# Robust Controller Design for Stochastic Nonlinear Systems via Convex Optimization

arXiv: https://arxiv.org/abs/2006.04359 · HTML: https://mlsanity.com/paper/2006.04359/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Jun 2020.

## Built on by (most cited first, 11 of 11)

- [Contraction Theory for Nonlinear Stability Analysis and Learning-based Control: A Tutorial Overview](https://mlsanity.com/paper/2110.00675/) (2021)
- [Learning-based Robust Motion Planning with Guaranteed Stability: A Contraction Theory Approach](https://mlsanity.com/paper/2102.12668/) (2021)
- [A Theoretical Overview of Neural Contraction Metrics for Learning-based Control with Guaranteed Stability](https://mlsanity.com/paper/2110.00693/) (2021)
- [Trajectory Optimization of Chance-Constrained Nonlinear Stochastic Systems for Motion Planning Under Uncertainty](https://mlsanity.com/paper/2106.02801/) (2021)
- [Neural-Rendezvous: Provably Robust Guidance and Control to Encounter Interstellar Objects](https://mlsanity.com/paper/2208.04883/) (2022)
- [Learning-based Adaptive Control using Contraction Theory](https://mlsanity.com/paper/2103.02987/) (2021)
- [Extended Neural Contractive Dynamical Systems: On Multiple Tasks and Riemannian Safety Regions](https://mlsanity.com/paper/2411.11405/) (2024)
- [H-TD2: Hybrid Temporal Difference Learning for Adaptive Urban Taxi Dispatch](https://mlsanity.com/paper/2105.02138/) (2021)
- [Guaranteed Trajectory Tracking under Learned Dynamics with Contraction Metrics and Disturbance Estimation](https://mlsanity.com/paper/2112.08222/) (2021)
- [CaRT: Certified Safety and Robust Tracking in Learning-based Motion Planning for Multi-Agent Systems](https://mlsanity.com/paper/2307.08602/) (2023)
- [Contraction-Aware Reinforcement Learning for Nonlinear Control with Statistical Robustness](https://mlsanity.com/paper/2506.15700/) (2025)

## Abstract (arXiv)

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.