Lyapunov Neural ODE Feedback Control Policies

Deep neural networks are increasingly used as an effective way to represent control policies in a wide-range of learning-based control methods. For continuous-time optimal control problems (OCPs), which are central to many decision-making tasks, control policy learning can be cast as a neural ordinary differential equation (NODE) problem wherein state and control constraints are naturally accommodated. This paper presents a Lyapunov-NODE control (L-NODEC) approach to solving continuous-time OCPs for the case of stabilizing a known constrained nonlinear system around a terminal equilibrium point. We propose a Lyapunov loss formulation that incorporates a control-theoretic Lyapunov condition into the problem of learning a state-feedback neural control policy. We establish that L-NODEC ensures exponential stability of the controlled system, as well as its adversarial robustness to uncertain initial conditions. The performance of L-NODEC is illustrated on a benchmark double integrator problem and for optimal control of thermal dose delivery using a cold atmospheric plasma biomedical system. L-NODEC can substantially reduce the inference time necessary to reach the equilibrium state.