Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization

TL;DR

This paper introduces CV-STEM, a convex optimization-based control framework for stochastic nonlinear systems that minimizes steady-state tracking error using an optimal contraction metric, with proven robustness and superior performance in spacecraft control.

Contribution

It develops a convex formulation for stochastic control design using contraction metrics, enabling efficient steady-state error minimization in nonlinear stochastic systems.

Findings

CV-STEM outperforms PID, H-infinity, and baseline controllers in spacecraft applications.

Provides a convex optimization approach for stochastic nonlinear control design.

Ensures exponential boundedness and robustness of the control system.

Abstract

This paper presents ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for a class of Ito 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 non-convex, its equivalent convex formulation is proposed utilizing state-dependent coefficient 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-infinity, and baseline nonlinear controllers for spacecraft attitude control and synchronization problems.