Practical prescribed-time fuzzy tracking control for uncertain nonlinear systems with time-varying actuators faults

The paper investigates the practical prescribed-time fuzzy tracking control problem for a category of nonlinear system subject to time-varying actuator faults.The presence of unknown nonlinear dynamics and actuator faults makes achieving tracking control within a prescribed-time challenging.To tackle this issue,we propose a novel practical prescribed-time fuzzy tracking control strategy,which is independent of the initial state of the system and does not rely on precise modeling of the system and actuators.We apply the approximation capabilities of fuzzy logic systems to handle the unknown nonlinear functions and unidentified actuator faults in the system.The piecewise controller and adaptive law constructed based on piecewise prescribed time-varying function and backstepping technique method establish the theoretical framework of practical prescribed-time tracking control,and extend the range of prescribed-time tracking control to infinity.Regardless of the initial conditions,the proposed control strategy can guarantee that all signals remain uniformly bounded within the practical prescribed time in the presence of unknown nonlinear item and time-varying actuator faults.Simulation example is presented to demonstrate the effectiveness of the proposed control strategy.

Backstepping adaptive fuzzy control of uncertain nonlinear systems against actuator faults

A class of unknown nonlinear systems subject to uncertain actuator faults and external disturbances will be studied in this paper with the help of fuzzy approximation theory. Using backstepping technique, a novel adaptive fuzzy control approach is proposed to accommodate the uncertain actuator faults during operation and deal with the external disturbances though the systems cannot be linearized by feedback. The considered faults are modeled as both loss of effectiveness and lock-in-place （stuck at some unknown place）. It is proved that the proposed control scheme can guarantee all signals of the closed-loop system to be semi-globally uniformly ultimately bounded and the tracking error between the system output and the reference signal converge to a small neighborhood of zero, though the nonlinear functions of the controlled system as well as the actuator faults and the external disturbances are all unknown. Simulation results demonstrate the effectiveness of the control approach.

Sensor Fault Diagnosis for a Class of Time Delay Uncertain Nonlinear Systems Using Neural Network

In this paper,a sliding mode observer scheme of sensor fault diagnosis is proposed for a class of time delay nonlinear systems with input uncertainty based on neural network.The sensor fault and the system input uncertainty are assumed to be unknown but bounded.The radial basis function (RBF) neural network is used to approximate the sensor fault.Based on the output of the RBF neural network,the sliding mode observer is presented.Using the Lyapunov method,a criterion for stability is given in terms of matrix inequality.Finally,an example is given for illustrating the availability of the fault diagnosis based on the proposed sliding mode observer.

Adaptive Fuzzy Dynamic Surface Control for Uncertain Nonlinear Systems

In this paper, a robust adaptive fuzzy dynamic surface control for a class of uncertain nonlinear systems is proposed. A novel adaptive fuzzy dynamic surface model is built to approximate the uncertain nonlinear functions by only one fuzzy logic system. The approximation capability of this model is proved and the model is implemented to solve the problem that too many approximators are used in the controller design of uncertain nonlinear systems. The shortage of ＂explosion of complexity＂ in backstepping design procedure is overcome by using the proposed dynamic surface control method. It is proved by constructing appropriate Lyapunov candidates that all signals of closed-loop systems are semi-globally uniformly ultimate bounded. Also, this novel controller stabilizes the states of uncertain nonlinear systems faster than the adaptive sliding mode controller （SMC）. Two simulation examples are provided to illustrate the effectiveness of the control approach proposed in this paper.

Non-intrusive hybrid interval method for uncertain nonlinear systems using derivative information

This paper proposes a new non-intrusive hybrid interval method using derivative information for the dynamic response analysis of nonlinear systems with uncertain-but- bounded parameters and/or initial conditions. This method provides tighter solution ranges compared to the existing polynomial approximation interval methods. Interval arith- metic using the Chebyshev basis and interval arithmetic using the general form modified affine basis for polynomials are developed to obtain tighter bounds for interval computation. To further reduce the overestimation caused by the ＂wrap- ping effect＂ of interval arithmetic, the derivative information of dynamic responses is used to achieve exact solutions when the dynamic responses are monotonic with respect to all the uncertain variables. Finally, two typical numerical examples with nonlinearity are applied to demonstrate the effective- ness of the proposed hybrid interval method, in particular, its ability to effectively control the overestimation for specific timepoints.

