mlsanityData to 7 Oct 2026

Imitation Learning of Stabilizing Policies for Nonlinear Systems

arXiv 2109.10854 ↗First posted 22 Sep 2021math.OC cs.LGcited by 2

On the map: Offline RL and imitation learning from data → Imitation learning methods

Abstract (arXiv)

There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which stabilizing imitation learning takes the form of a biconvex optimization problem. In this paper it is demonstrated that the same methods developed for linear systems and controllers can be readily extended to polynomial systems and controllers using sum of squares techniques. A projected gradient descent algorithm and an alternating direction method of multipliers algorithm are proposed as heuristics for solving the stabilizing imitation learning problem, and their performance is illustrated through numerical experiments.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data. Builds on 9 of its 18 references that are in the map. First posted on arXiv 22 Sep 2021.

Builds on

9 of 18 references.

Closest ancestors · 3

Same direction, newest first

  1. 2021On Imitation Learning of Linear Control Policies: Enforcing Stability and Robustness Constraints via LMI Conditions24 Mar
  2. 2020Imitation Learning with Stability and Safety Guarantees16 Dec
  3. 2020Infinite-Horizon Differentiable Model Predictive Control7 Jan

Other references · 6

  1. 2016CVXPY: A Python-Embedded Modeling Language for Convex Optimizationcited by 633
  2. 2014Convex Optimization: Algorithms and Complexitycited by 569
  3. 2018Differentiable MPC for End-to-end Planning and Controlcited by 178
  4. 2020Fitting a Linear Control Policy to Demonstrations with a Kalman Constraintcited by 9
  5. 2018ADMM for Multiaffine Constrained Optimizationcited by 6
  6. 2020Learning control for polynomial systems using sum of squares relaxationscited by 2

Built on by

Cited by year

Citing papers per year: 2023: 2.

2 papers.

  1. 2023CCIL: Context-conditioned imitation learning for urban drivingcited by 12
  2. 2023Dissipative Imitation Learning for Discrete Dynamic Output Feedback Control with Sparse Data Setscited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2023Learning Lyapunov-Stable Polynomial Dynamical Systems through Imitation
  2. 2019On the Global Convergence of Imitation Learning: A Case for Linear Quadratic Regulator
  3. 2022Dissipative Imitation Learning for Robust Dynamic Output Feedback
  4. 2025Imitation Learning of MPC with Neural Networks: Error Guarantees and Sparsification
  5. 2022Multi-Task Imitation Learning for Linear Dynamical Systems
  6. 2022Proximal Point Imitation Learning
  7. 2019Learning the optimal state-feedback via supervised imitation learning
  8. 2023On the Sample Complexity of Imitation Learning for Smoothed Model Predictive Control