Event-trigger-based adaptive fuzzy hierarchical sliding mode control of uncertain under-actuated switched nonlinear systems.

In this technical note, we present an adaptive fuzzy hierarchical sliding mode control method to deal with the control problem of under-actuated switched nonlinear systems. For the system under consideration, both the issues of unknown uncertain functions and aperiodically updating input are taken into account, which are of practical importance. A bounded time-varying function is employed to make a linear transformation of the control input, leading to a transformed system that can be applied to the control design. By introducing the so-called hierarchical structure, a top layer hierarchical sliding surface containing all the system states' information is obtained. Furthermore, by carrying out fuzzy logic systems' universal approximation, the problem caused by unknown system uncertainties is tackled. The approximation errors together with the measurement error resulted from the effects of the triggering event are lumped into a function, and its upper bound is estimated on-line. Based on these, the boundedness of all the signals are verified by combining the Lyapunov theory and projection algorithm. To testify the validity of our control scheme, a simulation example is carried out.