Controller design of uncertain nonlinear systems based on T-S fuzzy model

A robust control for uncertain nonlinear systems based on T-S fuzzy model is discussed in this paper. First, a T-S fuzzy system is adopted to model the uncertain nonlinear systems. Then, for the system with input variables adopting standard fuzzy partitions, the efficient maximal overlapped-rules group （EMORG） is presented, and a new sufficient condition to check the stability of T-S fuzzy system with uncertainty is derived, which is expressed in terms of Linear Matrix Inequalities. The derived stability condition, which only requires a local common positive definite matrix in each EMORG, can reduce the conservatism and difficulty in existing stability conditions. Finally, a simulation example shows the proposed approach is effective.

Active Disturbance Rejection Control for Uncertain Nonlinear Systems With Sporadic Measurements

This paper deals with the problem of active disturbance rejection control(ADRC)design for a class of uncertain nonlinear systems with sporadic measurements.A novel extended state observer(ESO)is designed in a cascade form consisting of a continuous time estimator,a continuous observation error predictor,and a reset compensator.The proposed ESO estimates not only the system state but also the total uncertainty,which may include the effects of the external perturbation,the parametric uncertainty,and the unknown nonlinear dynamics.Such a reset compensator,whose state is reset to zero whenever a new measurement arrives,is used to calibrate the predictor.Due to the cascade structure,the resulting error dynamics system is presented in a non-hybrid form,and accordingly,analyzed in a general sampled-data system framework.Based on the output of the ESO,a continuous ADRC law is then developed.The convergence of the resulting closed-loop system is proved under given conditions.Two numerical simulations demonstrate the effectiveness of the proposed control method.

Indirect Adaptive Fuzzy Output Feedback Control with Supervisory Controller for Uncertain Nonlinear Systems

In this paper, an indirect adaptive fuzzy output feedback controller with supervisory mode for a class of unknown nonlinear systems is developed. The proposed approach does not need the availability of the state variables, moreover, a supervisory controller is appended to the adaptive fuzzy controller to force the state to be within the constraint set. Therefore, if the adaptive fuzzy controller cannot maintain the stability, the supervisory controller starts to work to guarantee stability. On the other hand, if the adaptive fuzzy controller works well, the supervisory controller will be de-activated. The overall adaptive fuzzy control scheme guarantees the stability of the whole closed-loop systems. The simulation results confirm the effectiveness of the proposed method.

Disturbance observer based actor-critic learning control for uncertain nonlinear systems

This paper investigates the disturbance observer based actor-critic learning control for a class of uncertain nonlinear systems in the presence of unmodeled dynamics and time-varying disturbances.The proposed control algorithm integrates a filter-based design method with actor-critic learning architecture and disturbance observer to circumvent the unmodeled dynamic and the timevarying disturbance.To be specific,the actor network is employed to estimate the unknown system dynamic,the critic network is developed to evaluate the control performance,and the disturbance observer is leveraged to provide efficient estimation of the compounded disturbance which includes the time-varying disturbance and the actor-critic network approximation error.Consequently,highgain feedback is avoided and the improved tracking performance can be expected.Moreover,a composite weight adaptation law for actor network is constructed by utilizing two types of signals,the cost function and the modeling error.Eventually,theoretical analysis demonstrates that the developed controller can guarantee bounded stability.Extensive simulations and experiments on a robot manipulator are implemented to validate the performance of the resulted control strategy.

A Sliding Mode Observer for Uncertain Nonlinear Systems Based on Multiple Models Approach

This paper presents a method of state estimation for uncertain nonlinear systems described by multiple models approach. The uncertainties, supposed as norm bounded type, are caused by some parameters＇ variations of the nonlinear system. Linear matri~ inequalities （LMIs） have been established in order to ensure the stability conditions of the multiple observer which lead to determine the estimation gains. A sliding mode gain has been added in order to compensate the uncertainties. Numerical simulations through a state space model of a real process have been realized to show the robustness of the synthesized observer.

Robust adaptive control for uncertain nonlinear systems with unknown control directions and actuator nonlinearity

A robust adaptive control scheme is proposed for a class of uncertain nonlinear systems in strict feedback form with both unknown control directions and non-symmetric dead-zone nonlinearity based on backstepping design. The conditions that the dead-zone slopes and the boundaries are equal and symmetric are removed by simplifying nonlinear dead-zone input model, the assumption that the priori knowledge of the control directions to be known is eliminated by utilizing Nussbaum-type gain technique and neural networks （NN） approximation capability. The possible controller singularity problem and the effect of dead-zone input nonlinearity are avoided perfectly by combining integral Lyapunov design with sliding mode control strategy. All the signals in the closed-loop system are guaranteed to be semi-globally uniformly ultimately bounded and the tracking error of the system is proven to be converged to a small neighborhood of the origin. Simulation results demonstrate the effectiveness of the proposed control scheme.

