多变量非线性系统的间接模糊输出反馈自适应控制

针对一类多输入多输出非线性不确定系统，提出一种基于观测器的模糊间接自适应控制方法，并基于李亚普诺夫函数方法，导出了输出反馈控制律以及参数的自适应律，证明了整个控制方案不但能保证闭环系统稳定，而且取得了良好的跟踪控制性能。     

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

Robust fuzzy control of nonlinear stochastic delay systems with impulsive effects

The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive stochastic systems with time-varying delays is investigated. The nonlinear delay system is represented by the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for mean square exponential stability of the closed-loop system are derived in terms of linear matrix inequalities. Finally, a numerical example is given to illustrate the applicability of the theoretical results.     

Robust adaptive fuzzy tracking control for a class of strict-feedback nonlinear systems based on backstepping technique

In this paper, the robust adaptive fuzzy tracking control problem is discussed for a class of perturbed strict-feedback nonlinear systems. The fuzzy logic systems in Mamdani type are used to approximate unknown nonlinear functions. A design scheme of the robust adaptive fuzzy controller is proposed by use of the backstepping technique. The proposed controller guarantees semi-global uniform ultimate boundedness of all the signals in the derived closed-loop system and achieves the good tracking performance. The possible controller singularity problem which may occur in some existing adaptive control schemes with feedback linearization techniques can be avoided. In addition, the number of the on-line adaptive parameters is not more than the order of the designed system. Finally, two simulation examples are used to demonstrate the effectiveness of the proposed control scheme.     

Direct adaptive fuzzy control for a class of MIMO nonlinear systems

This article presents a direct adaptive fuzzy control scheme for a class of uncertain continuous-time multi-input multi-output nonlinear (MIMO) dynamic systems. Within this scheme, fuzzy systems are employed to approximate an unknown ideal controller that can achieve control objectives. The adjustable parameters of the used fuzzy systems are updated using a gradient descent algorithm that is designed to minimize the error between the unknown ideal controller and the fuzzy controller. The stability analysis of the closed-loop system is performed using a Lyapunov approach. In particular, it is shown that the tracking errors are bounded and converge to a neighborhood of the origin. Simulations performed on a two-link robot manipulator illustrate the approach and exhibit its performance.     

非线性模糊时滞系统鲁棒自适应控制

研究一类基于模糊T-S模型的非线性时滞系统鲁棒镇定问题．基于记忆型状态反馈策略，首先给出由T-S模糊模型描述的非线性时滞系统在时滞精确已知情况下的鲁棒镇定准则；然后给出非线性时滞系统在时滞未知情况下的鲁棒自适应控制策略．所设计的控制器可确保闭环系统渐近稳定，且具有良好的可操作性．最后通过仿真实例证明了该方法的正确性和有效性．     

Model reference adaptive robust fuzzy control for ship steering autopilot with uncertain nonlinear systems

A novel model reference adaptive robust fuzzy control algorithm is presented for ship steering autopilot, which is an uncertain nonlinear system. In the proposed algorithm, fuzzy logic systems have been used to approximate lumped unknown function in the ship steering systems and the adaptive mechanism with minimal learning parameter, i.e. only one parameter, has been achieved by use of Lyapunov approach. The proposed methodology is verified using the simulation mode of the Dalian Maritime University's ocean-going training ship named Yulong. It is shown that the proposed algorithm guarantees that the ship steering autopilot system is asymptotically stable and its tracking error can approach to zero.     

Event-triggered adaptive fuzzy tracking control of nonlinear MIMO systems

This paper addresses the problem of an adaptive fuzzy event-triggered control (ETC) for uncertain multi-input and multi-output nonlinear systems. To reduce the communication burden of the network control systems, a novel state-dependent event-triggering condition is designed to decide when to update the controllers. By combining the backstepping and event-trigged techniques, the adaptive fuzzy ETC strategies are developed and the resulting closed-loop system is semi-global bounded. Finally, the analytical results are substantiated using simulation studies.     

基于观测器的不确定非线性系统的自适应鲁棒模糊控制

针对单输入单输出不确定非线性系统提出了一种自适应鲁棒模糊控制算法.该算法通过设计观测器来估计系统的状态向量,因此不要求假设系统的状态向量是可测的.在这个算法中,主要的假设为最优逼近参数向量与标称参数向量之差的范数和逼近误差的界限是未知的.通过只对未知界限估计的调节,该算法减轻了在线计算量并且提高了系统的鲁棒性.所设计的自适应鲁棒模糊控制算法保证了闭环系统的所有信号是一致有界的并且跟踪误差估计收敛到一个小的零邻域内.仿真例子证实了所提方法的可行性.     

一类严格反馈非线性系统的间接自适应模糊控制

针对一类不确定严格反馈非线性系统,设计了间接自适应模糊控制方法．该方法用模糊逻辑系统逼近设计过程中的未知函数,基于时变宽度死区对模糊逻辑系统中的未知参数进行自适应调节,并对时变死区宽度设计了自适应律．证明了该方法能使闭环系统的所有信号有界,且可使跟踪误差收敛到原点的小邻域内．仿真算例验证了该方法的有效性．     

Fuzzy adaptive control of delayed high order nonlinear systems

This paper deals with the problem of tracking control for a class of high order nonlinear systems with input delay. The unknown continuous functions of the system are estimated by fuzzy logic systems (FLS). A state conversion method is introduced to eliminate the delayed input item. By means of the backstepping algorithm, the property of semi-globally uniformly ultimately bounded (SGUUB) of the closed-loop system is achieved. The stability of the closed-loop system is proved according to Lyapunov second theorem on stability. The tracking error is proved to be bounded which ultimately converges to an adequately small compact set. Finally, a computer simulation example of high order nonlinear systems is presented, which illustrates the effectiveness of the control scheme.     

