Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization

This article presents ConVex optimization-based Stochastic steady-state Tracking Error Minimization (CV-STEM), a new state feedback control framework for class of Itô stochastic nonlinear systems and Lagrangian systems. Its innovation lies in computing the input by an optimal contraction metric, which greedily minimizes upper bound mean squared tracking error system trajectories. Although problem minimizing is nonconvex, its equivalent convex formulation proposed utilizing SDC parameterizations equation. It shown using incremental analysis that CV-STEM provides sufficient guarantee exponential boundedness all time with ${\bf \mathcal {L}_2}$ -robustness properties. For sake sampling-based implementation, we present discrete-time respect to state- time-dependent metric along explicit connection continuous-time cases. We validate superiority PID, notation="LaTeX">$\mathcal {H}_\infty$ , baseline controllers spacecraft attitude synchronization problems.