Sliding Mode Control for Uncertain Discrete-Time Systems Using an Adaptive Reaching Law

This brief presents the design, analysis, and validation of a new adaptive reaching law and the corresponding sliding mode controller, which are dedicated to robust control of disturbed discrete-time systems with parameter uncertainties. In state-of-the-art discrete-time reaching law schemes, a priori boundedness assumption on the generalized uncertainty, consisting of the parameter uncertainties and the external disturbances, is required to guarantee the boundedness of the controlled system. However, a priori bounded generalized uncertainty imposes a priori boundedness assumption on the system state before designing the controller. Different from existing similar works, an adaptive law is integrated into the proposed reaching law to estimate the unknown system parameters and external disturbances in Lyapunov sense, which ensures robust control of uncertain discrete-time systems without requiring a priori bounded system state. The controlled system stability in the presence of parameter uncertainties and external disturbances is analyzed in theory. The feasibility of the reported method is verified and compared by conducting simulation studies.