严格反馈随机非线性系统的鲁棒自适应逆最优跟踪

针对具有未知定常参数和标准Wiener噪声扰动的严格反馈非线性系统,结合参考信号,构造了误差系统,使用Backstepping算法设计了误差系统的自适应逆最优控制律和参数自适应律,进而解决了原系统的鲁棒自适应逆最优跟踪.     

Decentralized adaptive stabilization in the presence of unknown backlash-like hysteresis

Due to the difficulty of handling both hysteresis and interactions between subsystems, there is still no result available on decentralized stabilization of unknown interconnected systems with hysteresis, even though the problem is practical and important. In this paper, we provide solutions to this challenging problem by proposing two new schemes to design decentralized output feedback adaptive controllers using backstepping approach. For each subsystem, a general transfer function with arbitrary relative degree is considered. The interactions between subsystems are allowed to satisfy a nonlinear bound with certain structural conditions. In the first scheme, no knowledge is assumed on the bounds of unknown system parameters. In case that the uncertain parameters are inside known compact sets, we propose an alternative scheme where a projection operation is employed in the adaptive laws. In both schemes, the effects of the hysteresis and the effects due to interactions are taken into consideration in devising local control laws. It is shown that the designed local adaptive controllers can ensure all the signals in the closed-loop system bounded. A root mean square type of bound is obtained for the system states as a function of design parameters. This implies that the transient system performance can be adjusted by choosing suitable design parameters. With Scheme II, the proposed control laws allow arbitrarily strong interactions provided their upper bounds are available. In the absence of hysteresis, perfect stabilization is ensured and the L₂ norm of the system states is also shown to be bounded by a function of design parameters when the second scheme is applied.     

连续回滞系统的模型参考自适应控制

采用Stop和Play算子表示的Prandtl-Ishlinskii回滞模型描述回滞特性,该模型便于实现控制器的设计．考虑带有未知回滞驱动且以状态空间形式表示的连续时间线性动态系统,给出了模型参考白适应控制设计方案．控制策略保证闭环系统的全局稳定性和期望的跟踪精度,有效地抑制回滞产生的不精确和振荡现象．数值仿真结果表明了控制算法的有效性．     

Zero-error tracking control of uncertain nonlinear systems in the presence of actuator hysteresis

In this paper, the problem of adaptive tracking control is addressed for a class of nonlinear systems with unknown constant parameters and unknown actuator nonlinearity. The actuator nonlinearity is modelled as the backlash-like hysteresis, which is described by a differential model. The prior knowledge on the control gain sign is not required, and only the assumption on the reference signal is made. By combining the adaptive backstepping technique with the Nussbaum gain approach, an adaptive compensation controller design approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking error can converge to zero asymptotically despite the presence of the actuator hysteresis. Two simulation examples are included to illustrate the effectiveness of the proposed approach.     

具有不确定Wiener噪声随机非线性系统的自适应逆最优控制

针对一类具有不确定Wiener噪声扰动和未知定常参数的随机非线性系统,采用随机微分方程描述系统,基于Backstepping算法,利用随机控制Lyapunov函数,研究了自适应逆最优控制问题的可解定理,系统地给出了全局依概率渐近稳定和自适应逆最优控制策略的设计方法.这种方法可同时获得控制律和自适应律,仿真结果表明该控制算法的有效性.     

DYNAMICAL ADAPTIVE SLIDING MODE OUTPUT TRACKING CONTROL OF A CLASS OF NONLINEAR SYSTEMS

An alternative adaptive scheme to achieve output tracking for a class of minimum-phase dynamically input–output linearizable nonlinear systems with parametric uncertainties is considered. The proposed approach is based upon a combination of the adaptive backstepping design method and a sliding mode control (SMC) scheme to design dynamical adaptive sliding mode controllers and provide robust output tracking even in the presence of unknown disturbances. The validity of the proposed approach, regarding tracking objectives and robustness with respect to bounded stochastic perturbation inputs, is tested through digital computer simulations. © 1997 by John Wiley & Sons, Ltd.     

具有不确定噪声的随机非线性系统的鲁棒自适应跟踪

研究了一类随机非线性系统的鲁棒自适应跟踪问题.文中利用随机控制Lyapunov设计方法,对于受方差不确定Wiener噪声干扰的参数严格反馈形式的系统,给出了参数自适应律和控制律,使得跟踪误差在4次均方意义下收敛到一个小范围内.     

