Adaptive fuzzy dynamic surface control for a class of perturbed nonlinear time-varying delay systems with unknown dead-zone

In this paper,adaptive dynamic surface control(DSC) is developed for a class of nonlinear systems with unknown discrete and distributed time-varying delays and unknown dead-zone.Fuzzy logic systems are used to approximate the unknown nonlinear functions.Then,by combining the backstepping technique and the appropriate Lyapunov-Krasovskii functionals with the dynamic surface control approach,the adaptive fuzzy tracking controller is designed.Our development is able to eliminate the problem of "explosion of complexity" inherent in the existing backstepping-based methods.The main advantages of our approach include:1) for the n-th-order nonlinear systems,only one parameter needs to be adjusted online in the controller design procedure,which reduces the computation burden greatly.Moreover,the input of the dead-zone with only one adjusted parameter is much simpler than the ones in the existing results;2) the proposed control scheme does not need to know the time delays and their upper bounds.It is proven that the proposed design method is able to guarantee that all the signals in the closed-loop system are bounded and the tracking error is smaller than a prescribed error bound,Finally,simulation results demonstrate the effectiveness of the proposed approach.     

Adaptive prescribed performance control for switched nonlinear systems with input saturation

In this paper, an adaptive prescribed performance output-feedback control scheme is proposed for a class of switched nonlinear systems with input saturation. The MT-filters are employed to estimate the unmeasured states and the unknown functions are approximated by the radial basis function neural networks in controller design procedure. It is proved that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error satisfies the prescribed performance. Finally, simulation results are given to illustrate the effectiveness of the proposed approach.     

Event-triggered adaptive tracking control for nonlinear systems with input saturation and unknown control directions

This article is concerned with event-triggered adaptive tracking control design of strict-feedback nonlinear systems, which are subject to input saturation and unknown control directions. In the design procedure, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. The Nussbaum gain technique is employed to address the issue of the unknown control directions. A predetermined time convergent performance function and a nonlinear mapping technique are introduced to guarantee that the tracking error can converge in the predetermined time with a fast convergence rate and a high accuracy. Then the event-triggered adaptive prescribed performance tracking control strategy is proposed, which not only ensures the boundedness of all the closed-loop signals and the convergence of tracking error but also reduces the communication burden from the controller to the actuator. At last, the simulation study further tests the availability of the proposed control strategy.     

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.     

Decentralized adaptive control for large-scale time-delay systems with dead-zone input

In this paper, a decentralized adaptive control scheme is proposed to address output tracking of a class of interconnected time-delay subsystems with the input of each loop preceded by an unknown dead-zone. Each local controller is designed using the backstepping technique and consists of a new robust control law and new updating laws. Unknown time-varying delays are compensated by using appropriate Lyapunov-Krasovskii functionals. Furthermore, by introducing a new smooth dead-zone inverse, the proposed backstepping design is able to eliminate the effects resulting from dead-zone nonlinearities in the input. It is shown that the proposed controller can guarantee not only stability, but also good transient performance.     

未知控制方向的迟滞非线性系统预设自适应控制

针对一类含有迟滞特性的未知控制方向严反馈非线性系统,设计了基于误差变换的反步自适应控制器.首先提出动态迟滞算子来扩展输入空间建立神经网络迟滞模型.然后利用径向基函数(RBF)神经网络逼近未知函数,并引入Nussbaum型函数来解决系统未知控制方向问题.最后采用误差变换将误差限定在预设的范围内,并利用反步法设计自适应控制器.该控制方案不仅能够保证跟踪精度,还可以提高系统暂态和稳态性能.仿真结果表明了控制方案的可行性.     

An adaptive dead-zone inverse controller for systems with sandwiched dead-zones

This paper addresses adaptive control of sandwich non-linear systems having an unknown sandwiched dead-zone between the linear dynamic blocks, as illustrated by a hydraulic valve system. An adaptive hybrid control scheme for control of such sandwiched dead-zone systems is developed. The proposed control scheme employs an inner-loop discrete-time feedback design and an outer-loop continuous-time feedback design, combined with an adaptive dead-zone inverse to cancel the dead-zone effect for improving output tracking. Stability and tracking performance of the closed-loop control system are analysed. Simulation results are used to illustrate the effectiveness of the proposed adaptive dead-zone inverse controller.     

Adaptive fixed-time prescribed performance control of vehicular platoons with unknown dead-zone and actuator saturation

This article focuses on the problem of fixed-time prescribed performance platoon control for heterogeneous vehicles with unknown dead-zone and actuator saturation. First, an equivalent transformation is developed to approximate the actuator nonlinearity (i.e., dead-zone and saturation), which reduces the complexity of controller design. Then, to guarantee the tracking errors converge to the predetermined region in the given time, a modified prescribed performance function is presented. Based on this, a novel adaptive sliding mode control scheme is developed in the context of fixed-time theory, which is proved to be capable of ensuring individual vehicle stability and string stability in fixed time. In addition, under the proposed control scheme, the convergence time is independent of initial conditions of the system. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed control scheme.     

