Class Of Strict-feedback Nonlinear Systems Research Articles

Funnel-Based Adaptive Neural Fault-Tolerant Control for Nonlinear Systems with Dead-Zone and Actuator Faults: Application to Rigid Robot Manipulator and Inverted Pendulum Systems

This study addresses an adaptive neural funnel fault-tolerant control problem for a class of strict-feedback nonlinear systems with actuator faults and input dead zone. To guarantee the boundedness of the tracking error, a modified transformation for funnel error is devised and incorporated into the control design process. To manage unknown nonlinear functions, radial basis function neural networks (RBFNN) are employed in designing an adaptive neural funnel fault-tolerant controller through the backstepping technique. The proposed controller guarantees the output tracking error stays within a predefined funnel, and all signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). Finally, simulations of a rigid robot manipulator system and an inverted pendulum system are conducted to validate the practicality and effectiveness of the proposed control method.

Prescribed-time tracking with prescribed performance for a class of strict-feedback nonlinear systems

In this paper, we will investigate the prescribed-time tracking with prescribed performance for a class of strict-feedback nonlinear systems. A control strategy will be proposed to achieve the tracking error constrain by prescribed performance bound (PPB) and converge to zero in prescribed-time. The PPB constrains not only the convergence rate, but also the maximum overshoot of the tracking error. The tracking error will converge to zero in prescribed-time. Such a prescribed-time is irrespective of both initial conditions and design parameters. First, by incorporating the PPB into the original system via a transformation, a equivalently transformed system is obtained, which is unconstrained and convenient for control design. Then, with the help of backstepping, a controller is recursively designed to guarantee that the tracking error satisfies the PPB all the time and converges to zero in prescribed-time. The key to designing the controller is that a fractional term is introduced when designing the virtual stabilizing function during each step of backstepping, which in turn decreases the Lyapunov function to origin within prescribed-time. Finally, two examples are presented to demonstrate the validity of our proposed control strategy.

Tuning function-based fault-tolerant finite-time control for nonlinear systems with sensor/actuator faults

This paper discusses the adaptive fault-tolerant finite-time control tracking problem for a class of strict-feedback nonlinear systems with multiple faults and disturbances. Our essay focuses on the problem of over-parameterisation in traditional backstepping methods. A new fault-tolerant control scheme is proposed by combining tuning function with fuzzy control technology and finite-time control. This scheme greatly simplifies the process of derivation and computation and avoids high computational cost and high memory consumption. Thus the purpose of improving the reliability and robustness of the system is achieved. Finally, according to the Lyapunov finite-time stability theory, the proposed method can ensure that the closed-loop system remains semi-globally practically finite-time stable and the tracking errors converge to a small neighbourhood near the origin in finite time under the condition of unmatched disturbances and sensor/actuator faults simultaneously. The effectiveness of the proposed control strategy is verified by a simulation example.

Event-Triggered Tracking Control for a Class of Nonlinear Systems: A Dynamic Gain Approach

This note presents a dynamic gain approach to the event-triggered tracking control for a class of strict-feedback nonlinear systems. A novel shifting function is designed to make the initial tracking error arbitrarily bounded, which significantly relaxes the requirement on the initial tracking error. To achieve the objective that the tracking error does not exceed the constraint after the pre-specified finite time, a barrier Lyapunov function and a new reduced-order observer are constructed by using the shifting function and the desired tracking signal. Based on the proposed dynamic gain approach, an event-triggered output feedback tracking controller is designed. It is proved that the developed control scheme guarantees that all the closed-loop signals are bounded and the tracking error constraint is strictly obeyed after a specified finite time. Compared with the celebrated backstepping method, the dynamic gain approach does not involve any virtual control variables, which avoids the complicated iterative procedure. The effectiveness of the proposed approach is verified by an example.

Prescribed Performance Fault-Tolerant Control of Strict-Feedback Systems via Error Shifting.

