The paper investigates an adaptive practical fixed- time control strategy for the output tracking control of a class of strict feedback nonlinear systems. By utilizing backstepping algo- rithm, finite-time Lyapunov stable theory and fuzzy logic control, a novel adaptive practical fixed-time controller is constructed. Fuzzy logic systems are introduced to approximate the unknown items of the system. Theoretical analysis proves that under the presented control strategy, the closed-loop system is practically fixed-time stable, and the tracking error converges to a small neighborhood of the origin within fixed-time interval, in which the convergence time has no connection with the initial states of the system. In the meantime, all the signals of the closed-loop system are bounded. At last, a numerical example is presented to indicate the feasibility and effectiveness of the proposed method.

The adaptive fuzzy fixed-time fault-tolerant tracking control problem for high-order nonlinear systems (HONS) with sensor and actuator faults is considered in this paper. The fuzzy logic systems is introduced to approximate the unknown nonlinear functions of the HONS. In addition, on the basis of backstepping technology and fixed-time theory, an adaptive fuzzy fixed-time fault-tolerant controller is developed to ensure all signals of the closed-loop HONS to be bounded. Eventually, the numerical example can be shown to prove rationality of developed method.

The paper takes into account the problem of adaptive fixed-time control for nonlinear systems in strict form via finite-time command filtered backstepping. Our presented control scheme gives consideration to rapidity by using fixed-time control and finite-time command filter, and its prime control objective is to ensure that the system output can be guided from any initial conditions to go after an ideal variable. Meanwhile, this control strategy makes sure that all the system states and other signals are bounded at finite time, and its convergence time doesn't have no connection with the system initial conditions and is determined by the design parameters. At every step in the design process, a fuzzy logic system is introduced to approximate the unknown part, and a finite-time command filter is also utilized so as to avoid the issue of derivation of virtual control laws and complex calculation. At last, we verify that the presented scheme is viable through a simulation example.

The article investigates an adaptive practical fixed-time tracking control of nonlinear systems with prescribed boundary constraints. The main control objective is that the system output variable tracks the desired signal at fixed time, and the tracking error can also converge to the prescribed boundary constraints. Primarily, a new coordinate transformation is introduced, which will be utilized in the proposed controller. Next, based on the backstepping scheme, the sufficient conditions for the existence of the adaptive practical fixed-time tracking controller are presented. Meanwhile, the fuzzy logic systems are employed to approximate to unknown parts in the controlled system. Theoretical analysis shows that the tracking error converges to the prescribed boundary constraints at fixed time. At the same time, all the signals in the closed-loop controlled system are bounded and the controlled system is practically fixed-time stable. At last, simulation results verify the effectiveness of the proposed scheme by comparing the cases with/wihtout prescribed boundary constraints.