Adaptive asymptotic fault-tolerant tracking of uncertain nonlinear systems with unknown control directions

In the article,the issues of asymptotic adaptive tracking control for the uncertain nonlinear systems in the presence of actuator faults and unknown control directions are investigated.By using the properties of the Nussbaum function and backstepping technique,the problems resulting from the unknown signs of the nonlinear control functions are circumvented successfully.Moreover,a new adaptive asymptotic tracking control method is presented with the fault-tolerant control framework,which is capable of realising zero-tracking performance.The stability of the controlled system is ensured through fractional Lyapunov stability analysis.Finally,the validity of the raised scheme is verified by a simulation example.

Adaptive fuzzy control for uncertain nonlinear systems

In this paper,a survey of adaptive fuzzy for uncertain nonlinear systems is presented.The first part introduces adaptive fuzzy control emergence and some typical control methods for uncertain nonlinear systems with matching conditions(single-input singleoutput systems,multi-input multi-output systems).The last part presents the adaptive fuzzy state feedback and output-feedback control methods for uncertain nonlinear systems with non-matching conditions based on the backstepping technique,including strictfeedback systems,pure-feedback systems and non-strict-feedback systems.

Prescribed Performance Finite-Time Tracking Control for Uncertain Nonlinear Systems

This work investigates the finite-time tracking control problem for a class of uncertain strict-feedback nonlinear systems from a new perspective. First, a novel concept called finite-time performance function (FTPF) is defined. Further, a new sufficien t condition of finite-time st ability is derived and the tracking error can converge to a predefined region within a finite-time interval. The design process of the proposed technique is simpler. Finally, four simulation examples are carried out to illustrate the effectiveness of presented method.

Evaluation of fault diagnosability for nonlinear uncertain systems with multiple faults occurring simultaneously

Up to present,the problem of the evaluation of fault diagnosability for nonlinear systems has been investigated by many researchers.However,no attempt has been done to evaluate the diagnosability of multiple faults occurring simultaneously for nonlinear systems.This paper proposes a method based on differential geometry theories to solve this problem.Then the evaluation of fault diagnosability for affine nonlinear systems with multiple faults occurring simultaneously is achieved.To deal with the effect of control laws on the evaluation results of fault diagnosability,a design scheme of the evaluation of fault diagnosability is proposed.Then the influence of uncertainties on the evaluation results of fault diagnosability for affine nonlinear systems with multiple faults occurring simultaneously is analyzed.The numerical simulation results are obtained to show the effectiveness of the proposed evaluation scheme of fault diagnosability.

Robust Neural Control of Discrete Time Uncertain Nonlinear Systems Using Sliding Mode Backpropagation Training Algorithm

This work deals with robust inverse neural control strategy for a class of single-input single-output(SISO) discrete-time nonlinear system affected by parametric uncertainties. According to the control scheme, in the first step, a direct neural model(DNM)is used to learn the behavior of the system, then, an inverse neural model(INM) is synthesized using a specialized learning technique and cascaded to the uncertain system as a controller. In previous works, the neural models are trained classically by backpropagation(BP) algorithm. In this work, the sliding mode-backpropagation(SM-BP) algorithm, presenting some important properties such as robustness and speedy learning, is investigated. Moreover, four combinations using classical BP and SM-BP are tested to determine the best configuration for the robust control of uncertain nonlinear systems. Two simulation examples are treated to illustrate the effectiveness of the proposed control strategy.

A trigonometric interval method for dynamic response analysis of uncertain nonlinear systems

This paper proposes a new non-intrusive trigonometric polynomial approximation interval method for the dynamic response analysis of nonlinear systems with uncertain-but-bounded parameters and/or initial conditions.This method provides tighter solution ranges compared to the existing approximation interval methods.We consider trigonometric approximation polynomials of three types:both cosine and sine functions,the sine function,and the cosine function.Thus,special interval arithmetic for trigonometric function without overestimation can be used to obtain interval results.The interval method using trigonometric approximation polynomials with a cosine functional form exhibits better performance than the existing Taylor interval method and Chebyshev interval method.Finally,two typical numerical examples with nonlinearity are applied to demonstrate the effectiveness of the proposed method.

Direct adaptive control for nonlinear uncertain system based on control Lyapunov function method

The problem of adaptive stabilization of a class of multi-input nonlinear systems with unknown parameters both in the state vector-field and the input vector-field has been considered. By employing the control Lyapunov function method, a direct adaptive controller is designed to complete the global adaptive stability of the uncertain system. At the same time, the controller is also verified to possess the optimality. Example and simulations are provided to illustrate the effectiveness of the proposed method.