Probabilistic Model-Based Fault-Tolerant Control for Uncertain Nonlinear Systems

Fault-tolerant control (FTC) is an effective control method designed to maintain a faulty system within an acceptable risk level while ensuring its safety. However, handling both uncertainties and faults in a system remains challenging. In this article, we propose two probabilistic model-based adaptive FTC methods for faulty nonlinear systems with unknown dynamics. We study Gaussian process (GP) regression in two cases: 1) an offline learning-based control method and 2) an event-triggered online data-driven modeling method, to learn unknown system dynamics. Considering the computational complexity of GP regression in practical applications, we discuss the case of computational delays in real-time predictions. Moreover, we develop four theoretical criteria to ensure the probabilistic stability of closed-loop systems. Finally, numerical simulations validate the effectiveness of proposed control methods and demonstrate their competitiveness compared to existing approaches.