Robust predictive tracking fault-tolerant control for multiphase switched systems with asynchronous switching: A Lyapunov–Razumikhin method

Abstract

This paper develops a robust predictive tracking fault-tolerant control approach for a class typical of multiphase switched systems, i.e., multiphase batch processes, accompanied by asynchronous switching, small time delays, partial actuator faults and disturbances. First, an equivalent extended asynchronous switching model, including a match sub-model and a mismatch sub-model, is built. In this model, the Lyapunov–Razumikhin function method is chosen to handle time delays due to its ability to make the original states of the systems remain invariant set characteristics. Meanwhile, this method has the characteristics of small computation and low conservativeness in solving the linear matrix inequalities, which is appropriate for systems with small delays. Next, according to the stable sufficient conditions based on robust positively invariant sets and terminal constraint sets, the controller gains, the minimum and maximum dwell time are solved online to eliminate the asynchronous switching situation. Moreover, unlike the iterative learning method with globally constant controller gain, its system state cannot change in real time with the action of the desired controller gain, making state deviations occur over time. In contrast, the controller gain in this method can be corrected and updated to avoid state deviation issue in real time. Finally, a simulation case of injection molding process is used to demonstrate the feasibility of the proposed approach.