Validation of Neural Network Controllers for Uncertain Systems Through Keep-Close Approach: Robustness Analysis and Safety Verification

Among the major challenges in neural control system technology is the validation and certification of the safety and robustness of neural network (NN) controllers against various uncertainties including unmodelled dynamics, nonlinearities, and time delays. One way in providing such validation guarantees is to maintain the closed-loop system output with a NN controller when its input changes within a bounded set, close to the output of a robustly performing closed-loop reference model. This paper presents a novel approach to analysing the performance and robustness of uncertain feedback systems with NN controllers. Due to the complexity of analysing such systems, the problem is reformulated as the problem of dynamical tracking errors between the closed-loop system with a neural controller and an ideal closed-loop reference model. Then, the approximation of the controller error is characterised by adopting the differential mean value theorem (DMV) and the Integral Quadratic Constraints (IQCs) technique. Moreover, the Relative Integral Square Error (RISE) and the Supreme Square Error (SSE) bounded set are derived for the output of the error dynamical system. The analysis is then performed by integrating Lyapunov theory with the IQCs-based technique. The resulting worst-case analysis provides the user a prior knowledge about the worst case of RISE and SSE between the reference closed-loop model and the uncertain system controlled by the neural controller.