Adaptive fuzzy control for pure-feedback stochastic nonlinear systems with unknown dead-zone input

This paper is concerned with the problem of adaptive fuzzy output tracking control for a class of nonlinear pure-feedback stochastic systems with unknown dead-zone. Fuzzy logic systems in Mamdani type are used to approximate the unknown nonlinearities, then a novel adaptive fuzzy tracking controller is designed by using backstepping technique. The control scheme is systematically derived without requiring any information on the boundedness of dead-zone parameters (slopes and break-points) and the repeated differentiation of the virtual control signals. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded in probability and the system output eventually converges to a small neighbourhood of the desired reference signal in the sense of mean quartic value. Simulation results further illustrate the effectiveness of the proposed control scheme.     

Neural adaptive prescribed performance control for interconnected nonlinear systems with output dead zone

This paper is concerned with the neural‐based decentralized adaptive control for interconnected nonlinear systems with prescribed performance and unknown dead zone outputs. In the controller design procedure, neural networks are employed to identify unknown auxiliary functions, and the control design obstacle caused by the output nonlinearity is resolved via introducing Nussbaum function. Then, a reliable neural decentralized adaptive control is developed through incorporating the backstepping method and the prescribed performance technique. In the light of Lyapunov stability theory, it is verified that the proposed control scheme can ensure that all the closed‐loop signals are bounded, and can also guarantee that the tracking errors remain within a small enough compact set with the prescribed performance bounds. Finally, some simulation results are given to illustrate the feasibility of the devised control strategy.     

Adaptive fuzzy ILC of nonlinear discrete-time systems with unknown dead zones and control directions

This paper presents an adaptive fuzzy iterative learning control (ILC) design for non-parametrized nonlinear discrete-time systems with unknown input dead zones and control directions. In the proposed adaptive fuzzy ILC algorithm, a fuzzy logic system (FLS) is used to approximate the desired control signal, and an additional adaptive mechanism is designed to compensate for the unknown input dead zone. In dealing with the unknown control direction of the nonlinear discrete-time system, a discrete Nussbaum gain technique is exploited along the iteration axis and applied to the adaptive fuzzy ILC algorithm. As a result, it is proved that the proposed adaptive fuzzy ILC scheme can drive the ILC tracking errors beyond the initial time instants into a tunable residual set as iteration number goes to infinity, and keep all the system signals bounded in the adaptive ILC process. Finally, a simulation example is used to demonstrate the feasibility and effectiveness of the adaptive fuzzy ILC scheme.     

Adaptive consensus control of nonlinear systems with unknown control directions

In this paper, we investigate the adaptive consensus control for a class of nonlinear systems with different unknown control directions where communications among the agents are represented by a directed graph. Based on the backstepping technique, a fully distributed adaptive control approach is proposed without using global information of the topology. Meanwhile, a novel Nussbaum-type function is proposed to address the consensus control with unknown control directions. It is proved that boundedness of all closed-loop signals and asymptotic consensus tracking for all the agents' outputs are ensured. In simulation studies, a numerical example is illustrated to show the effectiveness of the control scheme.     

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.     

未知多变量非线性系统自适应模糊预测控制

对一类未知多变量非线性系统提出了直接自适应模糊预测控制方法,此方法首先对被控对象提出了线性时变子模型加非线性子模型的预测模型,然后直接用模糊逻辑系统组成的向量来设计预测控制器,并基于时变死区函数对控制器中的未知向量和广义误差估计值中的未知矩阵进行自适应调整．文中证明了此方法可使广义误差向量估计值收敛到原点的一个邻域内．     

Adaptive dynamic surface control of nonlinear systems with unknown dead zone in pure feedback form

In this paper, adaptive dynamic surface control (DSC) is developed for a class of pure-feedback nonlinear systems with unknown dead zone and perturbed uncertainties using neural networks. The explosion of complexity in traditional backstepping design is avoided by utilizing dynamic surface control and introducing integral-type Lyapunov function. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness of all signals in the closed-loop system, with arbitrary small tracking error by appropriately choosing design constants. Simulation results demonstrate the effectiveness of the proposed approach.     

