An explicit-time and explicit-accuracy control for a state-constrained nonstrict-feedback uncertain system based on adaptive fuzzy dynamic-approximation

This article proposes a novel explicit-time and explicit-accuracy adaptive fuzzy control for a state-constrained nonlinear nonstrict-feedback uncertain system. This method can explicitly parameterize the upper bound of settling-time with low initial control input under a bounded initial condition. Meanwhile, this method can also explicitly parameterize the upper bound of accuracy while achieving low control input based on the adaptive fuzzy dynamic-approximation theorem. Firstly, a novel generalized explicit-time stability system is proposed by introducing the boundary gain term to render the time-parameter explicit, this method can solve the input conservatism problem caused by the unbounded-state gain term of traditional fixed/prdefined-time function. Then, according to the universal fuzzy approximation theorem, the novel dynamic relationship of adaptive fuzzy logic system between approximation error and adaptive parameters is presented. This relationship can lead to the adaptive fuzzy dynamic-approximation theorem, and an adaptive law designed by this theorem can realize the Lyapunov stability of adaptive control system under a Lasalle invariant set. In the end, a novel adaptive fuzzy control scheme is proposed by the generalized explicit-time function and adaptive fuzzy dynamic-approximation theorem. This scheme can achieve the explicit-time stability by the human-like activation function, and the accuracy can be parameterized by Lyapunov synthesis. Compared with other existing fixed/prdefined-time adaptive fuzzy control methods, the proposed explicit-time and explicit-accuracy controller achieves a significant reduction in the initial control input. Theoretical analysis and simulation results validate the effectiveness of the proposed method.     

Global practical tracking for nonlinear systems with uncertain dead-zone input via output feedback

In this paper, global practical tracking is investigated via output feedback for a class of uncertain nonlinear systems subject to unknown dead-zone input. The nonlinear systems under consideration allow more general growth restriction, where the growth rate includes unknown constant and output polynomial function. Without the precise priori knowledge of dead-zone characteristic, an input-driven observer is designed by introducing a novel dynamic gain. Based on non-separation principle, a universal adaptive output feedback controller is proposed by combining dynamic high-gain scaling approach with backstepping method. The controller proposed guarantees that the closed-loop output can track any smooth and bounded reference signal by any small pre-given tracking error, while all closed-loop signals are globally bounded. Finally, simulation examples are given to illustrate the effectiveness of our dynamic output feedback control scheme.     

Adaptive sliding mode control for uncertain nonlinear multi-agent tracking systems subject to node failures

The tracking problem of high-order nonlinear multi-agent systems (MAS) with uncertainty is solved by designing adaptive sliding mode control. During the tracking process, node failures are possible to occur, a new agent replaces the failed one. Firstly, a distributed nonsingular terminal sliding mode(NTSM) control scheme is designed for the tracking agents. A novel continuous function is designed in the NTSM to eliminate the singularity and meanwhile guarantee the estimation of finite convergence time. Secondly, the unknown uncertainties in the tracking agents are compensated by proposing an adaptive mechanism in the NTSM. The adaptive mechanism adjusts the control input through estimating the derivative bound of the unknown uncertainties dynamically. Thirdly, the tracking problem with node failures and agent replacements is further investigated. Based on the constructed impulsive-dependent Lyapunov function, it is proved that the overall system will track the target in finite time even with increase of jump errors. Finally, comparison simulations are conducted to illustrate the effectiveness of proposed adaptive nonsingular terminal sliding mode control method for tracking systems suffering node failures.     

An adaptive iterative learning algorithm for boundary control of a coupled ODE–PDE two-link rigid–flexible manipulator

To perform repetitive tasks, this paper proposes an adaptive boundary iterative learning control (ILC) scheme for a two-link rigid–flexible manipulator with parametric uncertainties. Using Hamilton?s principle, the coupled ordinary differential equation and partial differential equation (ODE–PDE) dynamic model of the system is established. In order to drive the joints to follow desired trajectory and eliminate deformation of flexible beam simultaneously, boundary control strategy is added based on the conventional joints torque control. The adaptive iterative learning algorithm for boundary control scheme includes a proportional-derivative (PD) feedback structure and an iterative term. This novel controller is designed to deal with the unmodeled dynamics and other unknown external disturbances. Numerical simulations are provided to verify the performance of proposed controller in MATLAB.     

