On Imitation Learning of Linear Control Policies: Enforcing Stability and Robustness Constraints via LMI Conditions

TL;DR

This paper introduces methods to incorporate stability and robustness constraints into the imitation learning of linear control policies using LMI conditions, ensuring reliable performance.

Contribution

It formulates the imitation learning of linear policies as a constrained optimization problem with LMI constraints and proposes efficient solution methods.

Findings

Guarantees of closed-loop stability and robustness through LMI constraints.

Effective application of projected gradient descent and ADMM methods.

Numerical results demonstrating stability and robustness of learned policies.

Abstract

When applying imitation learning techniques to fit a policy from expert demonstrations, one can take advantage of prior stability/robustness assumptions on the expert's policy and incorporate such control-theoretic prior knowledge explicitly into the learning process. In this paper, we formulate the imitation learning of linear policies as a constrained optimization problem, and present efficient methods which can be used to enforce stability and robustness constraints during the learning processes. Specifically, we show that one can guarantee the closed-loop stability and robustness by posing linear matrix inequality (LMI) constraints on the fitted policy. Then both the projected gradient descent method and the alternating direction method of multipliers (ADMM) method can be applied to solve the resulting constrained policy fitting problem. Finally, we provide numerical results to demonstrate the effectiveness of our methods in producing linear polices with various stability and robustness guarantees.