# Imitation Learning of Stabilizing Policies for Nonlinear Systems

arXiv: https://arxiv.org/abs/2109.10854 · HTML: https://mlsanity.com/paper/2109.10854/

## Key facts

- Cited by 2 papers in the map (data through 14 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.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Builds on (most cited first, 9 of 9)

- [CVXPY: A Python-Embedded Modeling Language for Convex Optimization](https://mlsanity.com/paper/1603.00943/) (2016)
- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Imitation Learning with Stability and Safety Guarantees](https://mlsanity.com/paper/2012.09293/) (2020)
- [Infinite-Horizon Differentiable Model Predictive Control](https://mlsanity.com/paper/2001.02244/) (2020)
- [On Imitation Learning of Linear Control Policies: Enforcing Stability and Robustness Constraints via LMI Conditions](https://mlsanity.com/paper/2103.12945/) (2021)
- [Fitting a Linear Control Policy to Demonstrations with a Kalman Constraint](https://mlsanity.com/paper/2001.07572/) (2020)
- [ADMM for Multiaffine Constrained Optimization](https://mlsanity.com/paper/1802.09592/) (2018)
- [Learning control for polynomial systems using sum of squares relaxations](https://mlsanity.com/paper/2004.00850/) (2020)

## Built on by (most cited first, 2 of 2)

- [CCIL: Context-conditioned imitation learning for urban driving](https://mlsanity.com/paper/2305.02649/) (2023)
- [Dissipative Imitation Learning for Discrete Dynamic Output Feedback Control with Sparse Data Sets](https://mlsanity.com/paper/2309.06658/) (2023)

## 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.