Adaptive distributed tracking control for non-affine multi-agent systems with state constraints and dead-zone input

In this paper, an adaptive distributed control protocol is proposed for non-affine multi-agent system with nonlinear dead-zone input and state constraints under the condition of directed topology. In order to overcome the difficulties caused by non-affine terms in the system, the nonlinear dynamics system is transformed. Then, the neural network technology is introduced to approximate the unknown non-affine terms for the obtained system. State constraints and dead-zone input are common system problems. In order to solve these problems, the barrier Lyapunov function is introduced in this paper. According to the barrier Lyapunov function and backstepping method, an adaptive distributed controller is designed, so that state variables do not violate constraint bounds and the system is not affected by dead-zone input. By Lyapunov stability theory, it is proved that the signals of each follower are cooperative semi-global uniform ultimate boundedness (CSUUB), and the outputs of the followers track the output of the leader. Simulation example is given to demonstrate the effectiveness of the proposed method.     

Behavior learning based distributed tracking control for human-in-the-loop multi-agent systems

In this study, the distributed tracking problem for human-in-the-loop multi-agent systems (HiTL MASs) has been investigated. First, we construct an HiTL MAS model with a non-autonomous leader which can receive the control signal from a human operator and generate the desired trajectory. The human control signal is assumed to be generated by a leader’s state feedback control law with an unknown gain matrix that represents the control behavior of the human operator. Then, we propose a fully distributed adaptive control method that enables all followers to simultaneously track the human-controlled leader and online learn the unknown human operator’s feedback gain matrix. Furthermore, the parameter estimation error is also discussed, and all followers will learn the true value of the human operator’s feedback gain matrix when the state of the leader satisfies the persistent excitation (PE) condition. Moreover, a novel distributed adaptive control law is developed for each follower to remove the PE condition by utilizing the concurrent learning (CL) technique. Finally, simulated examples demonstrating the effectiveness of the proposed methodologies are presented.     

Discrete-time adaptive fuzzy speed regulation control for induction motors with input saturation via command filtering

A discrete-time adaptive fuzzy control method is introduced to achieve the speed regulation for induction motors (IMs) with input saturation via command filtering in this paper. First, the continuous model of IMs drive system is transformed into discrete-time form by using Euler formula. Then, the fuzzy logic systems are used to approximate the unknown nonlinear functions in the discrete-time drive system. In addition, the command filtering control method is introduced to overcome the “explosion of complexity” problem in the design process of traditional backstepping method. It is verified that all the closed-loop signals are bounded and the outputs can track the given reference signals well. Finally, simulation results illustrate the validity of the discrete-time control method.     

Online adaptive policy iteration based fault-tolerant control algorithm for continuous-time nonlinear tracking systems with actuator failures

In this paper, a novel tracking control scheme for continuous-time nonlinear affine systems with actuator faults is proposed by using a policy iteration (PI) based adaptive control algorithm. According to the controlled system and desired reference trajectory, a novel augmented tracking system is constructed and the tracking control problem is converted to the stabilizing issue of the corresponding error dynamic system. PI algorithm, generally used in optimal control and intelligence technique fields, is an important reinforcement learning method to solve the performance function by critic neural network (NN) approximation, which satisfies the Lyapunov equation. For the augmented tracking error system with actuator faults, an online PI based fault-tolerant control law is proposed, where a new tuning law of the adaptive parameter is designed to tolerate four common kinds of actuator faults. The stability of the tracking error dynamic with actuator faults is guaranteed by using Lyapunov theory, and the tracking errors satisfy uniformly bounded as the adaptive parameters get converged. Finally, the designed fault-tolerant feedback control algorithm for nonlinear tracking system with actuator faults is applied in two cases to track the desired reference trajectory, and the simulation results demonstrate the effectiveness and applicability of the proposed method.     

Funnel-based adaptive fuzzy finite-time control for non-affine nonlinear systems preceded by unknown actuators

In this paper, an adaptive finite-time funnel control for non-affine strict-feedback nonlinear systems preceded by unknown non-smooth input nonlinearities is proposed. The input nonlinearities include backlash-like hysteresis and dead-zone. Unknown nonlinear functions are handled using fuzzy logic systems (FLS), based on the universal approximation theorem. An improved funnel error surface is utilized to guarantee the steady-state and transient predetermined performances while the differentiability problem in the controller design is averted. Using the Lyapunov approach, all the adaptive laws are extracted. In addition, an adaptive continuous robust term is added to the control input to relax the assumption of knowing the bounds of uncertainties. All the signals in the closed-loop system are shown to be semi-globally practically finite-time bounded with predetermined performance for output tracking error. Finally, comparative numerical and practical examples are provided to authenticate the efficacy and applicability of the proposed scheme.     