Robust adaptive tracking control of MIMO nonlinear systems in the presence of actuator hysteresis

Adaptive tracking control of a class of MIMO nonlinear system preceded by unknown hysteresis is investigated. Based on dynamic surface control, an adaptive robust control law is developed and compensators are designed to mitigate the influences of both the unknown bounded external uncertainties and the unknown Prandtl–Islinskii hysteresis. By adopting the low-pass filters, the explosion of complexity caused by tedious computation of the time derivatives of the virtual control laws is overcome. With the proposed control scheme, the closed-loop system is proved to be semi-globally ultimately bounded by the Lyapunov stability theory, and the output of the controlled system can track the desired trajectories with an arbitrarily small error. Finally, numerical simulations are given to verify the effectiveness of the proposed approach.     

Adaptive Stabilization for a Class of Stochastic Nonlinear Systems with Prandtl‐Ishlinskii Hysteresis

This paper deals with a class of stochastic nonlinear systems with unknown hysteresis. A stochastic Lyapunov method is applied for systems in strict‐feedback form driven by unknown Prandtl‐Ishlinskii hysteresis and Wiener noises of unknown covariance. An adaptive controller is obtained which guarantees the global asymptotic stabilization in probability. Simulation results are provided to illustrate the effectiveness of the proposed approach.     

Neural model-based adaptive control for systems with unknown Preisach-type hysteresis

An adaptive control scheme is presented for systems with unknown hysteresis. In order to handle the case where the hysteresis output is unmeasurale, a novel model is firstly developed to describe the characteristic of hysteresis. This model is motivated by Preisach model but implemented by using neural networks (NN). The main advantage is that it is easily used for controller design. Then, the adaptive controller based on the proposed model is presented for a class of SISO nonlinear systems preceded by unknown hysteresis, which is estimated by the proposed model. The hws for model updating and the control hws for the neural adaptive controller are derived from Lyaptmov stability theorem, therefore the semi - global stability of the closed-loop system is guaranteed. At last, the simulation results are illuswated.     

具有输入量化和全状态约束的非严格反馈随机非线性系统的有限时间动态面控制

研究具有输入量化和全状态约束的非严格反馈随机非线性系统的有限时间自适应跟踪控制.首先,利用双曲正切函数进行非线性映射,消除全状态约束的限制,将系统变换为无约束系统;其次,引入滞回量化器克服量化信号中的抖动和量化误差.为实现有限时间控制,提出概率意义下半全局有限时间稳定控制方法,加快系统的收敛速度,并在此基础上采用径向基函数神经网络逼近未知非线性函数;接着,基于动态面控制技术和高斯函数的性质,对变换后的非严格反馈随机系统进行自适应控制设计,所设计的控制器能够保证闭环系统中的所有信号在概率意义下有限时间稳定;最后通过仿真实验表明所设计控制方案的有效性.     

迟滞非线性动态系统神经网络自适应控制

为了减轻非线性动态系统中未知迟滞(Hysteresis)的不良影响，该文提出了一类Backlash型迟滞模型。将有限数量不同宽度的Backlash(Matlab／Simulink)算子进行叠加，来仿真执行器中的迟滞非线性动态。用此模型，提出了基于径向基函数神经网络的自适应控制方案，以控制伴有未知迟滞的非线性动态系统。该方案采用了动态逆的思想及伪控制的概念。利用Lyapunov稳定理论，设计了两个鲁棒控制项，保证动态系统的稳定性、系统中所有信号有界和误差收敛到起点的领域内。通过Matlab／Simulink仿真实验，证明了所提出方案的有效性。     

一类随机非线性系统自适应跟踪的模块化设计

对参数严格反馈形式的非线性系统,在含有未知方差Wiener噪声干扰下,为增进系统的稳定性,采用基于估计的模块化设计思想,研究了其跟踪问题。对方差不确定噪声抑制的控制机制,设计了具有鲁棒稳定特性的输入状态稳定控制器,确保系统满足控制器和辨识器的分离设计。应用Swapping技术,设计滤波器将动态参数模型转化为静态模型,并且运用梯度算法设计了参数自适应律。控制器与辨识器结合最终使跟踪误差在概率意义下收敛,试验证明采用方法有效。     

具有磁滞输入非线性系统的鲁棒自适应控制

就一类具有磁滞输入的严反馈非线性系统, 提出了一种鲁棒自适应动态面控制方案. 该方案可克服传统反推控制带来的“微分爆炸”问题, 保证闭环系统的半全局稳定性, 且跟踪误差可收敛到任意小的残集内. 特别地, 通过引入动态面修正及初始化技巧, 可保证系统跟踪误差的L∞ 性能指标. 数值仿真验证了本文所提方法案的有效性.     

