On Imitation Learning of Linear Control Policies: Enforcing Stability and Robustness Constraints via LMI Conditions
This work addresses the problem of ensuring stability and robustness in imitation learning for control systems, which is incremental as it applies existing LMI techniques to a specific learning context.
The paper tackles imitation learning for linear control policies by incorporating stability and robustness constraints via linear matrix inequalities, resulting in efficient methods like projected gradient descent and ADMM that produce policies with guaranteed control-theoretic properties.
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.