Adaptive sliding-mode control for nonlinear systems with uncertain parameters.

This correspondence proposes a systematic adaptive sliding-mode controller design for the robust control of nonlinear systems with uncertain parameters. An adaptation tuning approach without high-frequency switching is developed to deal with unknown but bounded system uncertainties. Tracking performance is guaranteed. System robustness, as well as stability, is proven by using the Lyapunov theory. The upper bounds of uncertainties are not required to be known in advance. Therefore, the proposed method can be effectively implemented. Experimental results demonstrate the effectiveness of the proposed control method.     

不确定高次随机非线性系统的自适应控制

针对一类含有噪声干扰和非线性参数的高次随机非线性系统,研究了依概率全局自适应稳定问题.在噪声的协方差未知的情况下,利用自适应增加幂积分方法和参数分离技术,提出了一种反馈占优设计方法并构造了一个光滑自适应控制器.该控制器能保证闭环系统依概率全局稳定,并且系统的状态几乎必然收敛到零.仿真例子验证了控制方案的有效性.     

Adaptive control of uncertain pure-feedback nonlinear systems

An adaptive control approach is proposed to solve the globally asymptotic state stabilisation problem for uncertain pure-feedback nonlinear systems which can be transformed into the pseudo-affine form. The pseudo-affine pure-feedback nonlinear system under consideration is with nonlinearly parameterised uncertainties and possibly unknown control coefficients. Based on the parameter separation technique, a novel backstepping controller is designed by adopting the adaptive high gain idea. The proposed control approach could avoid the drawbacks of the approximation-based approaches since no estimators are needed to estimate the virtual and the actual controllers. In addition, it could guarantee globally asymptotic state stabilisation even though there exist nonlinearly parameterised uncertainties in the considered system while comparing to the existing approximation-free approaches. A numerical and a realistic examples are employed to demonstrate the effectiveness of the proposed control method.     

Adaptive RCMAC sliding mode control for uncertain nonlinear systems

An adaptive recurrent cerebellar-model-articulation-controller (RCMAC) sliding-mode control (SMC) system is developed for the uncertain nonlinear systems. This adaptive RCMAC sliding-model control (ARCSMC) system is composed of two systems. One is an adaptive RCMAC system utilized as the main controller, in which an RCMAC is designed to identify the system models. Another is a robust controller utilized to achieve system’s robust characteristics, in which an uncertainty bound estimator is developed to estimate the uncertainty bound so that the chattering phenomenon of control effort can be eliminated. The on-line adaptive laws of the ARCSMC system are derived in the sense of Lyapunov so that the system stability can be guaranteed. Finally, a comparison between SMC and ARCSMC for a chaotic system and a car-following system are presented to illustrate the effectiveness of the proposed ARCSMC system. Simulation results demonstrate that the proposed control scheme can achieve favorable control performances for the chaotic system and car-following systems without the knowledge of system dynamic functions.     

Adaptive hybrid intelligent control for uncertain nonlinear dynamical systems

A new hybrid direct/indirect adaptive fuzzy neural network (FNN) controller with a state observer and supervisory controller for a class of uncertain nonlinear dynamic systems is developed in this paper. The hybrid adaptive FNN controller, the free parameters of which can be tuned on-line by an observer-based output feedback control law and adaptive law, is a combination of direct and indirect adaptive FNN controllers. A weighting factor, which can be adjusted by the tradeoff between plant knowledge and control knowledge, is adopted to sum together the control efforts from indirect adaptive FNN controller and direct adaptive FNN controller. Furthermore, a supervisory controller is appended into the FNN controller to force the state to be within the constraint set. Therefore, if the FNN controller cannot maintain the stability, the supervisory controller starts working to guarantee stability. On the other hand, if the FNN controller works well, the supervisory controller will be deactivated. The overall adaptive scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. Two nonlinear systems, namely, inverted pendulum system and Chua's (1989) chaotic circuit, are fully illustrated to track sinusoidal signals. The resulting hybrid direct/indirect FNN control systems show better performances, i.e., tracking error and control effort can be made smaller and it is more flexible during the design process.     

