A Control-Theoretic Study on Runge–Kutta Methods With Application to Real-Time Fault-Tolerant Control of Nonlinear Systems

This paper addresses real-time fault-tolerant control (FTC) of nonlinear systems by adopting the internal model control structure with embedded iterative computation. We first study the Runge-Kutta (RK) type methods for solving the nonlinear ordinary differential equations and derive the convergence conditions in the control-theoretic framework. Then, we propose an observer-like iterative solution to improve the convergence rate of the RK method by embedding the sensor signals into the iterative computation. Based on these results, real-time FTC is achieved and enhanced by employing the modified numerical algorithm in the iterative computation and estimation. This paper is mainly motivated by the increasing demands on the reliability of integrating the fast converging iterative solutions of differential equations into the embedded control systems. The effectiveness of the proposed schemes is demonstrated through the experimental and simulation results on three-tank systems.