Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization
This provides a robust control solution for stochastic nonlinear systems like spacecraft, though it is incremental as it builds on existing contraction analysis methods.
The paper tackles robust control for stochastic nonlinear systems by introducing CV-STEM, a convex optimization-based framework that minimizes an upper bound on steady-state tracking error, validated with spacecraft attitude control showing superiority over PID and other controllers.
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.