Global adaptive output-feedback control of nonlinear systems. I.Linear parameterization

The problem of designing global adaptive output-feedback tracking controls for single-input single-output nonlinear systems which are linear with respect to the input and an unknown constant parameter vector is addressed. A class of systems which can be globally controlled by adaptive observer-based output-feedback compensators is identified by geometric coordinate-free conditions. The nonlinearities depend on the output only: growth conditions are not required. Each system in the class admits observers with linear error dynamics and is minimum phase, i.e., it has linear asymptotically stable zero dynamics. When the parameters are known, new sufficient conditions for global output-feedback tracking control are obtained as a special case. For linear systems the result recovers a well-known fundamental adaptive result. Three examples are discussed     

一类不确定非线性系统的鲁棒输出反馈控制*

本文考虑一类具有输出反馈标准形的非线性系统的输出反馈控制问题，为了给出其不同于自适应控制的解决办法，设计出了新的鲁棒输出反馈控制方案。该方案不需辨识系统未知参数，也不需知识未知参数向量的上界，就能保证所有控制系统信号的全局有界性，并且顺参数的适当选择，可以使系统跟踪误差达到任意小。仿真结果表明可以获得良好的跟踪效果。     

Global adaptive control for a class of uncertain stochastic nonlinear systems with unknown output gain

This paper addresses the global adaptive control problem for a class of uncertain stochastic nonlinear systems in the output-feedback form. Due to the unknown output gain, we construct a full-order homogeneous observer instead of using the system output. Then, by adding a power integrator technique, an output-feedback controller is designed, as well as an adaptive law to deal with the unknown nonlinear growth rates. Based on the generalized stochastic Lyapunov stability theorem, it can be proved that all the signals of the closed-loop system are bounded in probability, and the system states converge to the origin almost surely.     

Adaptive fuzzy decentralized control for nonlinear large-scale systems based on high-gain observer

An adaptive fuzzy decentralized backstepping output-feedback control approach is proposed for a class of nonlinear large-scale systems with completely unknown functions,the interconnections mismatched in control inputs,and without the measurements of the states.Fuzzy logic systems are employed to approximate the unknown nonlinear functions,and an adaptive high-gain observer is developed to estimate the unmeasured states.Using the designed high-gain observer,and combining the fuzzy adaptive control theory with backstepping approach,an adaptive fuzzy decentralized backstepping output-feedback control scheme is developed.It is proved that the proposed control approach can guarantee that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded(SUUB),and that the observer errors and the tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters.Finally,a simulation example is provided to show the eectiveness of the proposed approach.     

一类不确定非线性系统的自适应输出反馈镇定

研究了一类不确定非线性系统的全局自适应输出反馈镇定问题. 由于不确定控制系数和未知线性增长率的存在, 这个问题比较复杂且很难解决. 本文引入一个新的在线调节的动态增益, 并基于此设计了高增益K-滤波器用于重构系统的状态. 然后, 受广义控制方法的启发, 发展了反推法并设计了自适应输出反馈镇定控制器. 结果表明, 通过选择恰当的设计参数可以保证闭环系统的全局稳定性. 给出的仿真算例验证了本文理论结果的正确性.     

随机非线性系统基于事件触发机制的自适应神经网络控制

针对一类具有严格反馈结构且控制方向未知的随机非线性系统,提出了基于事件触发机制的自适应神经网络（Adaptive neural network,ANN）输出反馈控制方法.利用径向基神经网络逼近系统中未知的非线性函数.通过引入Nussbaum增益函数并设计滤波器,解决了系统控制方向未知的问题.通过设计具有相对阈值的事件触发机制,保证了闭环随机非线性系统的有界性.最后给出数值仿真例子验证所提控制方法的有效性.     

Decentralized adaptive output-feedback stabilization for large-scale stochastic nonlinear systems

