Observer-based control of discrete-time piecewise affine systems : exploiting continuity twice

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Abstract

Output-based feedback control of discrete-time hybrid systems is an important problem, as in practice it is rarely the case that the full state variable is available for feedback. A typical approach for output-based feedback design for linear and smooth nonlinear systems is to use certainty equivalence control, in which an observer and a state feedback controller (using the observer state) are combined. Although for linear systems and some classes of nonlinear systems, separation principles exist to justify this approach, for hybrid systems this is not the case. In this paper, we isolate a class of hybrid systems for which a systematic design procedure for certainty equivalence controllers including a separation principle will be presented. This class consists of discrete-time piecewise-affine (PWA) systems with continuous dynamics. In the design procedure, we will exploit the continuity of the PWA dynamics twice. Firstly, it will be used to establish input-to-state stability (ISS) w.r.t. measurement errors from ISS w.r.t. additive disturbances. This is a crucial step as the latter problem is much easier to tackle than the former. Secondly, continuity will be used in the observer design procedure to obtain a significantly simplified set of LMIs with respect to existing observer design approaches for PWA systems. All the design conditions will be formulated in term of LMIs, which can be solved efficiently, as is also illustrated by a numerical example.
Original languageEnglish
Title of host publicationProceedings of the 47th IEEE Conference on Decision and Control (CDC 2008) : Mexico, Cancún, 9 - 11 December 2008
Place of PublicationPiscataway, NJ
PublisherInstitute of Electrical and Electronics Engineers
Pages4676-4680
ISBN (Print)978-1-4244-3123-6
DOIs
Publication statusPublished - 2008

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Hybrid systems
Nonlinear systems
Feedback
Controllers
Measurement errors
State feedback
Feedback control
Linear systems

Cite this

Heemels, W. P. M. H., Lazar, M., Wouw, van de, N., & Pavlov, A. (2008). Observer-based control of discrete-time piecewise affine systems : exploiting continuity twice. In Proceedings of the 47th IEEE Conference on Decision and Control (CDC 2008) : Mexico, Cancún, 9 - 11 December 2008 (pp. 4676-4680). Piscataway, NJ: Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2008.4739094
Heemels, W.P.M.H. ; Lazar, M. ; Wouw, van de, N. ; Pavlov, A. / Observer-based control of discrete-time piecewise affine systems : exploiting continuity twice. Proceedings of the 47th IEEE Conference on Decision and Control (CDC 2008) : Mexico, Cancún, 9 - 11 December 2008. Piscataway, NJ : Institute of Electrical and Electronics Engineers, 2008. pp. 4676-4680
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Heemels, WPMH, Lazar, M, Wouw, van de, N & Pavlov, A 2008, Observer-based control of discrete-time piecewise affine systems : exploiting continuity twice. in Proceedings of the 47th IEEE Conference on Decision and Control (CDC 2008) : Mexico, Cancún, 9 - 11 December 2008. Institute of Electrical and Electronics Engineers, Piscataway, NJ, pp. 4676-4680. https://doi.org/10.1109/CDC.2008.4739094

Observer-based control of discrete-time piecewise affine systems : exploiting continuity twice. / Heemels, W.P.M.H.; Lazar, M.; Wouw, van de, N.; Pavlov, A.

Proceedings of the 47th IEEE Conference on Decision and Control (CDC 2008) : Mexico, Cancún, 9 - 11 December 2008. Piscataway, NJ : Institute of Electrical and Electronics Engineers, 2008. p. 4676-4680.

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

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AB - Output-based feedback control of discrete-time hybrid systems is an important problem, as in practice it is rarely the case that the full state variable is available for feedback. A typical approach for output-based feedback design for linear and smooth nonlinear systems is to use certainty equivalence control, in which an observer and a state feedback controller (using the observer state) are combined. Although for linear systems and some classes of nonlinear systems, separation principles exist to justify this approach, for hybrid systems this is not the case. In this paper, we isolate a class of hybrid systems for which a systematic design procedure for certainty equivalence controllers including a separation principle will be presented. This class consists of discrete-time piecewise-affine (PWA) systems with continuous dynamics. In the design procedure, we will exploit the continuity of the PWA dynamics twice. Firstly, it will be used to establish input-to-state stability (ISS) w.r.t. measurement errors from ISS w.r.t. additive disturbances. This is a crucial step as the latter problem is much easier to tackle than the former. Secondly, continuity will be used in the observer design procedure to obtain a significantly simplified set of LMIs with respect to existing observer design approaches for PWA systems. All the design conditions will be formulated in term of LMIs, which can be solved efficiently, as is also illustrated by a numerical example.

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BT - Proceedings of the 47th IEEE Conference on Decision and Control (CDC 2008) : Mexico, Cancún, 9 - 11 December 2008

PB - Institute of Electrical and Electronics Engineers

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Heemels WPMH, Lazar M, Wouw, van de N, Pavlov A. Observer-based control of discrete-time piecewise affine systems : exploiting continuity twice. In Proceedings of the 47th IEEE Conference on Decision and Control (CDC 2008) : Mexico, Cancún, 9 - 11 December 2008. Piscataway, NJ: Institute of Electrical and Electronics Engineers. 2008. p. 4676-4680 https://doi.org/10.1109/CDC.2008.4739094