Class Of Nonstrict-feedback Nonlinear Systems Research Articles

Command Filter-Based Adaptive Neural Control for Nonstrict-Feedback Nonlinear Systems with Prescribed Performance

In this paper, a new command filter-based adaptive NN control strategy is developed to address the prescribed tracking performance issue for a class of nonstrict-feedback nonlinear systems. Compared with the existing performance functions, a new performance function, the fixed-time performance function, which does not depend on the accurate initial value of the error signal and has the ability of fixed-time convergence, is proposed for the first time. A radial basis function neural network is introduced to identify unknown nonlinear functions, and the characteristic of Gaussian basis functions is utilized to overcome the difficulties of the nonstrict-feedback structure. Moreover, in contrast to the traditional Backstepping technique, a command filter-based adaptive control algorithm is constructed, which solves the “explosion of complexity” problem and relaxes the assumption on the reference signal. Additionally, it is guaranteed that the tracking error falls within a prescribed small neighborhood by the designed performance functions in fixed time, and the closed-loop system is semi-globally uniformly ultimately bounded (SGUUB). The effectiveness of the proposed control scheme is verified by numerical simulation.

Adaptive fault-tolerant control for a class of nonstrict-feedback nonlinear systems with unmodeled dynamics and dead-zone output using multi-dimensional taylor networks

Adaptive fault-tolerant control for a class of nonstrict-feedback nonlinear systems with unmodeled dynamics and dead-zone output using multi-dimensional taylor networks

Neural networks-based adaptive fault-tolerant control for a class of nonstrict-feedback nonlinear systems with actuator faults and input delay

<abstract><p>This paper addresses the challenge of adaptive control for nonstrict-feedback nonlinear systems that involve input delay, actuator faults, and external disturbance. To deal with the complexities arising from input delay and unknown functions, we have incorporated Pade approximation and radial basis function neural networks, respectively. An adaptive controller has been developed by utilizing the Lyapunov stability theorem and the backstepping approach. The suggested method guarantees that the tracking error converges to a compact neighborhood that contains the origin and that every signal in the closed-loop system is semi-globally uniformly ultimately bounded. To demonstrate the efficacy of the proposed method, an electromechanical system application example, and a numerical example are provided. Additionally, comparative analysis was conducted between the Pade approximation proposed in this paper and the auxiliary systems in the existing method. Furthermore, error assessment criteria have been employed to substantiate the effectiveness of the proposed method by comparing it with existing results.</p></abstract>

Adaptive finite-time event-triggered command filtered control for nonlinear systems with unknown control directions

In this article, we study an adaptive finite-time event-triggered command filtered control problem based on output feedback for a class of nonstrict-feedback nonlinear systems with unknown control directions. Firstly, the unknown nonlinear continuous functions in the systems are approached by fuzzy logic systems, and the coordinate transformations and Nussbaum function technique are introduced to settle the problem caused by the unknown control directions in the systems. Then, in order to reduce the communication burden between the controller and the actuator, a finite-time adaptive event-triggered control algorithm is designed by means of backstepping technique. It is proved that the tracking and observer errors are adjusted around zero with a small neighborhood in a finite time and all the signals in the closed-loop systems are bounded. In addition, the command filtering technology based on error compensation system with fractional power is constructed to avoid the complexity explosion issue in the backstepping design process. Finally, the simulation examples are included to verify the availability and superiority of the control approach.

Event-Triggered Adaptive Fuzzy Fixed-Time Tracking Control for a Class of Nonstrict-Feedback Nonlinear Systems

The problem of fuzzy-based adaptive event-triggered tracking control is investigated for a class of non-strict-feedback nonlinear systems within fixed-time interval in this paper. Fuzzy logic system (FLS) is employed to approximate the packaged unknown nonlinearities. Event-triggered mechanism is employed to schedule the data transmission dependent upon errors exceeding certain threshold. And combining backstepping design algorithm with Lyapunov stability theorem, a fuzzy-based adaptive event-triggered controller is developed. The presented control scheme eliminates the singularity problem that may occur in the design process and guarantees the boundedness of all the closed-loop signals. And the tracking error converges into a small neighborhood of zero in fixed-time. Meanwhile, the Zeno behavior is also avoided. At last, the effectiveness of the proposed approach is demonstrated by simulation results.

Observer-Based Adaptive Neural Network Control for Nonstrict-Feedback Nonlinear Systems With Time Delays

An observer-based adaptive neural network control problem was investigated for a class of nonstrict-feedback nonlinear systems with time delays. A state observer was constructed to estimate unknown variables in nonlinear systems. With the approximation ability of RBF NNs and the backstepping technique, an adaptive neural network output feedback control approach was proposed. The designed controller ensures the semi-global uniform boundedness of all signals in the closed-loop system. Finally, the simulation example shows the effectiveness of the proposed control approach.