Adaptive output feedback control of systems preceded by the Preisach-type hysteresis.

An adaptive output feedback controller is presented for a class of single-input-single-output (SISO) nonlinear systems preceded by an unknown hysteresis nonlinearity represented by the Preisach model. First, a novel model is developed to represent the hysteresis characteristic in order to handle the case where the hysteresis output is not directly measured. The model is motivated by the Preisach model but implemented by the neural networks (NN). Therefore, it is easily used for controller design. Then, a radius-basis-functional-neural-networks (RBF NN) adaptive controller based on the model estimation is presented by combining the high-gain state observer. The updated laws and control laws of the controller are derived from Lyapunov stability theorem, so that the ultimate boundedness of the closed-loop system is guaranteed. At last, an example is used to verify the effectiveness of the controller.     

MLP-based adaptive neural control of nonlinear time-delay systems with the unknown hysteresis

In this note, the authors study the tracking problem for uncertain nonlinear time-delay systems with unknown non-smooth hysteresis described by the generalised Prandtl–Ishlinskii (P-I) model. A minimal learning parameters (MLP)-based adaptive neural algorithm is developed by fusion of the Lyapunov–Krasovskii functional, dynamic surface control technique and MLP approach without constructing a hysteresis inverse. Unlike the existing results, the main innovation can be summarised as that the proposed algorithm requires less knowledge of the plant and independent of the P-I hysteresis operator, i.e. the hysteresis effect is unknown for the control design. Thus, the outstanding advantage of the corresponding scheme is that the control law is with a concise form and easy to implement in practice due to less computational burden. The proposed controller guarantees that the tracking error converges to a small neighbourhood of zero and all states of the closed-loop system are stabilised. A simulation example demonstrates the effectiveness of the proposed scheme.     

A novel adaptive control design method for stochastic nonlinear systems using neural network

This paper presents a novel method for designing an adaptive control system using radial basis function neural network. The method is capable of dealing with nonlinear stochastic systems in strict-feedback form with any unknown dynamics. The proposed neural network allows the method not only to approximate any unknown dynamic of stochastic nonlinear systems, but also to compensate actuator nonlinearity. By employing dynamic surface control method, a common problem that intrinsically exists in the back-stepping design, called “explosion of complexity”, is resolved. The proposed method is applied to the control systems comprising various types of the actuator nonlinearities such as Prandtl–Ishlinskii (PI) hysteresis, and dead-zone nonlinearity. The performance of the proposed method is compared to two different baseline methods: a direct form of backstepping method, and an adaptation of the proposed method, named APIC-DSC, in which the neural network is not contributed in compensating the actuator nonlinearity. It is observed that the proposed method improves the failure-free tracking performance in terms of the Integrated Mean Square Error (IMSE) by 25%/11% as compared to the backstepping/APIC-DSC method. This depression in IMSE is further improved by 76%/38% and 32%/49%, when it comes with the actuator nonlinearity of PI hysteresis and dead-zone, respectively. The proposed method also demands shorter adaptation period compared with the baseline methods.

     

Design of global tracking controllers for flexible-joint robots

An approach to design control laws for trajectory tracking of robots having flexible joints is presented. An application to the adaptive control is also given with reference to a single-link robot with one revolute elastic joint whose parameters are unknown.     

Adaptive suboptimal tracking for the first-order plant with Lipschitz uncertainty

A tracking problem for the first-order discrete-time plant with time-invariant uncertainty of the Lipschitz type and bounded exogenous disturbance is considered in the adaptive setting and two different adaptive laws are proposed. The first law is based on a natural estimation of the unknown linear part of the plant and introduces some conservatism in stability margin and tracking performance. The second adaptive law is suboptimal and includes additionally the estimation of the unknown Lipshitz constant and the unknown norm of exogenous disturbance. The suboptimality is achieved by exploiting a cone estimation algorithm and the linearity of the control criterion with respect to unknown parameters. Both adaptive laws utilize the nonlinear feedback by Xie and Guo based on nonparametric estimation of the uncertainty.     

非线性时滞大系统自适应神经网络分散控制

针对一类未知非线性时滞关联大系统,提出一种自适应神经网络分散跟踪控制方案．采用神经网络逼近各子系统内部的非线性函数和关联项中的时滞非线性函数;利用占有方法处理时滞项,采用Backstepping技术设计分散控制律和参数自适应律．基于Lyapunov-Krasoviskii泛函证明了闭环大系统所有信号半全局一致最终有界．通过调节设计参数和增加神经元个数,可以实现任意输出跟踪精度．实例仿真说明了该方案的可行性。