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 with prespecified tracking performance for a class of nonlinear systems

This paper aims at exploring an adaptive fuzzy dynamic surface control (DSC) with prespecified tracking performance for a class of nonlinear systems in strict‐feedback form. Incorporating DSC technique into fuzzy logic systems (FLSs), it is shown that the design procedure and the computational burden can be greatly reduced. Moreover, by introducing a performance function in controller design, the prespecified tracking performance, i.e. the convergence rate, the allowed maximum overshoot and the steady state error, can be achieved. Simulation results are presented to demonstrate the efficiency of the proposed scheme. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

一类纯反馈非线性系统的动态面控制

针对一类非仿射输入纯反馈非线性系统,提出了一种动态面控制算法.不同于运用中值定理,该算法通过引入一个辅助系统,将原系统转化为输入仿射系统,结合动态面控制与反推设计法,消除了反推法中"计算膨胀"问题.所设计控制器保证了闭环系统所有信号半全局一致最终有界,且通过选择合适的设计参数可使跟踪误差收敛到原点的一个小邻域内.一个仿真实例进一步验证了所提控制算法的有效性.     

Adaptive output feedback control of uncertain nonlinear systems based on dynamic surface control technique

An adaptive output feedback control approach is studied for a class of uncertain nonlinear systems in the parametric output feedback form. Unlike the previous works on the adaptive output feedback control, the problem of ‘explosion of complexity’ of the controller in the conventional backstepping design is overcome in this paper by introducing the dynamic surface control (DSC) technique. In the previous schemes for the DSC technique, the time derivative for the virtual controllers is assumed to be bounded. In this paper, this assumption is removed. It can be proven that the resulting closed‐loop system is stable in the sense that all the signals are semi‐global uniformly ultimately bounded and the system output tracks the reference signal to a bounded compact set. A simulation example is given to verify the effectiveness of the proposed approach. Copyright © 2011 John Wiley & Sons, Ltd.     

Adaptive dynamic surface asymptotic tracking for a class of uncertain nonlinear systems

This paper contributes to dynamic surface asymptotic tracking for a class of uncertain nonlinear systems in strict‐feedback form. By utilizing the nonlinear filters with a positive time‐varying integral function, an adaptive state feedback controller is explicitly designed via a dynamic surface approach, where the compensating term with the estimate of an unknown bound is introduced to eliminate the effect raised by the boundary layer error at each step. Compared with the existing results in the literature, the proposed control scheme not only avoids the issue of “explosion of complexity” inherent in the backstepping procedure but also holds the asymptotic output tracking. Finally, simulation results are presented to verify the effectiveness of the proposed methodology.     

一种简化的自适应模糊动态面控制

针对一类不确定非线性时变时滞系统,提出了一种简化的自适应模糊动态面控制方法.该方法取消了对系统时滞常做的假设.仅采用一个模糊逼近器便使所有的未知函数得到补偿,简化了控制器的结构.通过构造合适的Lyapunov-Krasovskii泛函,闭环系统的所有信号被证明为半全局一致最终有界.仿真实例进一步验证了控制方案的有效性.     

Adaptive fuzzy dynamic surface control for uncertain nonlinear systems in pure-feedback form with input and state constraints using noisy measurements

This paper is concerned with the design of an adaptive fuzzy dynamic surface control for uncertain nonlinear pure-feedback systems with input and state constraints using a set of noisy measurements. The design approach is described as follows. The nonlinear uncertainties are approximated by using the fuzzy logic systems at the first stage, secondly the adaptive fuzzy dynamic surface control is introduced to remove the problem of the explosion of complexity for the derivation of the adaptive fuzzy backstepping control, thirdly a new saturation function for state constraints is proposed to design the controllers based on the Lyapunov function, fourthly the number of the adjustable parameters is reduced by using the simplified extended single input rule modules, and finally the weighted least squares estimator to take the estimates for the un-measurable states and the adjustable parameters is in a simplified structure designed. The proposed approach provides effective system performance in the simulation experiment.     

