Robust adaptive neural control of uncertain pure-feedback nonlinear systems

In this paper, a robust adaptive neural control design approach is presented for a class of uncertain pure-feedback nonlinear systems. To reduce the complexity of the both controller structure and computation, only one neural network is used to approximate the lumped unknown function of the system at the last step of the recursive design process. By this approach, the complexity growing problem existing in conventional methods can be eliminated completely. Stability analysis shows that all the closed-loop system signals are uniformly ultimately bounded, and the steady state tracking error can be made arbitrarily small by appropriately choosing control parameters. Simulation results demonstrate the effectiveness and merits of the proposed approach.     

一类不确定非线性纯反馈系统的自适应鲁棒模糊控制

针对一类带有不确定性的非线性MIMO纯反馈系统,提出一种自适应鲁棒模糊控制方法,该方法放宽了已有文献对系统模型的限制条件,基于李雅普诺夫分析方法获得了控制输入和自适应律．在控制输入设计中,鲁棒控制项用于补偿逼近误差向量．通过选择适当的设计参数。提出的控制方法使得闭环系统的所有信号是一致有界的和跟踪误差向量的范数收敛到小的零邻域内．仿真结果表明了所提出方法的有效性．     

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.     

Adaptive NN control of uncertain nonlinear pure-feedback systems

This paper is concerned with the control of nonlinear pure-feedback systems with unknown nonlinear functions. This problem is considered difficult to be dealt with in the control literature, mainly because that the triangular structure of pure-feedback systems has no affine appearance of the variables to be used as virtual controls. To overcome this difficulty, implicit function theorem is firstly exploited to assert the existence of the continuous desired virtual controls. NN approximators are then used to approximate the continuous desired virtual controls and desired practical control. With mild assumptions on the partial derivatives of the unknown functions, the developed adaptive NN control schemes achieve semi-global uniform ultimate boundedness of all the signals in the closed-loop. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters.     

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 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.     

Full state constraints-based adaptive control for switched nonlinear pure-feedback systems

This paper investigates the problem of full state constraints-based adaptive control for a class of switched nonlinear pure-feedback systems under arbitrary switchings. First, the switched pure-feedback system is transformed into a switched strict-feedback system with non-affine terms based on the mean value theorem. Then, by exploiting the common Lyapunov function (CLF) method, the Barrier Lyapunov function method and backstepping, state feedback controllers of individual subsystems and a common Barrier Lyapunov function (CBLF) are constructed, which guarantee that all signals in the closed-loop system are global uniformly bounded under arbitrary switchings, and full state constraints are not violated. Furthermore, the tracking error can converge to a bounded compact set. Two examples, which include a single-link robot as a practical example, are provided to demonstrate the effectiveness of the proposed design method.     

Adaptive neural network tracking control for a class of switched stochastic pure-feedback nonlinear systems with backlash-like hysteresis

In this paper, an adaptive neural network tracking control approach is proposed for a class of switched stochastic pure-feedback nonlinear systems with backlash-like hysteresis. In the design procedure, an affine variable is constructed, which avoids the use of the mean value theorem, and the additional first-order low-pass filter is employed to deal with the problem of explosion of complexity. Then, a common Lyapunov function and a state feedback controller are explicitly obtained for all subsystems. It is proved that the proposed controller that guarantees all signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error remains an adjustable neighbourhood of the origin. Finally, simulation results show the effectiveness of the presented control design approach.     

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 neural network control for a class of uncertain nonlinear systems in pure-feedback form

A procedure is developed for the design of adaptive neural network controller for a class of SISO uncertain nonlinear systems in pure-feedback form. The design procedure is a combination of adaptive backstepping and neural network based design techniques. It is shown that, under appropriate assumptions, the solution of the closed-loop system is uniformly ultimately bounded.     

Adaptive neural control for a class of non-affine pure-feedback nonlinear systems

A novel adaptive neural control scheme is designed for a class of pure-feedback nonlinear systems with non-affine functions possibly being discontinuous. The non-affine function is not necessary to be continuous with respect to control variables or input, and the bounds of non-affine function are unknown functions. Some compact sets are constructively introduced to investigate the bounds of non-affine function so as to cope with the difficulty from these unknown bounds. Moreover, the dynamic surface control technique has been utilised for handling with the problem of ‘explosion of complexity’, and the minimal learning parameter technique is also employed to overcome the problem of excessive parameters. Furthermore, it is highly proved that all the variables will always stay in the introduced compact sets, and all the signals in the closed-loop control system are semi-globally uniformly ultimately bounded by choosing the appropriate design parameters. Finally, simulation examples are provided to demonstrate the effectiveness of the designed approach.     

