Offline state estimation for hybrid systems via nonsmooth variable projection

We propose an offline algorithm that simultaneously estimates discrete and continuous components of a hybrid system’s state. We formulate state estimation as a continuous optimization problem by relaxing the discrete component and using a robust loss function to accommodate large changes in the cont...

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Bibliographic Details
Published in:Automatica (Oxford) Vol. 115; p. 108871
Main Authors: Zhang, Jize, Pace, Andrew M., Burden, Samuel A., Aravkin, Aleksandr
Format: Journal Article
Language:English
Published: Elsevier Ltd 01.05.2020
Subjects:
Hybrid systems
Mechanical systems
Nonlinear systems
Optimization
State estimation
Hybrid systems
Mechanical systems
State estimation
Nonlinear systems
Optimization
ISSN:0005-1098, 1873-2836
Online Access:Get full text
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Summary:We propose an offline algorithm that simultaneously estimates discrete and continuous components of a hybrid system’s state. We formulate state estimation as a continuous optimization problem by relaxing the discrete component and using a robust loss function to accommodate large changes in the continuous component during switching events. Subsequently, we develop a novel nonsmooth variable projection algorithm with Gauss–Newton updates to solve the state estimation problem and prove the algorithm’s global convergence to stationary points. We demonstrate the effectiveness of our approach by comparing it to a state-of-the-art filter bank method, and by applying it to simple piecewise-linear and -nonlinear mechanical systems undergoing intermittent impact.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2020.108871