Control theory-informed machine learning based control and performance monitoring of nonlinear dynamic systems

This paper explores control and performance monitoring of nonlinear dynamic systems with uncertainties and possible faults, focusing on scenarios where only partial model knowledge is available. We begin by developing optimal control and performance monitoring schemes from a nonlinear control theoretic framework, employing normalized stable kernel and image representation structures. These schemes form the basis for a unified design of the observer and feedback controller, which respectively serve as a state estimator/residual generator and a stabilizing control law. Moreover, performance indicators based on the corresponding Hamilton Jacobi Equations (HJEs), value functions, and residuals are extracted from the observer and controller structures. Then, we explore a data-driven implementation of the above framework that integrates control theory knowledge with machine learning, referred to as control theory-informed machine learning. Specifically, neural networks approximate the HJE solutions while preserving the lossless property, enabling a stable, data-driven realization of the proposed schemes. Finally, the proposed scheme is demonstrated through a case study.