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

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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
Number of pages6
ISBN (Electronic)978-1-4673-6090-6
ISBN (Print)978-1-4799-7746-8
Publication statusPublished - 2014
Event53rd IEEE Conference on Decision and Control, CDC 2014 - "J.W. Marriott Hotel", Los Angeles, United States
Duration: 15 Dec 201417 Dec 2014
Conference number: 53


Conference53rd IEEE Conference on Decision and Control, CDC 2014
Abbreviated titleCDC
Country/TerritoryUnited States
CityLos Angeles
Internet address


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