非线性系统的直接自适应输出反馈监督模糊控制

针对一类单输入单输出非线性不确定系统，提出一种稳定的直接自适应模糊输出反馈监督控制算法，该算法不需要系统的状态完全可测的假设条件，监督控制不仅迫使系统的状态在指定的集合内，而且当模糊自适应控制处于良好的工作状态时，监督控制可以关闭，证明了整个模糊自适应输出反馈控制算法可以保证闭环系统稳定。     

Robust adaptive self-structuring fuzzy control design for nonaffine,nonlinear systems

In this article, a robust adaptive self-structuring fuzzy control (RASFC) scheme for the uncertain or ill-defined nonlinear, nonaffine systems is proposed. The RASFC scheme is composed of a robust adaptive controller and a self-structuring fuzzy controller. In the self-structuring fuzzy controller design, a novel self-structuring fuzzy system (SFS) is used to approximate the unknown plant nonlinearity, and the SFS can automatically grow and prune fuzzy rules to realise a compact fuzzy rule base. The robust adaptive controller is designed to achieve an L ₂ tracking performance to stabilise the closed-loop system. This L ₂ tracking performance can provide a clear expression of tracking error in terms of the sum of lumped uncertainty and external disturbance, which has not been shown in previous works. Finally, five examples are presented to show that the proposed RASFC scheme can achieve favourable tracking performance, yet heavy computational burden is relieved.     

Stable adaptive fuzzy control of nonlinear systems using small-gain theorem and LMI approach

A new design scheme of stable adaptive fuzzy control for a class of nonlinear systems is proposed in this paper. The T-S fuzzy model is employed to represent the systems. First, the concept of the so-called parallel distributed compensation (PDC) and linear matrix inequality (LMI) approach are employed to design the state feedback controller without considering the error caused by fuzzy modeling. Sufficient conditions with respect to decay rate α are derived in the sense of Lyapunov asymptotic stability. Finally, the error caused by fuzzy modeling is considered and the input-tostate stable (ISS) method is used to design the adaptive compensation term to reduce the effect of the modeling error. By the small-gain theorem, the resulting closed-loop system is proved to be input-to-state stable. Theoretical analysis verifies that the state converges to zero and all signals of the closed-loop systems are bounded. The effectiveness of the proposed controller design methodology is demonstrated through numerical simulation on the chaotic Henon system.     

Coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control

The coordination of fractional-order nonlinear multi-agent systems via distributed impulsive control method is studied in this paper. Based on the theory of impulsive differential equations, algebraic graph theory, Lyapunov stability theory and Mittag-Leffler function, two novel sufficient conditions for achieving the cooperative control of a class of fractional-order nonlinear multi-agent systems are derived. Finally, two numerical simulations are verified to illustrate the effectiveness and feasibility of the proposed method.     

一类非线性系统的广义模糊双曲正切模型自适应控制器设计

针对一类非线性系统的稳定控制器设计问题, 根据广义模糊双曲正切模型的万能逼近性质, 提出一种带有可调参数的广义模糊双曲正切模型的自适应控制器设计方法. 该设计方法的优点是使得自适应律的个数不依赖于广义模糊双曲正切模型的线性基函数的输出形式, 可以有效减少在线估计的参数数目, 并且能够保证被控系统的状态一致终极有界. 最后通过数值算例表明了所提出的设计方法的有效性.

     

基于观测器的一类非线性系统的自适应模糊控制

针对一类有界的不确定非线性系统设计了模糊观测器和自适应控制器.该方法不需要系统状态完全可测的条件,而是通过模糊观测器估计系统的状态变量并且能保证观测误差是一致最终有界的.该自适应控制器取得了良好的控制效果并且保证了跟踪误差的一致最终有界性.仿真结果表明了本文所提出的方法有效性.     

Event-triggered adaptive fuzzy control for nonstrict-feedback nonlinear systems with output hysteresis

This paper concentrates upon the issue of adaptive fuzzy tracing control for a class of nonstrict-feedback nonlinear systems output with hysteresis via an event-triggered strategy. To handle the difficulty caused by the nonstrict nonlinear systems, the variable separation technique is introduced. The design difficulty of output hysteresis is addressed by employing a hysteresis inverse function and Nussbaum function to compensate unmeasurable state signal. Meanwhile, the fuzzy logic system (FLS) is used to estimate the unknown function at each step of recursion. Moreover, by devising the relative threshold event-triggered mechanism (ETM), the frequency of actuators and controllers can be largely decreased. Thus, the adaptive fuzzy event-triggered tracing control strategy is proposed by combining the barrier Lyapunov function and backstepping technique. With the proposed scheme, it is theoretically demonstrated that all signals in the closed-loop system are bounded, and the tracing errors are driven to a small neighborhood of the origin under the output constraint. Eventually, two examples demonstrate the efficacy of the proposed control strategy.     

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.     

一类非线性离散系统的直接自适应模糊控制

针对一类含延迟非线性离散系统,提出了一种直接自适应模糊控制器设计的新方案．将系统用T-S模糊模型来表示,并基于并行分布补偿(PDC)基本思想设计了一种具有未知参数的模糊控制器,同时采用梯度下降算法对该控制器的参数进行在线辨识．通过输入到状态稳定(ISS)方法,证明了系统输出和参考输出的误差有界且满足一定的平均性能．仿真表明本方法的有效性．