纯反馈非线性离散系统的自适应神经网络控制

针对一类未知的纯反馈非线性离散系统,提出了基于反步法设计的自适应神经网络控制方法.为避免反步法设计中可能出现的因果矛盾问题,首先将系统进行等价变换,然后利用隐函数定理证实了理想虚拟控制输入和实际控制输入的存在性.利用高阶神经网络估计这些控制量,并基于反步法设计自适应神经网络控制系统,证明了闭环系统半全局一致最终有界.仿真结果验证了所提出方法的有效性.     

一类纯反馈非线性系统的反推控制

研究了一类纯反馈非线性系统的输出跟踪问题.通过引入一个新的坐标变换,提出了一种基于反推设计的状态反馈控制算法.所得控制算法不仅保证了系统跟踪误差全局渐近稳定,同时使得闭环系统所有信号有界.最后,一个仿真实例验证了本文控制算法的有效性.     

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 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.     

Adaptive fault diagnosis and fault-tolerant control of MIMO nonlinear uncertain systems

This article presents an integrated fault diagnosis and fault-tolerant control (FTC) methodology for a class of nonlinear multi-input–multi-output systems. Based on the fault information obtained during the diagnostic procedure, an FTC component is designed to compensate for the effect of faults. In the presence of a fault, a baseline controller guarantees the boundedness of all the system signals until the fault is detected. After fault detection and then again after isolation, the controller is reconfigured to improve the tracking performance using online fault diagnostic information. Under certain assumptions, the stability and tracking performances of the closed-loop system are rigorously investigated. It is shown that the system signals always remain bounded and the output tracking error converges to a neighbourhood of the origin of the state space.     

Robust adaptive control for nonlinear uncertain systems

A direct robust adaptive control framework for nonlinear uncertain systems with constant linearly parameterized uncertainty and nonlinear state-dependent uncertainty is developed. The proposed framework is Lyapunov-based and guarantees partial asymptotic robust stability of the closed-loop system; that is, asymptotic robust stability with respect to part of the closed-loop system states associated with the plant. Finally, a numerical example is provided to demonstrate the efficacy of the proposed approach.     

Adaptive sliding mode control of uncertain nonlinear systems with preassigned settling time and its applications

This paper investigates the adaptive tracking control of second‐order nonlinear systems with nonlinearly parameterized uncertainties and disturbances, as well as multiplicative uncertainty in the control coefficient matrix. A novel adaptive function augmented sliding mode control approach is proposed such that the tracking error converges to a neighborhood of zero with the preassigned size within the preassigned settling time. In the proposed control scheme, the control gains increase as the adaptive estimate values increase only when necessary, that is, when the current control gains are not big enough to suppress the uncertainties or disturbances; as a result, the conservativeness of control design caused by unnecessary high control gains can be effectively reduced. Moreover, the chattering phenomenon well known in the sliding mode control is eliminated by using the saturation function to replace the signum function, and the possible persistent increasing problem of the adaptive estimate values due to measurement disturbances or noises on the feedback is also well addressed by introducing “dead‐zone” nonlinearities in the adaptive laws. In addition, an improved method to construct the desired error trajectory is proposed, and this method could avoid the large undershoot‐like or overshoot‐like phenomena, which the traditional one may result in. The obtained results are finally applied to the motion control of the underwater vehicle and the rendezvous control of spacecraft, and the simulation results illustrate the effectiveness and the advantages of the proposed control approach.     

Adaptive neural control of non-affine pure-feedback non-linear systems with input nonlinearity and perturbed uncertainties

In this article, two robust adaptive control schemes are investigated for a class of completely non-affine pure-feedback non-linear systems with input non-linearity and perturbed uncertainties using radial basis function neural networks (RBFNNs). Based on the dynamic surface control (DSC) technique and using the quadratic Lyapunov function, the explosion of complexity in the traditional backstepping design is avoided when the gain signs are known. In addition, the unknown virtual gain signs are dealt with using the Nussbaum functions. Using the mean value theorem and Young's inequality, only one learning parameter needs to be tuned online at each step of recursion. It is proved that the proposed design method is able to guarantee semi-global uniform ultimate boundedness (SGUUB) of all signals in the closed-loop system. Simulation results verify the effectiveness of the proposed approach.     

Adaptive finite-time stabilisation of high-order uncertain nonlinear systems

This paper studies the problem of finite-time stabilisation of more general high-order nonlinear systems with dynamic and parametric uncertainties. By characterising the unmeasured dynamic uncertainty with finite-time input-to-state stability (FTISS), skillfully combining Lyapunov function, sign function, backstepping, adaptive control and FTISS approaches, and using finite-time stability theory, an adaptive state feedback controller is designed to guarantee high-order uncertain nonlinear systems globally finite-time stable.