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Observer Design based on Observability Decomposition for Hybrid Systems with Linear Maps and Known Jump Times

Abstract : We propose an observer design method for hybrid systems with linear maps and known jump times based on decomposing the state into parts exhibiting different kinds of observability properties. Using a series of transformations depending on the time elapsed since the previous jump, the state may be decomposed into up to three parts, where the first one is instantaneously observable during flows from the flow output, the second one detectable at jumps from the jump output thanks to the combination of flows and jumps, and the remaining part naturally detectable at jumps still thanks to this combination of flows and jumps but implicitly from the flow output. An observer is then designed to estimate each part, relying on a flow-based Kalman-like observer exploiting the flow output for the first part, a jump-based observer exploiting the jump output for the second, and a jump-based observer exploiting a fictitious output for the third. Global exponential stability of the estimation error is proven using Lyapunov analysis.
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https://hal-mines-paristech.archives-ouvertes.fr/hal-03776225
Contributor : Florent Di Meglio Connect in order to contact the contributor
Submitted on : Tuesday, September 13, 2022 - 2:56:35 PM
Last modification on : Saturday, September 24, 2022 - 3:07:46 AM

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  • HAL Id : hal-03776225, version 1

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Gia Quoc Bao Tran, Pauline Bernard, Florent Di Meglio, Lorenzo Marconi. Observer Design based on Observability Decomposition for Hybrid Systems with Linear Maps and Known Jump Times. IEEE Conference on Decision and Control, Dec 2022, Cancún, Mexico. ⟨hal-03776225⟩

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