Imitation Learning with Stability and Safety Guarantees

A method is presented to learn neural network (NN) controllers with stability and safety guarantees through imitation learning (IL). Convex stability and safety conditions are derived for linear time-invariant systems with NN controllers by merging Lyapunov theory with local quadratic constraints to bound the activation functions in the NN. These conditions are incorporated in the IL process, which minimizes the IL loss, and maximizes the volume of the region of attraction associated with the NN controller simultaneously. An alternating direction method of multipliers based algorithm is proposed to solve the IL problem. The method is illustrated on a vehicle lateral control example.