Published October 2021 | Accepted Version + Submitted
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Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization

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Abstract

This article presents ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for a class of Itô stochastic nonlinear systems and Lagrangian systems. Its innovation lies in computing the control input by an optimal contraction metric, which greedily minimizes an upper bound of the steady-state mean squared tracking error of the system trajectories. Although the problem of minimizing the bound is nonconvex, its equivalent convex formulation is proposed utilizing SDC parameterizations of the nonlinear system equation. It is shown using stochastic incremental contraction analysis that the CV-STEM provides a sufficient guarantee for exponential boundedness of the error for all time with L₂-robustness properties. For the sake of its sampling-based implementation, we present discrete-time stochastic contraction analysis with respect to a state- and time-dependent metric along with its explicit connection to continuous-time cases. We validate the superiority of the CV-STEM to PID, H∞, and baseline nonlinear controllers for spacecraft attitude control and synchronization problems.

Additional Information

© 2020 IEEE. Manuscript received June 4, 2020; accepted October 28, 2020. Date of publication November 16, 2020; date of current version September 27, 2021. This work was supported in part by the Jet Propulsion Laboratory, California Institute of Technology and in part by the Raytheon Company. Recommended by Associate Editor U. V. Shanbhag.

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Submitted - 2006.04359.pdf

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August 20, 2023
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