Observer-based adaptive fuzzy hierarchical sliding mode control of uncertain under-actuated switched nonlinear systems with input quantization

In this article, an observer-based adaptive fuzzy hierarchical sliding mode control (HSMC) scheme is put forward for uncertain under-actuated switched nonlinear systems in the presence of quantized input signals. The issues of quantized input signals from a hysteretic quantizer, external disturbances, unmeasured system states and completely unknown nonlinear functions are taken into account for the under-actuated system. First, the chattering phenomena can be effectively avoided by adopting the considered hysteretic quantizer. Then, fuzzy logic systems (FLSs) is utilized to approximate the unknown smooth nonlinear functions representing the system uncertainties. Furthermore, a switched fuzzy state observer is established to estimate the unmeasured system states. Based on the Lyapunov stability theory, the proposed control scheme can ensure the boundedness of all signals in the closed-loop system and make the system output track given reference signals well. Finally, a numerical simulation example is given to verify the effectiveness of the proposed control scheme.

Automated summary

In this article, an observer-based adaptive fuzzy hierarchical sliding mode control scheme is proposed for uncertain under-actuated switched nonlinear systems with quantized input signals. The problems of quantized input signals, external disturbances, unmeasured system states, and unknown nonlinear functions are considered. The proposed control scheme effectively avoids chattering phenomena and utilizes fuzzy logic systems and a switched fuzzy state observer for approximation and estimation. Based on Lyapunov stability theory, the scheme ensures boundedness of all signals and good tracking performance. A numerical simulation example is provided to verify its effectiveness.