Partial-State-Constrained Adaptive Intelligent Tracking Control of Nonlinear Nonstrict-Feedback Systems with Unmodeled Dynamics and Its Application

In this paper, an adaptive intelligent control scheme is presented to investigate the problem of adaptive tracking control for a class of nonstrict-feedback nonlinear systems with constrained states and unmodeled dynamics. By approximating the unknown nonlinear uncertainties, utilizing Barrier Lyapunov functions (BLFs), and designing a dynamic signal to deal with the constrained states and the unmodeled dynamics, respectively, an adaptive neural network (NN) controller is developed in the frame of the backstepping design. In order to simplify the design process, the nonstrict-feedback form is treated by using the special properties of Gaussian functions. The proposed adaptive control scheme ensures that all variables involved in the closed-loop system are bounded, the corresponding state constraints are not violated. Meanwhile, the tracking error converges to a small neighborhood of the origin. In the end, the proposed intelligent design algorithm is applied to one-link manipulator to demonstrate the effectiveness of the obtained method.

A New Adaptive DS-Based Finite-Time Neural Tracking Control Scheme for Nonstrict-Feedback Nonlinear Systems

This article addresses the problem of adaptive finite-time neural tracking control for nonstrict-feedback nonlinear systems via dynamic surface (DS) technique. First, a new quasi-fast finite-time practical stability (QFPS) criterion is proposed for a class of general nonlinear systems. Then, the presented QFPS criterion is applied to design the desired adaptive finite-time neural tracking controller for a class of nonstrict-feedback nonlinear systems. The presented design scheme for the nonstrict-feedback nonlinear system has the following two features: 1) the “explosion of complexity” issue of the backstepping design is addressed by utilizing the DS technique and 2) the structural feature of Gaussian functions is applied to solve the design difficulties caused by the nonstrict-feedback form. It is proved that the designed controller for the nonstrict-feedback nonlinear system can make the resulting closed-loop system stabilizable in a quasi-fast finite time and the tracking error converges to a sufficiently small neighborhood of the origin. Finally, the simulation results are given to show the validity and practicability of the proposed design scheme.

Event-Triggered Adaptive Fuzzy Output-Feedback Control for Nonstrict-Feedback Nonlinear Systems With Asymmetric Output Constraint.

This article addresses the event-triggered adaptive fuzzy output-feedback control problem for a class of nonstrict-feedback nonlinear systems with asymmetric and time-varying output constraints, as well as unknown nonlinear functions. By designing a linear observer to estimate the unmeasurable states, a novel event-triggered adaptive fuzzy output-feedback control scheme is proposed. The barrier Lyapunov function (BLF) and the error transformation technique are used to handle the output constraint under a completely unknown initial tracking condition. It is shown that with the proposed control scheme, all the solutions of the closed-loop system are semiglobally bounded, and the tracking error converges to a small set near zero, while the output constraint is satisfied within a predetermined finite time, even when the constraint condition is violated initially. Moreover, with the proposed event-triggering mechanism (ETM), the Zeno behavior can be strictly ruled out. An example is finally provided to demonstrate the effectiveness of the proposed control method.

Barrier Lyapunov Function Based Adaptive Cross Backstepping Control for Nonlinear Systems with Time-varying Partial State Constraints

This paper focuses on an adaptive cross-backstepping control for a class of nonstrict-feedback nonlinear systems affected by time-varying partial state constraints. The nonstrict-feedback nonlinear systems considered in this paper are divided into two strict-feedback nonlinear subsystems. One constrained subsystems and another unconstrained subsystems. In view of the normal backstepping method is only an effective method to control lower-triangular systems, cross-backstepping control is introduced which successfully solves the problem of alternate time-varying state constraints. For the constrained subsystems, novel time-varying tan-type barrier Lyapunov function (TBLF) is employed in each step of backstepping design to guarantee the boundedness of the fictitious or actual state tracking errors. Besides, proper adaptive laws are designed for the upper bound of uncertain parameters, which successfully neutralize the influence of parametric uncertainties. Based on the stability analysis, it is concluded that the states of the closed-loop system maintain in the predefined time-varying compact sets and the output can be guaranteed to be as close to the desired trajectory as possible. The effectiveness of the proposed technique is illustrated by a constrained hyperchaotic system in two cases.

Finite-Time Adaptive Fuzzy Command Filtered Backstepping Control for a Class of Nonlinear Systems

In this article, the problem of adaptive fuzzy finite-time command filtered control is considered for a class of nonstrict-feedback nonlinear systems. The explosion of complexity problem is dealt with by employing the command filter approach. In order to design a finite-time control scheme, a finite-time semi-global practical stability criterion is first presented. Based on this criterion, by applying the command filter technology and backstepping technique, adaptive fuzzy finite-time tracking control scheme is developed with the help of fuzzy logic systems approximation. Under the presented adaptive control scheme, all the closed-loop variables are semi-global practical finite-time stable and the tracking error goes into an adjustable neighborhood around the origin in a finite time. Finally, simulations are utilized to verify the effectiveness of designed control scheme.

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.

Adaptive Fuzzy Finite-Time Control of Nonlinear Systems With Actuator Faults.

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.

