Semi-global Practical Finite-time Stability Research Articles

Adaptive Fuzzy Finite-Time Tracking Control for Nonstrict Full States Constrained Nonlinear System With Coupled Dead-Zone Input.

This article proposes an adaptive finite-time tracking control based on fuzzy-logic systems (FLSs) for an uncertain nonstrict nonlinear multi-input-multi-output (MIMO) full-state-constrained system with the coupled uncertain dead-zone input. By using three kinds of FLSs: the uncertain system, the uncertain dead zone, and the uncertain input transfer inverse matrix are approximated using the system function FLS, dead-zone FLS, and input transfer inverse matrix FLS, respectively. After defining the barrier Lyapunov function, the fuzzy-based adaptive tracking controllers are designed, and the fuzzy weights are updated through the proposed adaptive laws. Then, based on the extended finite-time convergence theorem, with the design parameters chosen properly, the target uncertain nonlinear system is guaranteed to be semiglobal practical finite-time stable (SGPFS); and the full-state constraints are not violated while avoiding the effects of the dead zones. Furthermore, a simulation is presented to verify the validity of the proposed algorithm.

Finite-Time Backstepping of a Nonlinear System in Strict-Feedback Form: Proved by Bernoulli Inequality

In this paper, we propose a novel state-feedback backstepping control design approach for a single-input single-output (SISO) nonlinear system in strict-feedback form. Rational-exponent Lyapunov functions (ReLFs) are employed in the backstepping design, and the Bernoulli inequality is primarily adopted in the stability proof. Semiglobal practical finite-time stability, or global asymptotically stability, is guaranteed by a continuous control law using a commonly used recursive backstepping-like approach. Unlike the inductive design of typical finite-time backstepping controllers, the proposed method has the advantage of reduced design complexity. The virtual control laws are designed by directly canceling the nonlinear terms in the derivative of the specific Lyapunov functions. The terms with exponents are transformed into linear forms as their bases. The stability proof is simplified by applying several inequalities in the final proof, instead of in each step. Furthermore, the singularity problem no longer exists. The weakness of the concept of practical finite-time stability is discussed. The method can be applied to smoothly extend numerous design methodologies with asymptotic stability with a higher convergence rate near the equilibrium. Two numerical case studies are provided to present the performance of the proposed control.

Practical Finite-Time Fuzzy Control for Hamiltonian Systems via Adaptive Event-Triggered Approach

This paper is to present our new results on practical finite-time fuzzy control scheme for a class of Hamiltonian systems by an adaptive event-triggered approach. An unknown function of the system is approximated by an adaptive fuzzy system. According to a semi-global practical finite-time stability criterion, a novel adaptive fuzzy finite-time controller is presented. In the interest of saving resources, an event-triggered approach is developed where the controller is updated under the respective triggering conditions. Based on the special structure of Hamiltonian systems and Lyapunov theory, a sufficient condition is obtained so that the states of original systems converge to a small neighborhood containing the origin in a finite time. Meanwhile, with the proposed controller, there exists a positive lower bound for the interexecution time, and the Zeno phenomenon is avoided. The design processes of the proposed controller, adaptive law and event-triggered conditions are also proved by a circuit system simulation example.

Neural networks-based adaptive finite-time control of switched nonlinear systems under time-varying actuator failures

This paper is dedicated to neural networks-based adaptive finite-time control design of switched nonlinear systems in the time-varying domain. More specifically, by employing the approximation ability of neural networks system, an integrated adaptive controller is constructed. The main aim is to make sure the closed-loop system in arbitrary switching signals is semi-global practical finite-time stable (SGPFS). A backstepping design with a common Lyapunov function is proposed. Unlike some existing control schemes with actuator failures, the key is dealing with the time-varying fault-tolerant job for the switched system. It is also proved that all signals in the system are bounded and the tracking error can converge in a small field of the origin in finite time. A practical example is presented to illustrate the validity of the theory.

