Sliding mode prediction based control algorithm for discrete-time non-linear uncertain coupled systems

By introducing predictive control strategy into the design of sliding mode control (SMC), a novel SMC algorithm for a class of discrete-time non-linear uncertain coupled systems is presented in this paper. To enlighten by the recursive sliding mode approach, a special sliding mode prediction model (SMPM) is created at first. Then taking model mismatch into consideration, the error between the output of SMPM and the practical sliding mode value is used to make feedback correction for SMPM. Applying receding horizon optimization, the desired sliding mode control law which is a non-switching type, is obtained subsequently. The reachability of sliding mode is achieved by making predictive value of sliding mode track the expected sliding mode reference value. Due to feedback correction and receding horizon optimization, the influence of uncertainties can be compensated in time, strong robustness to matched or unmatched uncertainties is possessed. Theoretical analysis proves the closed-loop system is robustly stable, without requiring the known boundaries of uncertainties. Simulation results of a numerical example and a rotational inverted pendulum illustrate the validity of the proposed algorithm.