In this paper, the problem of decentralized adaptive output-feedback stabilization is investigated for large-scale stochastic nonlinear systems with three types of uncertainties, including parametric uncertainties, nonlinear uncertain interactions and stochastic inverse dynamics. Under the assumption that the inverse dynamics of the subsystems are stochastic input-to-state stable, an adaptive output-feedback controller is constructively designed by the backstepping method. It is shown that under some general conditions, the closed-loop system trajectories are bounded in probability and the outputs can be regulated into a small neighborhood of the origin in probability. In addition, the equilibrium of interest is globally stable in probability and the outputs can be regulated to the origin almost surely when the drift and diffusion vector fields vanish at the origin. The contributions of the work are characterized by the following novel features: (1) even for centralized single-input single-output systems, this paper presents a first result in stochastic, nonlinear, adaptive, output-feedback asymptotic stabilization; (2) the methodology previously developed for deterministic large-scale systems is generalized to stochastic ones. At the same time, novel small-gain conditions for small signals are identified in the setting of stochastic systems design; (3) both drift and diffusion vector fields are allowed to be dependent not only on the measurable outputs but some unmeasurable states; (4) parameter update laws are used to counteract the parametric uncertainty existing in both drift and diffusion vector fields, which may appear nonlinearly; (5) the concept of stochastic input-to-state stability and the method of changing supply functions are adapted, for the first time, to deal with stochastic and nonlinear inverse dynamics in the context of decentralized control.     

随机非线性严格反馈系统的自适应神经网络输出反馈镇定

针对具有严格反馈形式的随机非线性系统, 首次引入神经网络控制技术, 设计了适当形式的随机控制 Lyapunov函数, 并运用反推(Backstepping)技术和非线性观测器设计技术, 构造出一类自适应神经网络输出反馈控制器. 在一定条件下, 证明了闭环系统平衡点依概率稳定. 仿真算例验证了所给控制方案的有效性.     

一类具有未知控制方向非线性系统的输出反馈自适应控制

研究了一类控制方向未知非线性系统的输出反馈自适应镇定问题. 首先, 通过一线性状态变换, 将未知控制系数集中起来, 从而将原系统变换为适于控制设计的新系统. 然后, 分别引入状态观测器和参数估计器, 并应用积分反推和调节函数方法, 给出了输出反馈稳定控制律的构造性设计过程. 可以证明,所设计的控制器确保原系统状态渐近收敛到原点, 而其它闭环系统状态有界. 仿真结论验证了所提出方法的有效性.     

Adaptive fuzzy decentralised control for stochastic nonlinear large-scale systems in pure-feedback form

This paper is concerned with the problem of adaptive fuzzy decentralised output-feedback control for a class of uncertain stochastic nonlinear pure-feedback large-scale systems with completely unknown functions, the mismatched interconnections and without requiring the states being available for controller design. With the help of fuzzy logic systems approximating the unknown nonlinear functions, a fuzzy state observer is designed estimating the unmeasured states. Therefore, the nonlinear filtered signals are incorporated into the backstepping recursive design, and an adaptive fuzzy decentralised output-feedback control scheme is developed. It is proved that the filter system converges to a small neighbourhood of the origin based on appropriate choice of the design parameters. Simulation studies are included illustrating the effectiveness of the proposed approach.     

Adaptive dynamic surface control for a class of output-feedback nonlinear systems with guaranteed ℒ∞ tracking performance

In this article, an output-feedback adaptive dynamic surface control (DSC) is proposed for a class of nonlinear systems. It is proved that, by using the new scheme, the explosion of the complexity problem in a traditional backstepping design can be eliminated, the semi-global stability of a closed-loop system can be guaranteed and, in particular, by choosing the design parameters and initialising the filters and the update law properly, we show that the ?_∞ performance of the system-tracking error can be achieved without over-parametrisation. Another advantage of the proposed scheme compared with those traditional backstepping control and current adaptive DSC schemes, whose adaptive control law is obtained through a series of steps recursively, is that the adaptive law is needed only at the first design step, and therefore significantly reduces the design procedure.     

State observer-based adaptive fuzzy output-feedback control for a class of uncertain nonlinear systems

This paper aims to develop state observer-based adaptive fuzzy control techniques for controlling a class of uncertain nonlinear systems with bounded external disturbances. An adaptive fuzzy observer is proposed to estimate the system state variables. It is shown that the observation errors obtained from the observer are uniformly ultimately bounded. Applying the estimated system state for design of an output-feedback controller, the uniformly ultimate boundedness of the tracking errors for the resulting closed-loop system can be guaranteed. A typical robot arm system is employed in our simulation studies, and the results demonstrate the usefulness and effectiveness of the proposed techniques for controlling nonlinear systems with bounded external disturbances.     