一类高次随机非线性系统的自适应动态面控制

针对一类含非线性参数高次随机非线性系统的输出跟踪控制问题,基于自适应增加幂次积分方法,利用参数分离技术和动态面技术,给出了一种自适应光滑状态反馈控制器设计方法。利用Sigmoid函数设计参数自适应律,保证了其导数连续。将低通滤波器引入控制器设计过程,避免了“微分爆炸”现象。通过构造适当形式的控制Lyapunov函数进行稳定性分析,证明了系统输出能被依概率地调节至参考信号的邻域范围。仿真结果验证了所提控制器设计方案的有效性。     

Adaptive fuzzy observer backstepping control for a class of uncertain nonlinear systems with unknown time-delay

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.     

动态不确定非线性系统直接自适应模糊backstepping控制

对一类单输入单输出动态不确定非线性系统,提出一种直接自适应模糊backstepping和小增益相结合的控制方法.设计中,首先用模糊逻辑系统逼近虚拟控制器:其次把自适应模糊控制和backstepping控制设计技术相结合.给出了直接自适应模糊控制设计方法.最后基于Lyapunov函数和小增益方法证明了整个闭环系统的稳定性.仿真实例进一步验证了所提方法的有效性.     

严格反馈非线性系统的自适应模糊控制

针对一类不确定非线性系统,基于backstepping方法提出了一种新的鲁棒自适应模糊控制器设计方案。该方案通过引入最优逼近误差的自适应补偿项和新的鲁棒项,削减建模误差和参数估计误差的影响,从而在稳定性分析中取消了要求逼近误差平方可积或逼近误差的上确界已知的条件。理论分析证明了闭环系统状态有界,跟踪误差收敛到零的较小邻域内。仿真结果表明了该方法的有效性。     

Adaptive dynamic surface control using disturbance observer for nonlinear systems with input saturation and output constraints

An adaptive dynamic surface control (DSC) approach using fuzzy approximation and nonlinear disturbance observer (NDO) for uncertain nonlinear systems in the presence of input saturation, output constraint and unknown external disturbances is proposed in this paper. The issue of input saturation is addressed by introducing a lower bound assumption on the approximation function of saturation. The output constraint is handled by introducing an appropriate barried Lyapunov function. The nonlinear disturbance observer (NDO) is employed to estimate the unknown unmatched disturbances. It is manifested that the ultimately bounded convergence of all the variables in the closed-loop system is guaranteed and the tracking error can be made farely small by tuning the design parameters. Finally, two simulation examples illustrate the effectiveness and feasibility of the proposed approach.     

Adaptive fuzzy tracking control for a class of uncertain MIMO nonlinear systems using disturbance observer

In this paper,the adaptive fuzzy tracking control is proposed for a class of multi-input and multioutput(MIMO)nonlinear systems in the presence of system uncertainties,unknown non-symmetric input saturation and external disturbances.Fuzzy logic systems(FLS)are used to approximate the system uncertainty of MIMO nonlinear systems.Then,the compound disturbance containing the approximation error and the timevarying external disturbance that cannot be directly measured are estimated via a disturbance observer.By appropriately choosing the gain matrix,the disturbance observer can approximate the compound disturbance well and the estimate error converges to a compact set.This control strategy is further extended to develop adaptive fuzzy tracking control for MIMO nonlinear systems by coping with practical issues in engineering applications,in particular unknown non-symmetric input saturation and control singularity.Within this setting,the disturbance observer technique is combined with the FLS approximation technique to compensate for the efects of unknown input saturation and control singularity.Lyapunov approach based analysis shows that semi-global uniform boundedness of the closed-loop signals is guaranteed under the proposed tracking control techniques.Numerical simulation results are presented to illustrate the efectiveness of the proposed tracking control schemes.     

