Fuzzy Adaptive Command Filtered Control of Strict-Feedback Fractional-Order Nonlinear Systems With State and Input Quantization

An adaptive fuzzy command filtering backstepping technique is given for strict-feedback fractional-order uncertain nonlinear systems. The controlled system includes unknown nonlinear functions, as well as state and input quantization. Considering fractional-order nonlinear systems that do not satisfy matching conditions, unknown nonlinear functions are approximated by fuzzy logic systems, and a sector bounded quantizer is used to quantify all input and state variables. During the plan process, command filtering backstepping scheme is used to avoid the use of nonsmooth states. Subsequently, in order to ensure the boundedness of a series of errors caused by continuous original states for stability analysis and discontinuous quantization states for control, a sufficiently smooth fractional-order projection operator is proposed. In addition, the fractional-order uniformly bounded criterion has been established and strictly proven, which solves the problem of uniformly bounded error signals in the fractional-order sense under the premise of known parameter boundedness. Thus, the boundedness of all closed-loop signals is ensured by the fractional-order uniformly bounded criterion. Finally, the simulation results have confirmed the efficacy of the method.