This article investigates the prescribed performance control (PPC) problem for a class of nonlinear strict-feedback systems with sensor/actuator faults. A shifting function is introduced to modify the output tracking error generated by the practically measured system state, based on which an improved PPC method is proposed to achieve the convergence of output tracking error to the prescribed region, and this convergence is shown to be independent of the initial tracking condition and insusceptible to sensor/actuator faults. The faults-induced uncertainties together with the nonlinear dynamics are compensated by involving a radial basis function neural network (RBFNN) to make the controller robust adaptive fault-tolerant without prior knowledge of fault coefficients. Via Lyapunov stability analysis, it is proven that all signals in the closed-loop system are semiglobally uniformly ultimately bounded. The effectiveness and superiority of the method are demonstrated by two simulation examples.

Observer-based event-triggered recursive optimal tracking control for a class of strict-feedback nonlinear systems

In this paper, an innovative event-triggered optimal tracking control algorithm is proposed for input saturated strict-feedback nonlinear systems with unknown dynamics. In order to reduce the requirement of configuring a complete suit of sensors and enhance the reliability of the controlled system, a neural networks (NNs) based adaptive state observer is developed firstly to reconstruct the system states. Subsequently, based on the state estimation information, a hybrid-triggered feedforward controller is designed to transform the original tracking control problem into an equivalent regulation issue, which is then solved by developing an event-triggered optimal controller. Therefore, the final controller consists of a hybrid-triggered feedforward controller and an event-triggered optimal controller. In order to make the actual input signals of the two controllers be updated simultaneously, a synchronization-oriented triggering rule is established by using multiple triggering errors. By virtue of this unique framework, the proposed control scheme can not only minimize the predefined cost function, but also greatly reduce the data transmission. What is more, the convergence properties of the proposed control strategy are achieved by using Lyapunov theory. It is important to note that unlike the widely adopted observer-controller framework, where the separation principle holds for the design of the state observer, there is a considerable coupling relationship between the error dynamics of the state observer and the event-triggered optimal controller in this paper. The distinguishing feature of the proposed method is its ability to ensure a satisfactory level of precision in both state estimation and tracking control, even in the presence of control saturation issues. At last, the proposed control strategy is applied to the tracking control problem of a high-order robot system and marine surface vehicle to demonstrate its effectiveness.

Event-Triggered Adaptive Fuzzy Optimal Control for a Class of Strict-Feedback Nonlinear Systems With External Disturbances

In this paper, the problem of the event-triggered optimal control for a class of strict-feedback nonlinear systems with external disturbances is investigated. Firstly, by introducing proper low-pass filters to the steps of backstepping design, the problem of “jump of the error surfaces” is avoided. What's more, it facilitates the design of a fuzzy hybrid-mode-triggered feedforward controller, which aims to transform the original controlled nonlinear strict-feedback system into an equivalent nonlinear system in affine form. Secondly, by utilizing the adaptive dynamic programming theory, an event-triggered feedback controller is developed for the equivalent affine nonlinear system. Differing from the existing methods, the real control input consists of two event-triggered terms, which can be updated synchronously under the proposed composite error-based triggering condition. Moreover, it is proven that all the closed-loop signals are bounded. At last, by taking a second-order nonlinear system and missile integrated guidance and control system as examples, simulation results demonstrate the effectiveness of the proposed approach.

Neuroadaptive tracking control of uncertain nonlinear systems with spatiotemporal constraints

This study investigates the neuroadaptive tracking control problem for a class of strict-feedback nonlinear systems with spatiotemporal constraints. An adaptive neural network-based control system is developed to alleviate the effects of modeling uncertainties and external disturbances. In particular, the proposed method ensures that the system tracking error has a predefined performance boundary (spatial constraint). Moreover, using a novel time-scale transformation method, uncertain nonlinear systems can achieve a prescribed finite-time convergence to a time-varying scaling function in the pointing position (temporal constraint). Finally, the efficiency of the proposed method is verified with two simulation examples.

Adaptive Finite-Time Tracking Control of Nonlinear Systems With Dynamics Uncertainties

In this paper, the problem of adaptive backstepping finite-time tracking control is investigated for a class of strict-feedback nonlinear systems with unmodeled dynamics and dynamic disturbances. A modified finite-time dynamic signal is first introduced to dominate the dynamic disturbance. By using the adaptive control, backstepping technique, and finite-time stability theory, an adaptive finite-time tracking controller is developed. Under the proposed control scheme, the finite-time tracking performance and the boundedness property of all signals in the closed-loop system are ensured. Finally, simulation results check the effectiveness of the suggested approach.

