Discrete-Time Adaptive Fuzzy Finite-Time Tracking Control for Uncertain Nonlinear Systems

The finite-time control problem of the generalized discrete-time systems is a major challenging problem to be solved. In this work, the discrete-time adaptive fuzzy finite-time control scheme is presented for nonlinear systems with discrete form and uncertain dynamics. The fuzzy logic systems (FLSs) are employed to approach uncertain dynamics of systems. Then, the sufficient condition of semiglobal finite-time stability of discrete-time nonlinear systems (DTNSs) is constructed. The discrete-time filters are used to overcome the noncausal problem from the traditional backstepping controller design processes of DTNSs. With the help of the discrete finite-time theorem, discrete-time filters, backstepping techniques, and FLSs, an adaptive fuzzy discrete finite-time control scheme is proposed in a unified framework. The stability analysis can ensure the boundedness of all signals of the closed-loop systems and the achieving the desired tracking control performance in the finite-time. Finally, two examples are adopted to verify abovementioned claims.