Adaptive quantised fault-tolerant tracking control of uncertain nonlinear systems with unknown control direction and the prescribed accuracy

In this paper, the problem of adaptive fault-tolerant tracking control for a class of uncertain nonlinear systems in the presence of input quantisation and unknown control direction is considered. By choosing a class of particular Nussbaum functions, an adaptive fault-tolerant control scheme is designed to compensate actuator faults and input quantisation while the control direction is unknown. Compared with the existing results, the proposed controller can directly compensate for the nonlinear term caused by actuator faults and the nonlinear decomposition on the quantiser without estimating its bound. Furthermore, via Barhalant's Lemma, it is proven that all the signals of the closed-loop system are globally uniformly bounded and the tracking error converges into a prescribed accuracy in prior. Finally, an illustrative example is used for verifying effectiveness of the proposed approach.     

Adaptive neural prescribed performance control for a class of strict-feedback stochastic nonlinear systems under arbitrary switchings

This paper presents an adaptive neural tracking control scheme for strict-feedback stochastic nonlinear systems with guaranteed transient and steady-state performance under arbitrary switchings. First, by utilising the prescribed performance control, the prescribed tracking control performance can be ensured, while the requirement for the initial error is removed. Second, radial basis function neural networks approximation are used to handle unknown nonlinear functions and stochastic disturbances. At last, by using the common Lyapunov function method and the backstepping technique, a common adaptive neural controller is constructed. The designed controller overcomes the problem of the over-parameterisation, and further alleviates the computational burden. Under the proposed common adaptive controller, all the signals in the closed-loop system are 4-Moment (or 2 Moment) semi-globally uniformly ultimately bounded, and the prescribed tracking control performance are guaranteed under arbitrary switchings. Three examples are presented to further illustrate the effectiveness of the proposed approach.     

Adaptive output control of nonlinear systems with uncertain dead-zone nonlinearity

In this note, we present a new scheme to design adaptive controllers for uncertain systems preceded by unknown dead-zone nonlinearity. The control design is achieved by introducing a smooth inverse function of the dead-zone and using it in the controller design with backstepping technique. For the design and implementation of the controller, no knowledge is assumed on the unknown system parameters. It is shown that the proposed controller not only can guarantee stability, but also transient performance.     

Sigma adaptive fuzzy sliding mode control of a class of nonlinear systems

Based on fuzzy approximators of nonlinear functions, a new adaptive fuzzy sliding mode control scheme is proposed for a class of nonlinear plants. In comparison with most existing methods, in which the parameter projection algorithm is often involved to prevent the estimated value of the input gain function from evolving into zero, the proposed control law has shown its success and simplicity in tackling the case when the value of the estimated input gain function becomes zero during online operations. A variant of adaptive law with dead-zone sigma-modification is introduced to help achieve this goal. The bounding parameters of the model approximation error and the external disturbance are all regarded as unknown constants in this paper, and adaptive laws for them are devised for tracking purposes. Based on Lyapunov's stability theory the proposed controller has been shown to render the tracking error arbitrarily close to zero. A comparably good tracking performance is obtained as illustrated by the simulation results for an inverted pendulum system.     

Adaptive neural practical fixed-time command filtered control for multi-input and multi-output nonlinear systems with dead zones input and unknown control direction

In this article, under the circumstance of dead zones input and unknown control direction, the adaptive practical fixed-time control strategy is presented for a general class of multi-input and multi-output (MIMO) nonlinear systems. The inherent explosion of computational complexity difficulty is eliminated by adopting a command filter technique and the universal approximation properties of radial basis function neural networks (RBFNNs) are applied to model the unknown nonlinear functions. The difficulties of the dynamic surface method and unknown directions can be handled by invoking error compensation mechanism and Nussbaum-type functions, respectively. The uniqueness of the presented control scheme is that the tracking system can achieve the fixed-time stability without relying on the boundedness of dead-zone parameters. The fixed-time convergence of the output tracking error and the semiglobally fixed-time stable of closed-loop system are assured via the developed adaptive fixed-time command filtered controller. Finally, a practical example is supplied to further validate the availability of the presented theoretic result.     

Adaptive tracking of nonlinear systems with non-symmetric dead-zone input

Quite successfully adaptive control strategies have been applied to uncertain dynamical systems subject to dead-zone nonlinearities. However, adaptive tracking of systems with non-symmetric dead-zone characteristics has not been fully discussed with minimal knowledge of the dead-zone parameters. It is shown that the controlled system preceded by a non-symmetric dead-zone input can be represented as an uncertain nonlinear system subject to a linear input with time-varying input coefficient. To cope with this problem, a new adaptive compensation algorithm is employed without constructing the dead-zone inverse. The proposed adaptive scheme requires only the information of bounds of the dead-zone slopes and treats the time-varying input coefficient as a system uncertainty. The new control scheme ensures bounded-error trajectory tracking and assures the boundedness of all the signals in the adaptive closed loop. By appropriate selections of the controller parameters, we show that the smoothness of the controller does not affect the accuracy of trajectory tracking control. A numerical example is included to show the effectiveness of the theoretical results.     

