Robust control design for nonlinear uncertain systems with anunknown time-varying control direction

A continuous robust control design approach is proposed for first-order nonlinear systems whose dynamics contain both nonlinear uncertainty and an unknown time-varying control direction. The so-called control direction is the multiplier of the control term in the dynamic equation, and it effectively represents the direction of motion under any given control. A nonlinear robust control is designed to online and continuously identify sign changes of the unknown control direction and to guarantee stability of uniform ultimate boundedness. The proposed robust control design requires only three conditions: the nominal system is stable, the control direction is smooth, and the uncertainty in the system is bounded by a known function. The necessity of these conditions is established in this paper. Continuity of the proposed robust control is achieved by using a so-called shifting law that changes smoothly the sign of robust control and tracks the change of the unknown control direction. Analysis and design is shown by using Lyapunov's direct method     

Global robust output regulation of lower triangular systems with unknown control direction

This paper presents the solvability conditions for the global robust output regulation problem for lower triangular nonlinear systems assuming the control direction is unknown. The approach used is an integration of the robust stabilization technique and Nussbaum gain technique.     

Adaptive iterative learning control for nonlinearly parameterized systems with unknown time-varying delay and unknown control direction

This paper proposes a new adaptive iterative learning control approach for a class of nonlinearly parameterized systems with unknown time-varying delay and unknown control direction.By employing the parameter separation technique and signal replacement mechanism,the approach can overcome unknown time-varying parameters and unknown time-varying delay of the nonlinear systems.By incorporating a Nussbaum-type function,the proposed approach can deal with the unknown control direction of the nonlinear systems.Based on a Lyapunov-Krasovskii-like composite energy function,the convergence of tracking error sequence is achieved in the iteration domain.Finally,two simulation examples are provided to illustrate the feasibility of the proposed control method.     

Fuzzy adaptive robust backstepping stabilization for SISO nonlinear systems with unknown virtual control direction

In this paper, a direct fuzzy adaptive robust control approach is proposed for a class of SISO nonlinear systems with completely unknown virtual control directions, unknown nonlinearities, unmodeled dynamics and dynamic disturbances. In the backstepping recursive design, fuzzy logic systems are employed to approximate the combined nonlinear uncertainties, a dynamic signal and Nussbaum gain technique are introduced into the control scheme to dominate the dynamic uncertainties and solve the unknown signs of virtual control directions, respectively. It is proved that the proposed robust fuzzy adaptive scheme can guarantee the all signals in the closed-loop system are semi-globally uniformly ultimately bounded. The effectiveness of the proposed approach is illustrated via three examples.     

Neural network-based robust adaptive control of nonlinear systems with unmodeled dynamics

A neural network-based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unmodeled dynamics. By on-line approximating the unknown nonlinear functions and unmodeled dynamics by radial basis function (RBF) networks, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. It is proved that with the proposed control law, the closed-loop system is stable and the tracking error converges to zero in the presence of unmodeled dynamics and unknown nonlinearity. A simulation example is presented to demonstrate the method.     

A new integral inequality and its applications to robust control problems of uncertain nonlinear systems

In this paper, a new integral inequality is presented. By combining this integral inequality with adaptive approach, new design methods can be developed to synthesize some adaptive robust control schemes for a large class of uncertain nonlinear systems and to deal with well the unknown nonlinearities appearing in uncertain nonlinear control dynamical systems. As an application of the presented integral inequality to control theory, the robust stabilization problem is considered for a class of uncertain strict‐feedback nonlinear systems with both time‐delay and unknown dead‐zone input nonlinearities. It is shown that there are two main merits in the design method based on the integral inequality presented in this paper. The first one is that one need not estimate and know the unknown nonlinearities to synthesize some stabilizing control schemes. The second one is that the resulting feedback control schemes have rather simple structure.     

