  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 plant dynamics with NN
controllers by merging Lyapunov theory with local quadratic constraints to
bound the nonlinear 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 an inverted
pendulum system, aircraft longitudinal dynamics, and vehicle lateral dynamics.