Adaptive dynamic surface control for uncertain nonaffine nonlinear systems

This paper focuses on the problem of adaptive control for uncertain nonaffine nonlinear systems. The original nonaffine systems are transformed into the augmented affine systems via adding an auxiliary integrator, which makes the explicit control design possible. By introducing a modified sliding mode filter in each step, a novel adaptive dynamic surface controller is proposed, where the ‘explosion of complexity’ problem inherent in the backstepping design is avoided. It is proven rigorously that for any initial control condition, the proposed adaptive scheme is able to ensure the semiglobal uniformly ultimately boundedness of all signals in the closed loop. An illustrative example is carried out to verify the effectiveness of the proposed approach. Copyright © 2016 John Wiley & Sons, Ltd.     

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.     

不确定非线性时滞系统的自适应滑模控制

针对一类不确定非线性时滞系统的鲁棒滑模控制器设计问题,提出了一种自适应滑模控制方法,该方法能够有效地削弱系统的输入抖动.基于自适应滑模控制技术和Lyapunov稳定方法,克服了系统不确定性和时滞特性影响,不但保证系统状态可以在有限的时间内到达滑模面,而且还保证了系统的渐近稳定特性.最后给出的仿真结果验证了该控制方案的有效性.     

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 NN control of uncertain nonlinear pure-feedback systems

This paper is concerned with the control of nonlinear pure-feedback systems with unknown nonlinear functions. This problem is considered difficult to be dealt with in the control literature, mainly because that the triangular structure of pure-feedback systems has no affine appearance of the variables to be used as virtual controls. To overcome this difficulty, implicit function theorem is firstly exploited to assert the existence of the continuous desired virtual controls. NN approximators are then used to approximate the continuous desired virtual controls and desired practical control. With mild assumptions on the partial derivatives of the unknown functions, the developed adaptive NN control schemes achieve semi-global uniform ultimate boundedness of all the signals in the closed-loop. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters.     

Adaptive control for uncertain nonlinear systems based on multiple neural networks.

A new adaptive multiple neural network controller (AMNNC) with a supervisory controller for a class of uncertain nonlinear dynamic systems was developed in this paper. The AMNNC is a kind of adaptive feedback linearizing controller where nonlinearity terms are approximated with multiple neural networks. The weighted sum of the multiple neural networks was used to approximate system nonlinearity for the given task. Each neural network represents the system dynamics for each task. For a job where some tasks are repeated but information on the load is not defined and unknown or varying, the proposed controller is effective because of its capability to memorize control skill for each task with each neural network. For a new task, most similar existing control skills may be used as a starting point of adaptation. With the help of a supervisory controller, the resulting closed-loop system is globally stable in the sense that all signals involved are uniformly bounded. Simulation results on a cartpole system for the changing mass of the pole were illustrated to show the effectiveness of the proposed control scheme for the comparison with the conventional adaptive neural network controller (ANNC).     

输出受限的不确定非线性系统的自适应固定时间控制

针对具有非对称输出约束和外界干扰的不确定非线性系统,提出自适应固定时间反步控制策略.首先,采用非对称障碍Lyapunov函数处理系统的输出约束问题;其次,通过构造固定时间干扰观测器估计外界干扰,设计自适应固定时间滤波器,解决传统反步控制的“计算爆炸”问题,通过自适应律估计虚拟控制输入导数的未知上界;再次,基于Lyapunov稳定性理论证明闭环系统在固定时间内有界稳定且输出保持在约束范围内;最后,通过永磁同步电机的仿真验证所设计的控制策略的有效性.     

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.     

一类非线性不确定系统的模糊自适应控制

利用模糊逻辑系统具有逼近连续函数的性质,研究了一类非线性不确定系统的自适应模糊控制问题.控制器和自适应律的构成直接利用了系统的结构信息和模糊逻辑系统的输出信息,在较弱的假设条件下,这种控制器使被控系统的状态及参数估计误差一致终极有界.最后的仿真算例说明了本文所采用方法的有效性.     

Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems

An adaptive fuzzy control approach is proposed for a class of multiple-input-multiple-output (MIMO) nonlinear systems with completely unknown nonaffine functions. The MIMO systems are composed of n subsystems and each of subsystems is in the nested lower triangular form. It is difficult and complicated to control this class of systems due to the existence of unknown nonaffine functions and the couplings among the nested subsystems. This difficulty is overcome by introducing some special type Lyapunov functions and taking advantage of the mean-value theorem, the backstepping design method and the approximation property of the fuzzy systems. The proposed control approach can guarantee that all the signals in the closed-loop system are bounded. A simulation experiment is utilized to verify the feasibility of the proposed approach.     

