systems.
Original languageEnglish
Title of host publicationProceedings of the 53rd IEEE Conference on Decision and Control, December 15-17, 2014, Los Angeles, CA, USA.
Place of PublicationPiscataway
PublisherInstitute of Electrical and Electronics Engineers
Pages3065-3070
Number of pages6
ISBN (Electronic)978-1-4673-6090-6
ISBN (Print)978-1-4799-7746-8
DOIs
Publication statusPublished - 2014
Event53rd IEEE Conference on Decision and Control (CDC2014) - "J.W. Marriott Hotel", Los Angeles, United States
Duration: 15 Dec 201417 Dec 2014
Conference number: 53
http://cdc2014.ieeecss.org/

Conference

Conference53rd IEEE Conference on Decision and Control (CDC2014)
Abbreviated titleCDC2014
CountryUnited States
CityLos Angeles
Period15/12/1417/12/14
Internet address

Fingerprint

Dive into the research topics of 'Sensitivity analysis of hybrid systems with state jumps with application to trajectory tracking'. Together they form a unique fingerprint.

Cite this