Adaptive output-feedback control for a class of uncertain stochastic non-linear systems with time delays

In this paper, we investigate the adaptive output-feedback stabilisation for a class of stochastic non-linear systems with time-varying time delays. First, we give some sufficient conditions to ensure the existence and uniqueness of the solution process for stochastic non-linear systems with time delays, and introduce a new stability notion and the related criterion. Then, for a class of stochastic non-linear systems with time-varying time delays, uncertain parameters in both drift and diffusion terms, and general constant virtual control coefficients, we present a systematic design procedure for a memoryless adaptive output-feedback control law by using the backstepping method. It is shown that under the control law based on a memoryless observer, the closed-loop equilibrium of interest is globally stable in probability, and moreover, the solution process can be regulated to the origin almost surely.     

Adaptive finite-time stabilizing control of fractional-order nonlinear systems with unmodeled dynamics via sampled-data output-feedback

This article realizes an adaptive finite-time sampled-data output-feedback stabilization for a class of fractional-order nonlinear systems with unmodeled dynamics and unavailable states. K-filters are constructed to estimate unavailable states, a dynamic signal is introduced to handle unmodeled dynamics and neural networks were used to approximate uncertain nonlinearities existed in stabilizer construction. With the help of backstepping technique, an adaptive sampled-data output-feedback stabilizer is exported, and such stabilizer with allowable design parameters and sampling period can render the corresponding closed-loop system reaches practically finite-time stable, which can be demonstrated by means of selected Lyapunov function candidates. In the end, two simulations with a numerical and an engineering examples are presented to verify the effectiveness of the proposed scheme.     

基于神经网络观测器的一类非线性系统的故障调节

将一般形式的非线性模型线性化为输出反馈型．针对该类系统,首先利用神经网络的一致逼近任意非线性连续函数的性质,构造神经网络自适应观测器,以获取反映故障信息的残差;然后根据残差信息在线估计故障;最后通过修正控制律来补偿故障所带来的影响．并采用Lyapunov稳定性理论证明了系统的稳定性．仿真结果验证了该方法的有效性．     

Adaptive fuzzy decentralized control for a class of large-scale nonlinear systems.

In this paper, direct and indirect adaptive output-feedback fuzzy decentralized controllers for a class of uncertain large-scale nonlinear systems are developed. The proposed controllers do not need the availability of the state variables. By designing the state observer, the adaptive fuzzy systems, which are used to model the unknown functions, can be constructed using the state estimations, and a new hybrid adaptive fuzzy control methodology is proposed by combining the adaptive fuzzy systems with H infinity control and the sliding mode control techniques. Based on Lyapunov stability theorem, the stability of the closed-loop systems can be verified. Moreover, the proposed overall control schemes guarantee that all the signals involved are bounded and achieve the H infinity-tracking performance. To demonstrate the effectiveness of the proposed methods, simulation results are illustrated in this paper.     

Adaptive backstepping controller design using stochastic small-gain theorem

A more general class of stochastic nonlinear systems with unmodeled dynamics and uncertain nonlinear functions are considered in this paper. With the concept of input-to-state practical stability (ISpS) and nonlinear small-gain theorem being extended to stochastic case, by combining stochastic small-gain theorem with backstepping design technique, an adaptive output-feedback controller is proposed. It is shown that the closed-loop system is practically stable in probability. A simulation example demonstrates the control scheme.     

Global adaptive output-feedback control of nonlinear systems. II.Nonlinear parameterization

For pt.I, see ibid., p.17-32 (1993). The problem of designing global output-feedback robust stabilizing controls for a class of single-input single-output minimum-phase uncertain nonlinear systems with known and constant relative degree is addressed. They are assumed to be linear with respect to the input and nonlinear with respect to an unknown constant parameter vector. The nonlinearities depend on the output only. The nonlinearities may be uncertain and are only required to be bounded by known smooth functions. The order of the robust compensator is equal to the relative degree minus one and is static when the relative degree is one. A self-tuning version of the robust control capable of achieving set point regulation is developed in which the control gains are tuned by an output-feedback adaptive algorithm. When the parameter vector enters linearly, the self-tuning regulator does not require the knowledge of parameter bounds and guarantees set point regulation for the same class of systems considered in Part I     

Switching adaptive output-feedback control of nonlinearly parametrized systems

In this paper, we consider global adaptive output-feedback control of nonlinear systems in output-feedback form, with unknown parameters entering nonlinearly. Such unknown parameters are not required to lie in a known compact set. Our proposed adaptive output-feedback controller is a switching-type controller, in which the controller parameter is tuned in a switching manner via a switching logic. Global stability results of the closed-loop system have been proved.