具有Preisach类型磁滞输入的不确定非线性系统 自适应神经网络控制

本文针对一类执行器受Preisach磁滞约束的不确定非线性系统, 提出一种基于神经网络的直接自适应控制 方案, 旨在解决系统的预定精度轨迹跟踪问题. 由于Preisach算子与系统动态发生耦合, 导致算子输出信号不可测 量, 给磁滞的逆补偿造成了困难. 为解决此问题, 本文首先将Preisach模型进行分解, 以提取出控制命令信号用于 Backstepping递归设计, 并在此基础上融合一类降阶光滑函数与直接自适应神经网络控制策略, 形成对磁滞非线性 和被控对象非线性的强鲁棒性能, 且所设计方案仅包含一个需要在线更新的自适应参数, 同时可保证Lyapunov函数 时间导数的半负定性. 通过严格数学分析, 已证明该方案不仅保证闭环系统所有信号均有界, 而且输出跟踪误差随 时间渐近收敛到用户预定区间. 基于压电定位平台的半物理仿真实验进一步验证了所提出控制方案的有效性.     

一类高阶非线性不确定系统自适应稳定控制

研究了一类高阶非线性不确定性系统的自适应稳定控制设计问题.因该系统的非线性程度高,其控制系数不等同、符号已知、但数值未知,故在此之前其稳定控制设计问题没有得到解决.本文应用自适应技术,结合设计参数的适当选取,从而得到了设计该类非线性系统状态反馈稳定控制器的新方法,并基于反推技术,给出了稳定控制器的设计步骤.所设计的状态反馈控制器使得闭环系统的状态全局渐近收敛于零,其余闭环信号一致有界.最后通过一个仿真例子说明了控制设计方法的有效性.     

一类不确定非线性系统反步自适应神经网络控制研究

针对合有高阶不确定扰动项且不可参数线性化的一类非线性系统，采用反步递推方法设计基于多层神经网络的自适应控制器，多层神经网络可较好地逼近非线性系统，其权值能在系统先验知识不多的情况下在线调整，给出了神经网络Lyapunov意义下稳定的在线自适应律，在设计控制器的过程中，采用类加权形式Lyapunov函数，使得控制器能有效处理自适应控制奇异性问题，仿真结果表明，该控制器对系统参数的不确定性和有界干扰具有一定的鲁棒性，并能保证闭环系统全局稳定。     

RCMAC-based adaptive control for uncertain nonlinear systems.

An adaptive control system, using a recurrent cerebellar model articulation controller (RCMAC) and based on a sliding mode technique, is developed for uncertain nonlinear systems. The proposed dynamic structure of RCMAC has superior capability to the conventional static cerebellar model articulation controller in an efficient learning mechanism and dynamic response. Temporal relations are embedded in RCMAC by adding feedback connections in the association memory space so that the RCMAC provides a dynamical structure. The proposed control system consists of an adaptive RCMAC and a compensated controller. The adaptive RCMAC is used to mimic an ideal sliding mode controller, and the compensated controller is designed to compensate for the approximation error between the ideal sliding mode controller and the adaptive RCMAC. The online adaptive laws of the control system are derived based on the Lyapunov stability theorem, so that the stability of the system can be guaranteed. In addition, in order to relax the requirement of the approximation error bound, an estimation law is derived to estimate the error bound. Finally, the simulation and experimental studies demonstrate the effectiveness of the proposed control scheme for the nonlinear systems with unknown dynamic functions.     

Hysteresis-based switching algorithms for supervisory control of uncertain systems

We address the problem of controlling a linear system with unknown parameters ranging over a continuum by means of switching among a finite family of candidate controllers. We present a new hysteresis-based switching logic, designed specifically for this purpose, and derive a bound on the number of switches produced by this logic on an arbitrary time interval. The resulting switching control algorithm is shown to provide stability and robustness to arbitrary bounded noise and disturbances and sufficiently small unmodeled dynamics.