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

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