A finite‐time adaptive fuzzy backstepping control for multiple‐input multiple‐output coupled nonlinear systems with tracking error constraints

Abstract

SUMMARYIn this study, a finite‐time adaptive fuzzy backstepping control strategy with tracking error constraints is designed for a class of multiple‐input multiple‐output (MIMO) coupled nonlinear systems with uncertainties. First, the uncertainty of the system is approximated by adaptive fuzzy logic systems (AFLSs), then, the rapidity of the state tracking of the control system are ensured by backstepping and finite time theory. The problem of error constraints is solved by the combination of performance function and simplified barrier Lyapunov function (SBLF). It is proved that the states of a closed‐loop adaptive control system are semi‐globally practical finite‐time stable (SGPFS) by the finite‐time Lyapunov function, and in a finite time, the tracking error of the system state converges to a narrow block of origin with the prescribed bounded. Finally, the scheme's effectiveness is verified by the simulation.