Adaptive backstepping controller design for nonlinear uncertain systems using fuzzy neural systems

In this article, we propose an adaptive backstepping control scheme using fuzzy neural networks (FNNs), ABC_FNN, for a class of nonlinear non-affine systems in non-triangular form. The nonlinear non-affine system contains the uncertainty, external disturbance or parameters variations. Two kinds of FNN systems are used to estimate the unknown system functions. According to the FNN estimations, the adaptive backstepping control (ABC_FNN) signal can be generated by backstepping design procedure such that the system output follows the desired trajectory. To ensure robustness and performance, a proportional-integral-surface function and robust controller are designed to improve the control performance. Based on the Lyapunov stability theory, the stability of a closed-loop system is guaranteed and the adaptive laws of the FNN parameters are obtained. This approach is also valid for nonlinear affine system with uncertainty or disturbance. The uncertainty and disturbance terms are estimated by FNNs and treated by the ABC_FNN scheme. Finally, the effectiveness of the proposed ABC_FNN is demonstrated through the simulation of controlling a nonlinear non-affine system and the continuously stirred tank reactor plant to demonstrate the performances of our approach.     

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.     

非线性离散时间系统的自适应模糊补偿控制

针对一类非线性离散时间系统,提出一种自适应模糊逻辑补偿控制方案.控制律由跟踪控制律和逼近误差补偿控制律两部分组成,利用模糊逻辑系统对系统参数扰动和外界干扰进行自适应补偿,由模糊滑模控制律实现对模糊逻辑系统逼近误差的进一步补偿.所设计的控制器可保证闭环系统一致最终有界.将该控制器用于月球探测车动态转向系统中,仿真结果表明了该方法的有效性.     

Adaptive fuzzy output-feedback fault-tolerant tracking control of a class of uncertain nonlinear switched systems

ABSTRACT

This paper considers the output-feedback fault-tolerant tracking control problem for a class of uncertain nonlinear switched systems with nonlinear faults and strict-feedback form, where the faults which are nonaffine occur on the actuator. As a kind of specialised function approximating tool, fuzzy logic systems (FLSs), are employed to approximate the unknown smooth nonlinear functions. A switched fuzzy observer is designed to address the problem of unmeasurable states, filtered signals are used to address algebraic loop problem and the average dwell time (ADT) method is further utilised to prove the stability of the resulting closed-loop systems under a type of slowly switching signals. Based on the backstepping recursive design technique and Lyapunov function method, an adaptive fuzzy output-feedback control scheme is developed. The developed control method can ensure all the signals are semi-globally uniformly ultimately bounded (SGUUB) and the system output tracks the reference signal tightly even if unknown fault occurs. A simulation carried on an example demonstrates the validity of the obtained control scheme.     

Adaptive dynamic surface control for MIMO nonlinear time-varying systems with prescribed tracking performance

In this paper, an adaptive dynamic surface control scheme is proposed for a class of multi-input multi-output (MIMO) nonlinear time-varying systems. By fusing a bound estimation approach, a smooth function and a time-varying matrix factorisation, the obstacle caused by unknown time-varying parameters is circumvented. The proposed scheme is free of the problem of explosion of complexity and needs only one updated parameter at each design step. Moreover, all tracking errors can converge to predefined arbitrarily small residual sets with a prescribed convergence rate and maximum overshoot. Such features result in a simple adaptive controller which can be easily implemented in applications with less computational burden and satisfactory tracking performance. Simulation results are presented to illustrate the effectiveness of the proposed scheme.     

一类纯反馈力学系统的自适应模糊动态面控制

针对一类纯反馈形式的不稳定力学系统,提出自适应模糊动态面控制方法。在一般动态面控制的设计框架下,引入模糊系统逼近模型的未知函数,设计自适应律在线估计模糊系统权参数和模型未知参数,通过Lyapunov方法证明得出闭环系统半全局稳定。该策略避免了传统反演设计存在的“微分爆炸”现象,并且解决了纯反馈系统控制设计中通常存在的循环设计问题。仿真结果表明,控制系统能够克服不确定性,且能够简单有效地实现跟踪控制。     

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.