Adaptive coordinated attitude control for spacecraft formation with saturating actuators and unknown inertia

In this paper, an adaptive attitude coordination control problem for spacecraft formation flying is investigated under a general directed communication topology containing a directed spanning tree with a leader as the root. In the presence of unknown time-varying inertia, persistent external disturbances and control input saturation, a novel robust adaptive coordinated attitude control algorithm with no prior knowledge of inertia for spacecraft is proposed to coordinately track the common time-varying reference states. Aiming at optimizing the control algorithm, a dynamic adjustment function is introduced to adjust the control gain according to the tracking errors. The effectiveness of the proposed control scheme is illustrated through numerical simulation results.     

Adaptive fuzzy output feedback controller design for a HAGC system with input saturation and output error constraints

The comprehensive effect of external disturbance, measurement delay, unmeasurable states and input saturation makes the difficulties and challenges for a HAGC system. In this paper, an adaptive fuzzy output feedback control scheme is designed for a HAGC system under the simultaneous consideration of those factors. At the first place, by state transformation technique, the dynamic model of a HAGC system is simply expressed as a strict feedback form, where measurement delay is converted into input delay. Then, an auxiliary system is employed to compensate for the effect of input delay. Furthermore, an asymmetric barrier Lyapunov function (BLF) is constructed to ensure the output error constraint requirement of thickness error and the fuzzy observer is established to solve unmeasurable states, unknown nonlinear functions at the same time. With the aid of backstepping method, adaptive fuzzy controller is developed to assure that the closed-loop system is semi-globally boundedness and the output error of thickness error doesn’t violate its constraint. At the end, compared simulations are carried out to verify the efficiency of the proposed control scheme.     

Approximation-based decentralized output-feedback control for uncertain stochastic interconnected nonlinear time-delay systems with input delay and asymmetric input saturation

This paper proposes an adaptive observer-based neural controller for a class of uncertain large-scale stochastic nonlinear systems with actuator delay and time-delay nonlinear interactions, where drift and diffusion terms contain all state variables of their own subsystem. First, a state observer is established for estimating the unmeasured states, and a predictor-like term is utilized to transform the input delayed system into the delay-free system. Second, novel appropriate Lyapunov–Krasovskii functionals are used to compensate the time-delay terms, and neural networks are employed to approximate unknown nonlinear functions. At last, an output-feedback adaptive neural control scheme is constructed by using Lyapunov stability theory and backstepping technique. It is shown that the designed neural controller can ensure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking error is driven to a small neighborhood of the origin. The simulation results are presented to further show the effectiveness of the proposed approach.     

一类非线性不确定多时滞中立型系统的鲁棒自适应控制（英文）

针对一类不确定多时滞中立型非线性系统，在其非线性不确定项的范数有界，但其上界未知的情况下，论证了自适应鲁棒控制器存在的条件，并给出了能适应未知参数变化且使得最终闭环系统一致最终有界的鲁棒控制律的设计方法。最后，具体算例的仿真结果说明了此法的有效性。     

Finite-time event-triggered containment control of multiple Euler–Lagrange systems with unknown control coefficients

This paper researches the finite-time event-triggered containment control problem of multiple Euler–Lagrange systems (ELSs) with unknown control coefficients. To realize an accurate convergence time, the settling-time performance function is employed to ensures the steady-state and dynamic properties of the containment errors in the resulting system. Meanwhile, to handle unknown control coefficients, adaptive neural networks (ANNs) with an additional saturated term are designed, which removes the requirement of full rank control coefficients in traditional control methods. By establishing an event-triggered mechanism, a novel finite-time event-triggered containment control law is designed, which yields the semi-global practical finite-time stable (SGPFS) of the resulting closed-loop system without Zeno phenomenon according to the finite-time stability criterion. The effectiveness of the designed methodology is verified by simulation.     

Adaptive iterative learning protocol design for nonlinear multi-agent systems with unknown control direction

This paper investigates a new adaptive iterative learning control protocol design for uncertain nonlinear multi-agent systems with unknown gain signs. Based on Nussbaum gain, adaptive iterative learning control protocols are designed for each follower agent and the adaptive laws depend on the information available from the agents in the neighbourhood. The proper protocols guarantee each follower agent track the leader perfectly on the finite time interval and the Nussbaum-type item can seek control direction adaptively. Furthermore, the formation problem is studied as an extension. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method in this article.     