Finite-time Adaptive Integral Backstepping Fast Terminal Sliding Mode Control Application on Quadrotor UAV

This paper presents a reliable and novel quadrotor flight control system designed to enhance trajectory tracking performance, robustness and adaptiveness against the uncertain parameters and the external wind disturbance. By combining a recursive control methodology with a robust control algorithm, a finite-time adaptive integral backstepping fast terminal sliding mode control is designed for major control loops related to position tracking and attitude stabilization. To estimate quadrotor mass and inertia moments, only four adaptation laws are developed. To compensate the unknown upper bound on the disturbances, a robust and adaptive switching gain is designed. The designed controller guarantees that all the closed signals are semi-global practical finite-time stability while the tracking error converges to a small neighborhood of the origin. The obtained numerical results and comparison studies show the effectiveness, robustness, adaptiveness and energy efficiency of the proposed flight control system.

Observed-based adaptive finite-time tracking control for a class of nonstrict-feedback nonlinear systems with input saturation

This paper concentrates upon the problem of adaptive neural finite-time tracking control for uncertain nonstrict-feedback nonlinear systems with input saturation. The design difficulty of non-smooth input saturation nonlinearity is solved by applying a smooth non-affine function to approximate the saturation signal. Neural networks, as a kind of specialized function estimators, are used to estimate the uncertain function. Meanwhile, a neural network-based observer is constructed to observe the unavailable states, and thus an observer-based adaptive finite-time tracking control strategy is developed by combining dynamic surface control (DSC) technique and backstepping approach. Furthermore, the stability of the considered system is analyzed via semi-global practical finite-time stability theory. Under the proposed control method, all the signals in the closed-loop system are bounded, and the system output can almost surely track the desired trajectory within a specified bounded error in a finite time. In the end, two examples are adopted to illustrate the validity of our results.

Finite-time adaptive fuzzy tracking control for nonlinear systems with disturbances and dead-zone nonlinearities

This paper studies the problem of finite-time adaptive fuzzy tracking control for a class of nonlinear systems with unknown parameter uncertainties, nonsymmetric dead-zone inputs and mismatched external disturbances. Firstly, fuzzy logic systems (FLSs) are used to approximate the unknown nonlinear functions of the system model. Then, a novel finite-time adaptive tracking control scheme with disturbance estimator is developed to handle the unknown disturbance, which is more effective than the existing methods of disturbance rejection. Moreover, based on Lyapunov stability analysis of semi-global practical finite-time stable (SGPFS), it is proved that the proposed control scheme can guarantee that the states of system can quickly converge in finite time, and all the closed-loop system error signals are bounded. Finally, two simulation examples are used to demonstrate the effectiveness of the presented control approach.

Fuzzy Adaptive Finite Time Fault-tolerant Control for Multi-input and Multi-output Nonlinear Systems with Actuator Faults

This paper investigates the problem of fuzzy adaptive finite-time fault tolerant control (FTC) for a class of multi-input and multi-output (MIMO) nonlinear systems with actuator failure. In control design, the fuzzy logic systems (FLSs) are adopted to identify the unknown nonlinear functions and a state observer is constructed to estimate the unmeasurable states. By combining dynamic surface control (DSC) technique with backstepping design, a novel finite-time fuzzy adaptive FTC strategy is proposed based on fault-tolerant control technique to overcomes the “explosion of complexity” problem. The presented control method demonstrates that all signals of the closed-loop system are semi-global practical finite-time stability (SGPFS), and the tracking errors converge to a small neighborhood of zero in a finite time. Finally, a numerical example is provided to illustrate the effectiveness of the presented control method.