Adaptive Iterative Learning Control for a Class of Nonlinear Strict-Feedback Systems With Unknown State Delays.

In this article, an adaptive iterative learning control scheme is presented for a class of nonlinear parametric strict-feedback systems with unknown state delays, aiming to achieve the point-wise tracking of desired trajectory in a finite interval. The appropriate Lyapunov-Krasovskii functions are established to compensate the influence of time-delay uncertainties on the control systems. As the main features, the proposed approach integrates the command filter into the backstepping procedure to avoid the differential explosion problem that may occur with the increase of system order, and introduces the hyperbolic tangent functions into the learning controller to handle the singularity problem thus maintaining the continuity of input signal. The results of theoretical analysis and numerical simulation demonstrate that the tracking errors at the entire period will converge to a compact set along the iteration axis. Compared with the existing works, the proposed control scheme is promising to manifest the better performance and practicability owing to the learning mechanism, the dynamic model, as well as the implementation of controller.

Stabilization for a class of strict-feedback nonlinear systems via the PWM control law

This paper studies the PWM control problem of a class of nonlinear systems. During a modulation period, the PWM control signal maintains a pulse waveform with tunable width and fixed magnitude. The PWM control only possesses finite states, and has relatively limited control capability. This causes the degradation of system performance, and even the instability when implementing into a nonlinear system. We will introduce a novel method to design both the state feedback stabilizer and the output feedback stabilizer for strict-feedback nonlinear systems via the PWM control. The system performance is analyzed in a novel framework and the stability criteria is derived to ensure the system convergence. At last, two examples are considered to illustrate the effectiveness of our proposed method.

Low-Computation Adaptive Saturated Self-Triggered Tracking Control of Uncertain Networked Systems

In this paper, a low-computation adaptive self-triggered tracking control scheme is proposed for a class of strict-feedback nonlinear systems with input saturation. By introducing two novel error transformation functions, the designed low-computation adaptive control scheme can overcome the problem of complexity explosion in the absence of any filters, such that the developed control scheme is more applicable. In addition, to save communication resources in networked systems, a self-triggered communication strategy is proposed which can predict the next trigger point based on the current information. Compared with traditional event-triggered mechanisms, the computational burden arising from continuous monitoring of threshold conditions was successfully avoided. Furthermore, the input saturation problem considered in this paper prevents the overload phenomenon caused by signal jumps, and the adverse effects are compensated by introducing an auxiliary system. The effectiveness of the developed control scheme is verified through a simulation example.

Observer-Based Output-Feedback Control for Nonlinear Time-Delay Systems

In this article, the output feedback control design problem for a class of strict-feedback nonlinear systems with unknown state time-varying delays is addressed. Two output feedback control schemes are considered which are based on full-order and reduced-order observer, respectively. Lyapunov–Krasovskii functionals with static gain are used to develop novel memoryless control strategies. The above work ensures that all the signals in the closed-loop system are bounded and the system is asymptotically stable. Finally, two simulation examples illustrate the effectiveness of the two control schemes we proposed.

Adaptive Dynamic Programming-based Adaptive Optimal Tracking Control of a Class of Strict-feedback Nonlinear System

Adaptive Dynamic Programming-based Adaptive Optimal Tracking Control of a Class of Strict-feedback Nonlinear System

Exponential output feedback control for a class of strict-feedback nonlinear systems with different time-delay states

In this paper, the output feedback control scheme is developed to investigate the exponential stabilisation problem for a class of strict-feedback nonlinear systems subject to different time-delay states. First of all, the memoryless full-order observer and output feedback controller which depend on the same designed parameter are provided respectively. And then, by tactfully introducing the suitable Lyapunov–Krasovskii functional and selecting the applicable parameter to be designed, the exponential stability of the closed-loop system can be achieved. Finally, a numerical example is used to illustrate the effectiveness of the proposed control scheme.

