Adaptive tracking control of uncertain MIMO nonlinear systems with time-varying delays and unmodeled dynamics

In this paper, adaptive neural tracking control is proposed based on radial basis function neural networks (RBFNNs) for a class of multi-input multi-output (MIMO) nonlinear systems with completely unknown control directions, unknown dynamic disturbances, unmodeled dynamics, and uncertainties with time-varying delay. Using the Nussbaum function properties, the unknown control directions are dealt with. By constructing appropriate Lyapunov-Krasovskii functionals, the unknown upper bound functions of the time-varying delay uncertainties are compensated. The proposed control scheme does not need to calculate the integral of the delayed state functions. Using Young s inequality and RBFNNs, the assumption of unmodeled dynamics is relaxed. By theoretical analysis, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded.     

Adaptive fuzzy tracking control for a class of uncertain MIMO nonlinear systems using disturbance observer

In this paper,the adaptive fuzzy tracking control is proposed for a class of multi-input and multioutput(MIMO)nonlinear systems in the presence of system uncertainties,unknown non-symmetric input saturation and external disturbances.Fuzzy logic systems(FLS)are used to approximate the system uncertainty of MIMO nonlinear systems.Then,the compound disturbance containing the approximation error and the timevarying external disturbance that cannot be directly measured are estimated via a disturbance observer.By appropriately choosing the gain matrix,the disturbance observer can approximate the compound disturbance well and the estimate error converges to a compact set.This control strategy is further extended to develop adaptive fuzzy tracking control for MIMO nonlinear systems by coping with practical issues in engineering applications,in particular unknown non-symmetric input saturation and control singularity.Within this setting,the disturbance observer technique is combined with the FLS approximation technique to compensate for the efects of unknown input saturation and control singularity.Lyapunov approach based analysis shows that semi-global uniform boundedness of the closed-loop signals is guaranteed under the proposed tracking control techniques.Numerical simulation results are presented to illustrate the efectiveness of the proposed tracking control schemes.     

Adaptive tracking control of uncertain MIMO nonlinear systems with input constraints

In this paper, adaptive tracking control is proposed for a class of uncertain multi-input and multi-output nonlinear systems with non-symmetric input constraints. The auxiliary design system is introduced to analyze the effect of input constraints, and its states are used to adaptive tracking control design. The spectral radius of the control coefficient matrix is used to relax the nonsingular assumption of the control coefficient matrix. Subsequently, the constrained adaptive control is presented, where command filters are adopted to implement the emulate of actuator physical constraints on the control law and virtual control laws and avoid the tedious analytic computations of time derivatives of virtual control laws in the backstepping procedure. Under the proposed control techniques, the closed-loop semi-global uniformly ultimate bounded stability is achieved via Lyapunov synthesis. Finally, simulation studies are presented to illustrate the effectiveness of the proposed adaptive tracking control.     

Adaptive dynamic surface control for MIMO nonlinear time-varying systems with prescribed tracking performance

In this paper, an adaptive dynamic surface control scheme is proposed for a class of multi-input multi-output (MIMO) nonlinear time-varying systems. By fusing a bound estimation approach, a smooth function and a time-varying matrix factorisation, the obstacle caused by unknown time-varying parameters is circumvented. The proposed scheme is free of the problem of explosion of complexity and needs only one updated parameter at each design step. Moreover, all tracking errors can converge to predefined arbitrarily small residual sets with a prescribed convergence rate and maximum overshoot. Such features result in a simple adaptive controller which can be easily implemented in applications with less computational burden and satisfactory tracking performance. Simulation results are presented to illustrate the effectiveness of the proposed scheme.     

MIMO非仿射非线性系统的自适应模糊控制

针对一类多输入多输出非仿射非线性系统,设计了一种自适应模糊H∞控制方案,该方案把自适应模糊控制和高增益观测器结合起来.利用多变量的隐函数定理,证明了非仿射系统控制器的存在性.通过设计高增益观测器,解决了系统的状态不可测量问题,实现系统的输出反馈控制,模糊自适应控制增强了系统在线逼近干扰及处理系统不确定的能力.仿真结果表明了控制方案的有效性及优越性.     

Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics

A practical design method is developed for cooperative tracking control of higher-order nonlinear systems with a dynamic leader. The communication network is a weighted directed graph with a fixed topology. Each follower node is modeled by a higher-order integrator incorporating with unknown nonlinear dynamics and an unknown disturbance. The leader node is modeled as a higher-order nonautonomous nonlinear system. It acts as a command generator giving commands only to a small portion of the networked group. A robust adaptive neural network controller is designed for each follower node such that all follower nodes ultimately synchronize to the leader node with bounded residual errors. Moreover, these controllers are distributed in the sense that the controller design for each follower node only requires relative state information between itself and its neighbors. A simulation example demonstrates the effectiveness of the algorithm.     