Prescribed performance adaptive fault tolerant control approach for nonlinear large-scale systems with time delay interconnection and dead zone input

In this study, a prescribed performance adaptive fault tolerant tracking control scheme is presented for a class of nonlinear large-scale systems with time delay interconnection, dead zone input, and actuator fault. The radial basis function neural networks are used to approximate unknown nonlinear functions. Different from the barrier Lyapunov functions used to achieve the symmetrical prescribed performance, a new error transformation is introduced in this study to achieve the desired asymmetrical prescribed performance. In addition, Nussbaum function is introduced to solve the difficulties caused by dead zone input and actuator fault. Based on the appropriate Lyapunov–Krasovskii functions, the effect of time delay interconnection could be compensated. By using backstepping procedures, an adaptive fault tolerant tracking control approach is developed for the considered large-scale systems, and the stability of the closed-loop systems is analyzed by Lyapunov theory. Meanwhile, the prescribed performance of the tracking error could be guaranteed. Finally, the effectiveness of the proposed control approach is illustrated by two simulation examples.     

Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance

In order to accommodate actuator failures which are uncertain in time, pattern and value, we propose two adaptive backstepping control schemes for parametric strict feedback systems. Firstly a basic design scheme on the basis of existing approaches is considered. It is analyzed that, when actuator failures occur, transient performance of the adaptive system cannot be adjusted through changing controller design parameters. Then we propose a new controller design scheme based on a prescribed performance bound (PPB) which characterizes the convergence rate and maximum overshoot of the tracking error. It is shown that the tracking error satisfies the prescribed performance bound all the time. Simulation studies also verify the established theoretical results that the PPB based scheme can improve transient performance compared with the basic scheme, while both ensure stability and asymptotic tracking with zero steady state error in the presence of uncertain actuator failures.     

一类非参数不确定系统的自适应重复学习控制

本文针对一类非参数不确定系统提出一种全限幅自适应重复学习控制方法. 利用期望轨迹的周期特性, 构 造周期性期望控制输入, 并基于Lyapunov方法设计自适应重复学习控制器, 实现系统对周期性期望轨迹的高精度跟 踪, 且无需已知非参数不确定性的上界. 设计全限幅学习律估计未知的期望控制输入, 保证估计值被限制在指定的 界内. 同时, 通过构造完全平方式消除部分误差相关项, 控制器设计中可避免使用符号函数, 从而抑制控制器抖振问 题. 最后, 基于Lyapunov方法对误差收敛性进行了分析, 并通过仿真对比验证本文所提方法的有效性.     

Adaptive fuzzy robust control of PMSM with smooth inverse based dead-zone compensation

It is a challenging work to design high precision/high performance motion controller for permanent magnet synchronous motor (PMSM) due to some difficulties, such as varying operating conditions, parametric uncertainties and external disturbances. In order to improve tracking control performance of PMSM, this paper proposes an adaptive fuzzy robust control (AFRC) algorithm with smooth inverse based dead-zone compensation. Instead of nonsmooth dead-zone inverse which would cause the possible control signal chattering phenomenon, a new smooth dead-zone inverse is proposed for non-symmetric dead-zone compensation in PMSM system. AFRC controller is synthesized by combining backstepping technique and small gain theorem. Discontinuous projectionbased parameter adaptive law is used to estimate unknown system parameters. The Takagi-Sugeno fuzzy logic systems are employed to approximate the unstructured dynamics. Robust control law ensures the robustness of closed loop control system. The proposed AFRC algorithm with smooth inverse based dead-zone compensation is verified on a practical PMSM control system. The comparative experimental results indicate that the smooth inverse for non-symmetric dead-zone nonlinearity can effectively avoid the chattering phenomenon which would be caused by nonsmooth dead-zone inverse, and the proposed control strategy can improve the PMSM output tracking performance.     

基于性能指标约束的一类输入死区非线性系统最优控制

针对一类考虑指定性能和带有输入死区约束的严格反馈非线性系统,本文提出了一种自适应模糊最优控制方法.采用模糊逻辑系统逼近系统的未知非线性函数及代价函数,利用backstepping方法及命令滤波技术,设计前馈控制器.针对仿射形式的误差系统,结合自适应动态规划技术,设计最优反馈控制器.采用指定性能控制方法,将系统跟踪误差约束在指定范围内.利用死区斜率信息解决具有死区输入的非线性系统的控制问题.基于Lyapunov稳定性理论,证明闭环系统内所有信号是一致最终有界的.最后仿真结果验证了本文方法的可行性和有效性.     

Prescribed performance adaptive neural output feedback dynamic surface control for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics

This paper studies the output feedback tracking control problem for a class of strict‐feedback uncertain nonlinear systems with full state constraints and unmodeled dynamics using a prescribed performance adaptive neural dynamic surface control design approach. A nonlinear mapping technique is employed to address the state constraints. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. The unmodeled dynamics is addressed by introducing an available dynamic signal. Subsequently, we construct the controller and parameter adaptive laws using a backstepping technique. Based on Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobally uniformly ultimately bounded and that the tracking error always remains within the prescribed performance bound. Simulation results are presented to demonstrate the effectiveness of the proposed control scheme.