Fuzzy Adaptive Practical Finite-Time Control for Time Delays Nonlinear Systems

This paper focuses on fuzzy adaptive practical finite-time output feedback control problem for a class of single-input and single-output nonlinear system with time-varying delays in nonstrict feedback form. Fuzzy logic systems are adopted to approximate the unknown nonlinear functions, and state observer is constructed to estimate the unmeasured states. By combining practical finite-time Lyapunov stability theory with the backstepping design, an observer-based fuzzy adaptive practical finite-time control strategy is proposed. Meanwhile, the stability of the closed-loop system is proved, which means that the output can follow the given reference signal in a finite time, and the closed-loop system is semi-global practical finite-time stability. Finally, two simulation examples are provided to elaborate the effectiveness of the presented control strategy.

Finite-Time Adaptive Fuzzy Output Feedback Dynamic Surface Control for MIMO Nonstrict Feedback Systems

This paper investigates the finite-time adaptive fuzzy control problem for a class of multi-input and multi-output (MIMO) nonlinear nonstrict feedback systems. During the control design process, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions, and fuzzy state observer is constructed to estimate the unmeasured states. By combining adaptive backstepping with the dynamic surface control (DSC) technique, a finite-time fuzzy adaptive control scheme is presented to overcome the “explosion of complexity” problem. The stability of the close-loop systems can be proved based on the finite-time Lyapunov stability theory. The presented control scheme demonstrates that the closed-loop systems are semiglobal practical finite-time stability, and tracking errors converge to a small neighborhood of the origin in a finite time. Finally, two simulation examples are provided to show the effectiveness of the presented control method.

Adaptive Neural Network Finite-Time Control for Multi-Input and Multi-Output Nonlinear Systems With Positive Powers of Odd Rational Numbers.

This article investigates the adaptive neural network (NN) finite-time output tracking control problem for a class of multi-input and multi-output (MIMO) uncertain nonlinear systems whose powers are positive odd rational numbers. Such designs adopt NNs to approximate unknown continuous system functions, and a controller is constructed by combining backstepping design and adding a power integrator technique. By constructing new iterative Lyapunov functions and using finite-time stability theory, the closed-loop stability has been achieved, which further verifies that the entire system possesses semiglobal practical finite-time stability (SGPFS), and the tracking errors converge to a small neighborhood of the origin within finite time. Finally, a simulation example is given to elaborate the effectiveness and superiority of the developed.

Adaptive Finite-Time NN Control for 3-DOF Active Suspension Systems With Displacement Constraints

In this paper, the displacement constraints and finite-time control problems are handled for 3 degrees of freedom (DOF) active suspension systems (ASSs). In order to ensure that seat and active suspension's displacements do not violate their limits, the Barrier Lyapunov functions (BLFs) are employed to handle displacement constraints problem, and the ride comfort and safety are improved at the same time. The unknown functions in the ASSs are approximated by using the neural networks (NNs). The traditional finite-time controller often contains the sign functions or absolute value functions, and they cause the problem about buffeting of the controller. By using NNs, finite-time theory, and BLFs, an adaptive finite-time control approach is constructed to avoid this problem. Then, the boundedness of all signals of 3-DOF ASSs is testified by the semi-global practical finite-time stability analysis and a zero dynamics analysis. In addition, the results of two numerical examples demonstrate the effectiveness of the established adaptive finite-time NN control scheme.

Adaptive finite‐time control for a class of uncertain high‐order non‐linear systems based on fuzzy approximation

The problem of adaptive practical finite-time control is considered for a class of single-input and single-output non-linear systems, in which the system non-linear functions are assumed to be unknown. By combining adaptive fuzzy control approach with the backstepping technology, a backstepping-based adaptive fuzzy finite-time control scheme is proposed. In the control design procedure, fuzzy logic systems are employed to identify the non-linear uncertainties. The stability analysis of the adaptive closed-loop systems is proposed based on the finite-time Lyapunov stability theory. The proposed adaptive fuzzy controller guarantees that all the closed signals are semi-global practical finite-time stability while the tracking error converges to a small neighbourhood of the origin. Finally, simulation results are presented to validate the effectiveness of our results.