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Convex Optimization-based Controller Design for Stochastic Nonlinear Systems using Contraction Analysis

Tsukamoto, Hiroyasu and Chung, Soon-Jo (2019) Convex Optimization-based Controller Design for Stochastic Nonlinear Systems using Contraction Analysis. In: 2019 IEEE 58th Conference on Decision and Control (CDC). IEEE , Piscataway, NJ, pp. 8196-8203. https://resolver.caltech.edu/CaltechAUTHORS:20190918-132428278

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Abstract

This paper presents an optimal feedback tracking controller for a class of Itô stochastic nonlinear systems, the design of which involves recasting a nonlinear system equation into a convex combination of multiple non-unique State-Dependent Coefficient (SDC) models. Its feedback gain and controller parameters are found by solving a convex optimization problem to minimize an upper bound of the steady-state tracking error. Multiple SDC parametrizations are utilized to provide a design flexibility to mitigate the effects of stochastic noise and to ensure that the system is controllable. Incremental stability of this controller is studied using stochastic contraction analysis and it is proven that the controlled trajectory exponentially converges to the desired trajectory with a non-vanishing error due to the linear matrix inequality state-dependent algebraic Riccati equation constraint. A discrete-time version of stochastic contraction analysis with respect to a state- and time-dependent metric is also presented in this paper. A simulation is performed to show the superiority of the proposed optimal feedback controller compared to a known exponentially-stabilizing nonlinear controller and a PID controller.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/CDC40024.2019.9028942DOIArticle
ORCID:
AuthorORCID
Chung, Soon-Jo0000-0002-6657-3907
Additional Information:© 2019 IEEE. This work was in part funded by the Jet Propulsion Laboratory, California Institute of Technology and Raytheon Company.
Group:GALCIT, Center for Autonomous Systems and Technologies (CAST)
Funders:
Funding AgencyGrant Number
JPL/CaltechUNSPECIFIED
Raytheon CompanyUNSPECIFIED
Record Number:CaltechAUTHORS:20190918-132428278
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20190918-132428278
Official Citation:H. Tsukamoto and S. Chung, "Convex Optimization-based Controller Design for Stochastic Nonlinear Systems using Contraction Analysis," 2019 IEEE 58th Conference on Decision and Control (CDC), Nice, France, 2019, pp. 8196-8203, doi: 10.1109/CDC40024.2019.9028942.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:98728
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:18 Sep 2019 20:42
Last Modified:10 Sep 2020 20:55

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