This paper addresses the finite-time tracking problem of nonlinear pure-feedback systems. Unlike the literature on traditional finite-time stabilization, in this paper the nonlinear system functions, including the bounding functions, are all totally unknown. Fuzzy logic systems are used to model those unknown functions. To present a finite-time control strategy, a criterion of semiglobal practical stability in finite time is first developed. Based on this criterion, a novel adaptive fuzzy control scheme is proposed by a backstepping technique. It is shown that the presented controller can guarantee that the tracking error converges to a small neighborhood of the origin in a finite time, and the other closed-loop signals remain bounded. Finally, two examples are used to test the effectiveness of proposed control strategy.

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.

This work investigates a finite-time adaptive fuzzy tracking control problem for a class of non-strict feedback nonlinear systems from a new point of view. A new concept, named Finite-Time Performance Function (FTPF), is defined in this paper for the first time. Moreover, a finite-time adaptive state feedback fuzzy tracking controller is derived based on fuzzy approximation, backstepping technique and Prescribed Performance Control (PPC), which guarantees that all the signals of the closed-loop system are bounded, the output tracking error converges to a prescribed arbitrarily small region within a finite-time interval, and maximum overshoot is not more than a predefined level. In addition, a controller design process is given, which is less complex than the existing finite-time control design methods. Three simulation studies are provided to verify the feasibility and effectiveness of the theoretical finding in this study.

This paper addresses the trajectory tracking control problem of a class of nonstrict-feedback nonlinear systems with the actuator faults. The functional relationship in the affine form between the nonlinear functions with whole state and error variables is established by using the structure consistency of intermediate control signals and the variable-partition technique. The fuzzy control and adaptive backstepping schemes are applied to construct an improved fault-tolerant controller without requiring the specific knowledge of control gains and actuator faults, including both stuck constant value and loss of effectiveness. The proposed fault-tolerant controller ensures that all signals in the closed-loop system are semiglobally practically finite-time stable and the tracking error remains in a small neighborhood of the origin after a finite period of time. The developed control method is verified through two numerical examples.

This paper addresses the problem of adaptive neural tracking control for nonlinear nonstrict-feedback systems. The state variables are immeasurable and only the system output is available. A neural observer is constructed to estimate these unknown system state variables. An observer-based adaptive neural tracking control scheme is developed via backstepping approach. It is shown that the designed controller guarantees that the system output well follows the desired reference signal, and meanwhile, other closed-loop signals remain bounded. Finally, two simulation examples are used to test our results.

This paper investigates an adaptive finite-time control (FTC) problem for a class of strict-feedback nonlinear systems with both time-delays and quantized input from a new point of view. First, a new concept, called preassigned finite-time performance function (PFTF), is defined. Then, another novel notion, called practically preassigned finite-time stability (PPFTS), is introduced. With PFTF and PPFTS in hand, a novel sufficient condition of the FTC is given by using the neural network (NN) control and direct adaptive backstepping technique, which is different from the existing results. In addition, a modified barrier function is first introduced in this work. Moreover, this work is first to focus on the FTC for the situation that the time-delay and quantized input simultaneously exist in the nonlinear systems. Finally, simulation results are carried out to illustrate the effectiveness of the proposed scheme.