Output tracking control of MIMO fuzzy nonlinear systems using variable structure control approach

The output tracking control problem for nonlinear systems in the presence of both parameter perturbations and external disturbances is studied. Our approach is based on the Takagi-Sugeno (T-S) fuzzy modeling method and a variable structure control (VSC) technique. Therefore, the systems considered are not and need not be in the triangular and parametric strict-feedback form, which are prevalent among adaptive model following control for nonlinear systems, or in the normal form, which pervades almost all existing results in neuro-fuzzy model following control approach. We first study the problem of stabilization of T-S fuzzy systems by using a VSC technique. A method for the design of a switching surface based on linear matrix inequalities is developed and a stabilizing controller based on a reaching law concept in the presence of both parameter perturbations and external disturbances is proposed. Then, the method is extended to design controllers for output tracking of T-S fuzzy nonlinear systems in two cases, i.e. systems which possess the so-called strong passive subsystems and strong stable zero dynamics, respectively. Finally, illustrative examples are presented to demonstrate the whole design procedure from the original nonlinear systems to their fuzzification and finally to the realization of the desired controllers. Simulation results show that the goal of output tracking can be achieved by the proposed controllers.     

Adaptive neural control of uncertain MIMO nonlinear systems

In this paper, adaptive neural control schemes are proposed for two classes of uncertain multi-input/multi-output (MIMO) nonlinear systems in block-triangular forms. The MIMO systems consist of interconnected subsystems, with couplings in the forms of unknown nonlinearities and/or parametric uncertainties in the input matrices, as well as in the system interconnections without any bounding restrictions. Using the block-triangular structure properties, the stability analyses of the closed-loop MIMO systems are shown in a nested iterative manner for all the states. By exploiting the special properties of the affine terms of the two classes of MIMO systems, the developed neural control schemes avoid the controller singularity problem completely without using projection algorithms. Semiglobal uniform ultimate boundedness (SGUUB) of all the signals in the closed-loop of MIMO nonlinear systems is achieved. The outputs of the systems are proven to converge to a small neighborhood of the desired trajectories. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters. The proposed schemes offer systematic design procedures for the control of the two classes of uncertain MIMO nonlinear systems. Simulation results are presented to show the effectiveness of the approach.     

Adaptive neural network control for strict-feedback nonlinear systems using backstepping design

This paper focuses on adaptive control of strict-feedback nonlinear systems using multilayer neural networks (MNNs). By introducing a modified Lyapunov function, a smooth and singularity-free adaptive controller is firstly designed for a first-order plant. Then, an extension is made to high-order nonlinear systems using neural network approximation and adaptive backstepping techniques. The developed control scheme guarantees the uniform ultimate boundedness of the closed-loop adaptive systems. In addition, the relationship between the transient performance and the design parameters is explicitly given to guide the tuning of the controller. One important feature of the proposed NN controller is the highly structural property which makes it particularly suitable for parallel processing in actual implementation. Simulation studies are included to illustrate the effectiveness of the proposed approach.     

Adaptive PI Hermite neural control for MIMO uncertain nonlinear systems

This paper presents an adaptive PI Hermite neural control (APIHNC) system for multi-input multi-output (MIMO) uncertain nonlinear systems. The proposed APIHNC system is composed of a neural controller and a robust compensator. The neural controller uses a three-layer Hermite neural network (HNN) to online mimic an ideal controller and the robust compensator is designed to eliminate the effect of the approximation error introduced by the neural controller upon the system stability in the Lyapunov sense. Moreover, a proportional–integral learning algorithm is derived to speed up the convergence of the tracking error. Finally, the proposed APIHNC system is applied to an inverted double pendulums and a two-link robotic manipulator. Simulation results verify that the proposed APIHNC system can achieve high-precision tracking performance. It should be emphasized that the proposed APIHNC system is clearly and easily used for real-time applications.     

Event-triggered adaptive fuzzy tracking control of nonlinear MIMO systems

This paper addresses the problem of an adaptive fuzzy event-triggered control (ETC) for uncertain multi-input and multi-output nonlinear systems. To reduce the communication burden of the network control systems, a novel state-dependent event-triggering condition is designed to decide when to update the controllers. By combining the backstepping and event-trigged techniques, the adaptive fuzzy ETC strategies are developed and the resulting closed-loop system is semi-global bounded. Finally, the analytical results are substantiated using simulation studies.     

一类不确定非线性MIMO系统的神经网络输出反馈跟踪控制

针对一类具有外部干扰的不确定仿射非线性MIMO系统提出了一种神经网络输出反馈跟踪控制方法. 在仅输出可测的情况下, 控制律和神经网络权值更新律中仅用到输出误差, 无需设计状态观测器或加入低通滤波器使得估计误差动态满足严格正实条件. 为抑制外部干扰和子系统间的交叉耦合及神经网络逼近误差, 在控制律中加入鲁棒控制项. 基于Lyapunov稳定性定理证明了系统的稳定性及信号的有界性. 仿真例子证实了所提方法的可行性.     