Adaptive neural network dynamic surface control of uncertain strict-feedback nonlinear systems with unknown control direction and unknown actuator fault

In this paper, the tracking control problem of a class of uncertain strict-feedback nonlinear systems with unknown control direction and unknown actuator fault is studied. By using the neural network control approach and dynamic surface control technique, an adaptive neural network dynamic surface control law is designed. Based on the neural network approximator, the uncertain nonlinear dynamics are approximated. Using the dynamic surface control technique, the complexity explosion problems in the design of virtual control laws and adaptive updating laws can be overcome. Moreover, to solve the unknown control direction and unknown actuator fault problems, a type of Nussbaum gain function is incorporated into the recursive design of dynamic surface control. Based on the designed adaptive control law, it can be confirmed that all of the signals in the closed-loop system are semi-global bounded, and the convergence of the tracking error to the specified small neighborhood of the origin could be ensured by adjusting the designing parameters. Finally, two examples are provided to demonstrate the effectiveness of the proposed adaptive control law.     

A new method for fault prediction of model-unknown nonlinear system

In this paper, the subspace identification based robust fault prediction method which combines optimal track control with adaptive neural network compensation is presented for prediction the fault of unknown nonlinear system. At first, the local approximate linear model based on input-output of unknown system is obtained by subspace identification. The optimal track control is adopted for the approximate model with some unknown uncertainties and external disturbances. An adaptive RBF neural network is added to the track control in order to guarantee the robust tracking ability of the observation system. The effect of the system nonlinearity and the error caused by subspace modeling can be overcome by adaptive tuning of the weights of the RBF neural network online without any requisition of constraint or matching conditions. The stability of the designed closed-loop system is thus proved. A density function estimation method based on state forecasting is then used to judge the fault. The proposed method is applied to fault prediction of model-unknown fighter F-8II of China airforce and the simulation results show that the proposed method can not only predict the fault, but has strong robustness against uncertainties and external disturbances.     

Command filtered robust adaptive NN control for a class of uncertain strict-feedback nonlinear systems under input saturation

This paper develops a robust adaptive neural network (NN) tracking control scheme for a class of strict-feedback nonlinear systems with unknown nonlinearities and unknown external disturbances under input saturation. The radial basis function NNs with minimal learning parameter (MLP) are employed to online approximate the uncertain system dynamics. The adaptive laws are designed to online update the upper bound of the norm of ideal NN weight vectors, and the sum of the bounds of NN approximation errors and external disturbances, respectively. An auxiliary dynamic system is constructed to generate the augmented error signals which are used to modify the adaptive laws for preventing the destructive action due to the input saturation. Moreover, the command filtering backstepping control method is utilized to overcome the shortcoming of dynamic surface control method, the tracking-differentiator-based control method, etc. Our proposed scheme is qualified for simultaneously dealing with the input saturation effect, the heavy computational burden and the “explosion of complexity” problems. Theoretical analysis illuminates that our scheme ensures the boundedness of all signals in the closed-loop systems. Simulation results on two examples verify the effectiveness of our developed control scheme.     

Adaptive sliding mode control for persistent dwell-time switched nonlinear systems with matched/mismatched uncertainties and its application

In this paper, the adaptive sliding mode control issue for switched nonlinear systems with matched and mismatched uncertainties is addressed, where the persistent dwell-time switching rule is introduced to describe the switching of parameters. Besides, considering the case that the upper bound of the matched uncertainty is unknown, the purpose of this paper is to utilize an adaptive control method to estimate its upper bound parameters. To begin with, a linear sliding surface is constructed, and then the reduced-order sliding mode dynamics can be obtained through a reduced-order method. Next, sufficient conditions can be derived based on the Lyapunov stability and the persistent dwell-time switching analysis techniques ensuring that the reduced-order sliding mode dynamics is globally uniformly exponentially stable. Moreover, a switched adaptive sliding mode control law is designed, which can not only ensure the reachability of the sliding surface but also estimate the upper bound parameters of the matched uncertainty. Finally, a numerical example and a circuit model are introduced to verify the effectiveness of the proposed method.     

基于逆系统的变轨迹迭代学习控制

针对一类未知非线性时变系统,本文提出一种不同次迭代运行过程中期望轨迹可变的迭代学习控制算法。该算法利用高斯径向基网络逼近系统逆的未知参数,并采用迭代学习的方式修正网络逼近的系数,然后结合变结构技术设计控制律。收敛性分析表明,随着迭代次数的增加,逼近系数与最佳系数的差异逐渐减小。最后,在机械臂上的仿真验证了算法的有效性。