Fixed-Time Stabilization of a Class of Strict-Feedback Nonlinear Systems via Dynamic Gain Feedback Control

This paper presents a novel fixed-time stabilization control (FSC) method for a class of strict-feedback nonlinear systems involving unmodelled system dynamics. The key feature of the proposed method is the design of two dynamic parameters. Specifically, a set of auxiliary variables is first introduced through state transformation. These variables combine the original system states and the two introduced dynamic parameters, facilitating the closed-loop system stability analyses. Then, the two dynamic parameters are delicately designed by utilizing the Lyapunov method, ensuring that all the closed-loop system states are globally fixed-time stable. Compared with existing results, the “explosion of complexity” problem of backstepping control is avoided. Moreover, the two designed dynamic parameters are dependent on system states rather than a time-varying function, thus the proposed controller is still valid beyond the given fixed-time convergence instant. The effectiveness of the proposed method is demonstrated through two practical systems.

Adaptive Control Design for Uncertain Underactuated Cranes With Nonsmooth Input Nonlinearities

This article investigates the control of underactuated crane systems with unknown system parameters and nonsmooth input nonlinearities. To solve this problem, a novel filter-based adaptive control method is designed for the underactuated crane systems. First, since the backstepping control scheme cannot be directly applied to the crane systems, a group of filters is designed such that the crane systems become a class of strict-feedback nonlinear systems in each step of backstepping. Then, in order to ensure that the swing angle and position error converge to the origin, the variable transformation method is adopted. The result demonstrates that the tracking errors of the underactuated crane systems could be guaranteed to converge to a ball of origin with an arbitrarily small radius. Finally, the simulation results show that the proposed scheme is effective.

Type-B Nussbaum function-based fault-tolerant control for a class of strict-feedback nonlinear systems

This paper studies the fault-tolerant control (FTC) problem of a class of strict-feedback nonlinear systems. First, we put forward a key theorem which shows that type-B Nussbaum functions can be extended to the cases containing multiple Nussbaum functions in the same Lyapunov inequality under certain conditions. Then, by using the techniques of Nussbaum functions and adaptive control, a new fault-tolerant control scheme is proposed. Compared with the previous work, this paper considers unknown time-varying control coefficients and unknown time-varying fault coefficients of actuators. It is proved that all the signals of the closed-loop system are globally bounded and the tracking error converges to zero asymptotically. Finally, simulations are provided to verify the effectiveness of the proposed control scheme.

Event-triggered adaptive tracking control of uncertain nonlinear systems with prescribed performance and actuator failures

This article studies adaptive prescribed performance tracking control problem for a class of strict-feedback nonlinear systems with parametric uncertainties and actuator failures. Firstly, in order to compensate the multiple uncertainties and eliminate the influence of actuator failure, a new adaptive tracking controller based on first-order filter technology will be proposed, which simplifies the algorithm design process. Then, by introducing an asymmetric state transition function, the transient and steady performances of the output tracking error are both constrained such that the predetermined performance control goal is achieved. Moreover, to reduce the communication burden from the controller to the actuator, the event-triggered mechanism is designed, and there will be no Zeno phenomenon. Based on Lyapunov stability theory, it is strictly proved that output signal can track the reference signal and all the signals of the closed-loop system are bounded. Finally, a simulation example is performed and the results demonstrate effectiveness of the proposed strategy.

Adaptive reinforcement learning optimal tracking control for strict-feedback nonlinear systems with prescribed performance

The reinforcement learning-based prescribed performance optimal tracking control problem is considered for a class of strict-feedback nonlinear systems in this paper. The unknown nonlinearities and cost function are approximated by radial-basis-function (RBF) neural network (NN). The overall controller consists of an adaptive controller and an optimal compensation term. Firstly, the adaptive controller is designed by backstepping control method. Subsequently, the optimal compensation term is derived via policy iteration by minimizing cost function. In addition, depending on the prescribed performance control, the tracking error can be limited in the prescribed area. Therefore, the whole control scheme can effectively guarantee that the tracking error converges to a bound with prescribed performance while the cost function is minimized. The stability analysis shows that all signals in the closed-loop system are bounded. Finally, the effectiveness and advantages of the designed control strategy are illustrated by the simulation examples.