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Observer Design for Stochastic Nonlinear Systems using Contraction Analysis

Dani, Ashwin P. and Chung, Soon-Jo and Hutchinson, Seth (2012) Observer Design for Stochastic Nonlinear Systems using Contraction Analysis. In: 2012 IEEE 51st IEEE Conference on Decision and Control (CDC). IEEE Conference on Decision and Control . IEEE , New York, NY, pp. 6028-6035. ISBN 978-1-4673-2066-5.

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This paper presents a new observer for Itô stochastic nonlinear systems with guaranteed stability. Contraction analysis is used to analyze incremental stability of the observer for an Itô stochastic nonlinear system. A bound on the mean squared distance between the trajectories of original dynamics and the observer dynamics is obtained as a function of contraction rate and maximum noise intensity. The observer design is based on non-unique state-dependent coefficient (SDC) forms which parametrize the nonlinearity in an extended linear form. In this paper, a convex combination of several parametrizations is used. An optimization problem with state-dependent linear matrix inequality (SDLMI) constraints is formulated to select the free parameters of the convex combination for achieving faster convergence and robustness against disturbances. Moreover, the L_2 norm of the disturbance and noise to the estimation error is shown to be finite. The present algorithm shows improved performance in comparison to the extended Kalman filter (EKF) and the state-dependent differential Riccati equation (SDDRE) filter in simulation.

Item Type:Book Section
Related URLs:
URLURL TypeDescription
Chung, Soon-Jo0000-0002-6657-3907
Hutchinson, Seth0000-0002-3949-6061
Additional Information:© 2012 IEEE. Date Added to IEEE Xplore: 04 February 2013. This project was supported by the Office of Naval Research (ONR) under Award No. N00014-11-1-0088. This paper benefited from discussions with Prof. Jean-Jacques Slotine. We thank the anonymous reviewers for their valuable comments.
Funding AgencyGrant Number
Office of Naval Research (ONR)N00014-11-1-0088
Series Name:IEEE Conference on Decision and Control
Record Number:CaltechAUTHORS:20161109-083117350
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Official Citation:A. P. Dani, S. J. Chung and S. Hutchinson, "Observer design for stochastic nonlinear systems using contraction analysis," 2012 IEEE 51st IEEE Conference on Decision and Control (CDC), Maui, HI, 2012, pp. 6028-6035. doi: 10.1109/CDC.2012.6425977
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:71865
Deposited By: Ruth Sustaita
Deposited On:09 Nov 2016 18:14
Last Modified:03 Oct 2019 16:11

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