Designing neural controllers with optimality and stability guarantees by learning input-output dissipativity

Deep learning methods have demonstrated significant potential for addressing complex nonlinear control problems. For real-world safety-critical tasks, however, it is crucial to provide formal stability guarantees for the designed controllers. In this paper, we propose a new framework for designing neural controllers that achieve both stability and optimality with respect to certain functions. Our key idea is to exploit the concept of input–output dissipativity of nonlinear systems by learning neural storage functions and supply rate functions. As a generalization of Lyapunov theory, dissipativity theory provides a natural connection to optimal control theory, offering both stability guarantees and meaningful optimality certificates. The neural controllers can be directly derived from the learned supply rate functions and guarantee closed-loop stability while inheriting optimality properties that can be shaped towards user-defined control objectives. Extensive numerical experiments demonstrate the effectiveness of our approach.