Adaptive Neural Tracking Control of Nonlinear Nonstrict-Feedback Systems With Unmodeled Dynamics

In this paper, an adaptive neural control approach for a class of nonstrict-feedback nonlinear systems with unmodeled dynamic is presented. During the controller design process, the main difficulties arise from unknown functions and unmodeled dynamics, which are inevitable in practical applications. The unknown functions are approximated by utilizing the radial basis function neural networks' (RBF NNs) method, and for the problem of the unmodeled dynamics, a dynamic signal is introduced. The innovation of this paper is that we use the property of Gaussian functions to deal with the nonstrict-feedback form. Based on the above precondition, an adaptive NNs controller design scheme is developed by applying the backstepping recursive design. The proposed adaptive control approach guarantees that all the signals in closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error converges to a small neighborhood around the origin by choosing appropriate parameters. In the end, a simulation example is provided to demonstrate the effectiveness of the proposed method.

ADAPTIVE FUZZY OUTPUT FEEDBACK TRACKING CONTROL FOR A CLASS OF NONLINEAR TIME-VARYING DELAY SYSTEMS WITH UNKNOWN BACKLASH-LIKE HYSTERESIS

This paper considers the problem of adaptive output feedback tracking control for a class of nonstrict-feedback nonlinear systems with unknown time-varying delays and unknown backlash-like hysteresis. Fuzzy logic systems are used to estimate the unknown nonlinear functions. Based on the Lyapunov–Krasovskii method, the control scheme is constructed by using the backstepping and adaptive technique. The proposed adaptive controller guarantees that all the closed-loop signals are semiglobally uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin. Finally, Simulation results further show the effectiveness of the proposed approach.

Constrained adaptive neural control for a class of nonstrict-feedback nonlinear systems with disturbances

This paper focuses on the tracking problem for a class of nonstrict-feedback nonlinear systems with mismatched unknown nonlinear functions and external disturbances. First, a disturbance observer is developed to estimate the disturbance generated by an exogenous system. Then, based on the output of the disturbance observer, a constrained adaptive neural controller is developed for the nonstrict-feedback nonlinear system. In the control scheme design, the modified variable separation approach is applied to establish the relationship between the bounded function of nonstrict-feedback nonlinear function and the error variable. Furthermore, the barrier Lyapunov function is applied to guarantee that full state constraints are not violated. As a result, all the signals of the closed-loop system are semi-global uniformly ultimately bounded. Finally, two simulation examples are used to demonstrate the effectiveness of the developed constrained adaptive neural control law.

Adaptive Neural Hierarchical Sliding Mode Control of Nonstrict-Feedback Nonlinear Systems and an Application to Electronic Circuits

This paper proposes an adaptive sliding mode control method for a class of nonstrict-feedback nonlinear systems where some widely used restrictions on system structure are relaxed. Based on the calculus principle, the original system is first transformed into a new defined system. Then, by using sliding mode control technology and the concept of hierarchical design, a series of control signals are sequentially designed for the new defined system where radial basis function neural networks are used to approximate the unknown functions. Based on the Lyapunov stability theory, the closed-loop system together with the proposed sliding surfaces is proved to be uniformly ultimately bounded under our designed adaptive neural controller. The main contributions of this paper lie in that some strict restrictions on uncertain system functions are removed; a hierarchical control method is proposed for the considered systems, which can avoid the problem of “causes and consequences” that may be encountered by using traditional backstepping design method; and the proposed control method is also available for underactuated nonlinear systems. Finally, simulation results demonstrate the effectiveness of the proposed design techniques.

Adaptive neural control for nonstrict-feedback time-delay systems with input and output constraints

An adaptive tracking control is investigated for a class of nonstrict-feedback nonlinear systems with time delays subject to input saturation nonlinearity and output constraint. First, the Gaussian error function is used to express the continuous differentiable asymmetric saturation model, and a barrier Lyapunov function is designed to ensure that the output parameters are restricted. Then, an appropriate Lyapunov–Krasovskii functional is chosen to deal with the unknown time-delay terms, and the neural network is used to model the unknown nonlinearities. Finally, based on Lyapunov stability theory, an adaptive neural controller is designed to establish the closed-loop system stability. The example is provided to further illustrate the effectiveness and applicability of the proposed approach.

Adaptive output-feedback neural tracking control for a class of nonstrict-feedback nonlinear systems

This paper focuses on the problem of adaptive neural output-feedback control for a class of nonstrict-feedback nonlinear systems where the system coefficient functions are unknown. First, the original system is transformed into a new defined system by a linear state transformation. Then, by using the dynamic surface control (DSC) technique, an improved input-driven filter is proposed. Based on this filter and the approximation property of radial basis function (RBF) neural networks, an adaptive neural output-feedback controller is designed via backstepping technique, which can guarantee that all the signals in the closed-loop system are ultimately bounded. The main contribution of this paper lies in that a simpler and more effective design procedure of adaptive neural output-feedback tracking controller is proposed for the underlying system which is more general than some existing ones in literature. Finally, simulation results are given to demonstrate the feasibility and effectiveness of the new design algorithm.