Adaptive prescribed performance tracking control for strict‐feedback nonlinear systems with zero dynamics

This paper focuses on the adaptive tracking control problem for strict‐feedback nonlinear systems with zero dynamics via prescribed performance. Based on polynomial fitting, an adjustable performance function is firstly proposed, whose parameters can be adjusted in real time according to the tracking error. Furthermore, an adaptive prescribed performance tracking controller is constructed via the backstepping method, which guarantees that all the states in the closed‐loop system are bounded. Meanwhile, the output tracking error falls within an adjustable performance boundary and asymptotically converges to zero. Simulation comparison demonstrates the advantages of the developed controller as follows: (1) the parameters of the adjustable performance function are adjusted online according to the tracking errors for a faster convergent performance boundary; (2) the steady‐state performance of the system is further optimized simultaneously.     

多输入多输出多重时延非线性系统的自适应模糊控制

针对多输入多输出多重时延非线性系统,提出了一种自适应模糊跟踪控制方案．该方案有机综合了自适应控制和H∞控制.文中构建了一种自适应时延模糊逻辑系统用来逼近有多重时延的未知函数;设计了H∞补偿器来抵消模糊逼近误差和外部扰动．根据跟踪误差给出了参数调节规律．构造了包含时延的李雅普诺夫函数,从而证明了误差闭环系统满足期望的H∞跟踪性能．仿真结果表明了该方案的可行性．     

多输入多输出多重时延非线性系统的白适应模糊控制

针对多输入多输出多重时延非线性系统,提出了一种自适应模糊跟踪控制方案.该方案有机综合了自适应控制和H∞控制.文中构建了一种自适应时延模糊逻辑系统用来逼近有多重时延的未知函数;设计了H∞补偿器来抵消模糊逼近误差和外部扰动.根据跟踪误差给出了参数调节规律.构造了包含时延的李雅普诺夫函数,从而证明了误差闭环系统满足期望的H∞跟踪性能.仿真结果表明了该方案的可行性.     

Adaptive tracking control of nonlinear systems with dynamic uncertainties using neural network

In this paper, an adaptive neural tracking control approach is proposed for a class of nonlinear systems with dynamic uncertainties. The radial basis function neural networks (RBFNNs) are used to estimate the unknown nonlinear uncertainties, and then a novel adaptive neural scheme is developed, via backstepping technique. In the controller design, instead of using RBFNN to approximate each unknown function, we lump all unknown functions into a suitable unknown function that is approximated by only a RBFNN in each step of the backstepping. It is shown that the designed controller can guarantee that all signals in the closed-loop system are semi-globally bounded and the tracking error finally converges to a small domain around the origin. Two examples are given to demonstrate the effectiveness of the proposed control scheme.     

Adaptive neural control for MIMO nonlinear systems with state time-varying delay

In this paper,adaptive neural control is proposed for a class of multi-input multi-output(MIMO)nonlinear unknown state time-varying delay systems in block-triangular control structure.Radial basis function(RBF)neural networks (NNs)are utilized to estimate the unknown continuous functions.The unknown time-varying delays are compensated for using integral-type Lyapunov-Krasovskii functionals in the design.The main advantage of our result not only efficiently avoids the controller singularity,but also relaxes the restriction on unknown virtual control coefficients.Boundedness of all the signals in the closed-loop of MIMO nonlinear systems is achieved,while The outputs of the systems are proven to converge to a small neighborhood of the desired trajectories.The feasibility is investigated by two simulation examples.     

Observer-based adaptive fuzzy quantized tracking DSC design for MIMO nonstrict-feedback nonlinear systems

Neural Computing and Applications - This paper concerned with the problem of observer-based adaptive fuzzy quantized tracking dynamic surface control (DSC) is investigated for the uncertain...     

Novel adaptive neural control design for nonlinear MIMO time-delay systems

In this paper, we address the problem of adaptive neural control for a class of multi-input multi-output (MIMO) nonlinear time-delay systems in block-triangular form. Based on a neural network (NN) online approximation model, a novel adaptive neural controller is obtained by constructing a novel quadratic-type Lyapunov-Krasovskii functional, which not only efficiently avoids the controller singularity, but also relaxes the restriction on unknown virtual control coefficients. The merit of the suggested controller design scheme is that the number of online adapted parameters is independent of the number of nodes of the neural networks, which reduces the number of the online adaptive learning laws considerably. The proposed controller guarantees that all closed-loop signals remain bounded, while the output tracking error dynamics converges to a neighborhood of the origin. A simulation example is given to illustrate the design procedure and performance of the proposed method.     

Adaptive neural tracking control of a class of MIMO pure-feedback time-delay nonlinear systems with input saturation

Considering interconnections among subsystems, we propose an adaptive neural tracking control scheme for a class of multiple-input-multiple-output (MIMO) non-affine pure-feedback time-delay nonlinear systems with input saturation. Neural networks (NNs) are employed to approximate unknown functions in the design procedure, and the separation technology is introduced here to tackle the problem induced from unknown time-delay items. The adaptive neural tracking control scheme is constructed by combining Lyapunov–Krasovskii functionals, NNs, the auxiliary system, the implicit function theory and the mean value theorem along with the dynamic surface control technique. Also, it is proven that the strategy guarantees tracking errors converge to a small neighbourhood around the origin by appropriate choice of design parameters and all signals in the closed-loop system uniformly ultimately bounded. Numerical simulation results are presented to demonstrate the effectiveness of the proposed control strategy.