Adaptive neural control for a class of stochastic nonlinear time‐delay systems with unknown dead zone using dynamic surface technique

This paper investigates the problem of adaptive control for a class of stochastic nonlinear time‐delay systems with unknown dead zone. A neural network‐based adaptive control scheme is developed by using the dynamic surface control (DSC) technique and the minimal learning parameters algorithm. The dynamic surface control technique, which can avoid the problem of ‘explosion of complexity’ inherent in the conventional backstepping design procedure, is first extended to the stochastic nonlinear time‐delay system with unknown dead zone. The unknown nonlinearities are approximated by the function approximation technique using the radial basis function neural network. For the purpose of reducing the numbers of parameters, which are updated online for each subsystem in the process of approximating the unknown functions, the minimal learning parameters algorithm is then introduced. Also, the adverse effects of unknown time‐delay are removed by using the appropriate Lyapunov–Krasovskii functionals. In addition, the proposed control scheme is systematically derived without requiring any information on the boundedness of the dead zone parameters and avoids the possible controller singularity problem in the approximation‐based adaptive control schemes with feedback linearization technique. It is shown that the proposed control approach can guarantee that all the signals of the closed‐loop system are bounded in probability, and the tracking errors can be made arbitrary small by choosing the suitable design parameters. Finally, a simulation example is provided to illustrate the performance of the proposed control scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

Observer-based adaptive fuzzy tracking control for a class of MIMO nonlinear systems with unknown dead zones and time-varying delays

The adaptive tracking control strategy is investigated for a class of multi-input and multi-output pure-feedback nonlinear delayed systems with unknown dead-zone inputs. This problem is challenging due to the existence of unknown dead zones, time-varying delays and unavoidable state variables. By constructing fuzzy approximators and state observers, the difficulties from unknown nonlinearities and unavailable state variables are surmounted, respectively. Lyapunov–Krasovskii functions are introduced to deal with the time-varying delays. The adaptive controllers are designed by a backstepping method and adaptive technique so that the closed-loop systems remain stable and the target signals can be tracked within a small error as well. At last, two examples are provided to show the effectiveness of the proposed scheme.     

Adaptive neural control for pure-feedback nonlinear time-delay systems with unknown dead-zone: a Lyapunov-Razumikhin method

This paper addresses the problem of adaptive neural control for a class of uncertain pure-feedback nonlinear systems with multiple unknown state time-varying delays and unknown dead-zone. Based on a novel combination of the Razumikhin functional method, the backstepping technique and the neural network parameterization, an adaptive neural control scheme is developed for such systems. All closed-loop signals are shown to be semiglobally uniformly ultimately bounded, and the tracking error remains in a small neighborhood of the origin. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control schemes.     

一类不确定非线性系统自适应模糊滑模控制

针对一类带有未知外部扰动的不确定非线性系统,建立自适应模糊滑模控制器。基于Lyapunov稳定性理论,设计系统可调参数的自适应规则,控制器的设计过程中无需知道系统的具体模型及未知非线性函数的先验知识。数值仿真的结果也验证了该方法的有效性。     

Adaptive fuzzy control of MIMO nonlinear systems with fuzzy dead zones

In this paper, the problem of adaptive fuzzy tracking control is investigated for a class of multi-input multi-output nonlinear systems with fuzzy dead zones. The virtual control gain functions and uncertain functions considered in the studied system are all unknown. Fuzzy logic systems are employed to approximate the unknown functions. With the combination of adaptive backstepping design technique and dynamic surface control method, the problem caused by differentiating nonlinear functions repeatedly is avoided. Furthermore, only one adaptive parameter needs to be updated online for each subsystem, which reduces the computation burden considerably. The presented controller not only guarantees the desired control performance, but also guarantees the boundedness of all closed-loop signals. Simulation results are shown to demonstrate the effectiveness of the proposed algorithm.     

Global regulation for a class of stochastic high-order nonlinear systems with multiple unknown control directions

This paper concerns the global regulation for a class of stochastic high-order nonlinear systems which admit more general system form than the existing works. For details, except for the serious system nonlinearities which show that the considered systems are the generalisations of the strict-feedback systems, the most distinct feature of the systems is exhibited by the multiple unknown control directions, that is, all control coefficients of the virtual and actual control have unknown signs. By skillfully employing the Nussbaum function, and applying the method of adding a power integrator, an effective regulation control scheme is successfully provided for the considered systems. In particular, the presented controller can guarantee that all the closed-loop system states are bounded, and especially the original system states converge to the origin, both in the sense of probability one.     

Global adaptive output feedback control for a class of stochastic nonlinear systems with unknown homogeneous growth rates

This article focuses on the adaptive output feedback stabilization for a class of stochastic nonlinear systems whose drift and diffusion terms satisfy homogeneous growth conditions. Since the homogeneous growth rates are unknown, two dynamic gains are coupled into the full-order homogeneous observer. By virtue of adding a power integrator technique and the homogeneity theory, two adaptive laws and a homogeneous output feedback controller are designed. Based on the celebrated nonnegative semimartingale convergence theorem and the general stochastic Barbˇlat's lemma, it is indicated that all the signals of the closed-loop system are bounded almost surely, and all the system states of the closed-loop system converge to origin almost surely. Finally, the effectiveness of the proposed control scheme is verified by means of both numerical and practical examples.     

Adaptive fuzzy decentralized output feedback control for stochastic nonlinear large‐scale systems using DSC technique

In this paper, an adaptive fuzzy decentralized backstepping output feedback control approach is proposed for a class of uncertain large‐scale stochastic nonlinear systems without the measurements of the states. The fuzzy logic systems are used to approximate the unknown nonlinear functions, and a fuzzy state observer is designed for estimating the unmeasured states. Using the designed fuzzy state observer, and by combining the adaptive backstepping technique with dynamic surface control technique, an adaptive fuzzy decentralized output feedback control approach is developed. It is shown that the proposed control approach can guarantee that all the signals of the resulting closed‐loop system are semi‐globally uniformly ultimately bounded in probability, and the observer errors and the output of the system converge to a small neighborhood of the origin by choosing appropriate design parameters. A simulation example is provided to show the effectiveness of the proposed approaches. Copyright © 2011 John Wiley & Sons, Ltd.     

Approximation-based adaptive fuzzy control for a class of non-strict-feedback stochastic nonlinear systems

This paper considers the problem of adaptive fuzzy control of a class of single-input/single-output （SISO） nonlinear stochastic systems in non-strict-feedback form. Fuzzy logic systems are used to approximate the uncertain nonlinearities and backstepping technique is utilized to construct an adaptive fuzzy controller. The proposed controller guarantees that all the signals in the resulting closed-loop system are bounded in probability. The main contribution of this note lies in providing a control strategy for a class of nonlinear systems in non- strict-feedback form. Simulation result is used to test the effectiveness of the suggested approach.     

控制方向未知非线性系统的自适应重复控制

针对控制方向未知的、存在周期性非参数不确定性的一类非线性系统,给出零误差跟踪的重复控制方法.引入Nussbaum函数设计自适应重复控制器,参数估计修正律采用完全饱和形式,将参数估计囿于预先给定的范围内.分析表明,闭环系统中所有信号本身有界,且跟踪误差本身趋于零.数值仿真结果验证了算法的有效性.     

Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems

In this paper,a new fuzzy adaptive control approach is developed for a class of SISO uncertain pure-feedback nonlinear systems with immeasurable states.Fuzzy logic systems are utilized to approximate the unknown nonlinear functions;and the filtered signals are introduced to circumvent algebraic loop systems encountered in the implementation of the controller,and a fuzzy state adaptive observer is designed to estimate the immeasurable states.By combining the adaptive backstepping technique,an adaptive fuzzy output feedback control scheme is developed.It is proven that the proposed control approach can guarantee that all the signals of the resulting closed-loop system are semi-globally uniformly ultimately bounded(SGUUB),and the observer and tracking errors converge to a small neighborhood of the origin by appropriate choice of the design parameters.Simulation studies are included to illustrate the efectiveness of the proposed approach.     

Robust adaptive fuzzy control for a class of perturbed pure-feedback nonlinear systems

A new design scheme of direct adaptive fuzzy controller for a class of perturbed pure-feedback nonlinear systems is proposed. The design is based on backstepping and the approximation capability of the first type fuzzy systems. A continuous robust term is adopted to minify the influence of modeling errors or disturbances. By introducing the modified integral-type Lyapunov function, the approach is able to avoid the requirement of the upper bound of the first time derivation of the high frequency control gain. Through theoretical analysis, the closed-loop control system is proven to be semi-globally uniformly ultimately bounded, with tracking error converging to a residual set.     

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.