Robust control approach for input–output linearizable nonlinear systems using high‐gain disturbance observer

This paper addresses a robust control approach for a class of input–output linearizable nonlinear systems with uncertainties and modeling errors considered as unknown inputs. As known, the exact feedback linearization method can be applied to control input–output linearizable nonlinear systems, if all the states are available and modeling errors are negligible. The mentioned two prerequisites denote important problems in the field of classical nonlinear control. The solution approach developed in this contribution is using disturbance rejection by applying feedback of the uncertainties and modeling errors estimated by a specific high‐gain disturbance observer as unknown inputs. At the same time, the nonmeasured states can be calculated from the estimation of the transformed system states. The feasibility and conditions for the application of the approach on mechanical systems are discussed. A nonlinear multi‐input multi‐output mechanical system is taken as a simulation example to illustrate the application. The results show the robustness of the control design and plausible estimations of full‐rank disturbances.Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive neural control for a class of uncertain nonlinear systems with unknown time delay

A neural network (NN)‐based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unknown time delay. By approximating on‐line the unknown nonlinear functions with a three‐layer feedforward NN, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. The control law is delay independent and possible controller singularity problem is avoided. It is proved that with the proposed neural control law, all the signals in the closed‐loop system are semiglobally bounded in the presence of unknown time delay and unknown nonlinearity. A simulation example is presented to demonstrate the method. Copyright © 2008 John Wiley & Sons, Ltd.     

Robust adaptive control of nonlinear systems with unknown time delays

In this paper, robust adaptive control is presented for a class of parametric-strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for. Controller singularity problems are solved by employing practical robust control and regrouping unknown parameters. By using differentiable approximation, backstepping design can be carried out for a class of nonlinear systems in strict-feedback form. It is proved that the proposed systematic backstepping design method is able to guarantee global uniform ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin. Simulation results are provided to show the effectiveness of the proposed approach.     

Robust approximation-free prescribed performance control for nonlinear systems and its application

This paper presents a robust prescribed performance control approach and its application to nonlinear tail-controlled missile systems with unknown dynamics and uncertainties. The idea of prescribed performance function (PPF) is incorporated into the control design, such that both the steady-state and transient control performance can be strictly guaranteed. Unlike conventional PPF-based control methods, we further tailor a recently proposed systematic control design procedure (i.e. approximation-free control) using the transformed tracking error dynamics, which provides a proportional-like control action. Hence, the function approximators (e.g. neural networks, fuzzy systems) that are widely used to address the unknown nonlinearities in the nonlinear control designs are not needed. The proposed control design leads to a robust yet simplified function approximation-free control for nonlinear systems. The closed-loop system stability and the control error convergence are all rigorously proved. Finally, comparative simulations are conducted based on nonlinear missile systems to validate the improved response and the robustness of the proposed control method.     

Robust adaptive control of a class of nonlinear systems including actuator hysteresis with Prandtl-Ishlinskii presentations

This paper deals with robust adaptive control of a class of nonlinear systems preceded by unknown hysteresis nonlinearities. By using a Prandtl-Ishlinskii model with play and stop operators, we attempt to fuse the model of hysteresis with the available control techniques without necessarily constructing a hysteresis inverse. A robust adaptive control scheme is therefore proposed. The global stability of the adaptive system and tracking a desired trajectory to a certain precision are achieved. Simulation results attained for a nonlinear system are presented to illustrate and further validate the effectiveness of the proposed approach.     

控制方向未知的时变非线性系统鲁棒控制

针对一类具有未知时变控制方向、不确定时变参数以及未知时变有界干扰的严反馈非线性系统,给出一种带有死区修正算法的鲁棒控制方法.在控制系数符号未知的情况下,通过在反步法中引入Nussbaum增益和死区修正技术,得到一种修正的鲁棒反步设计方法.该方法不需要未知时变控制系数的上下界先验知识以及不确定参数和外界干扰的上界信息.算法保证了闭环系统所有信号的有界性,同时使得跟踪误差收敛于零的任意小邻域内.     

Operator-Based Robust Nonlinear Free Vibration Control of a Flexible Plate With Unknown Input Nonlinearity

In this paper,a robust nonlinear free vibration control design using an operator based robust right coprime factorization approach is considered for a flexible plate with unknown input nonlinearity.With considering the effect of unknown input nonlinearity from the piezoelectric actuator,operator based controllers are designed to guarantee the robust stability of the nonlinear free vibration control system.Simultaneously,for ensuring the desired tracking performance and reducing the effect of unknown input nonlinearity,operator based tracking compensator and estimation structure are given,respectively.Finally,both simulation and experimental results are shown to verify the effectiveness of the proposed control scheme.     

Event-triggered adaptive consensus control of nonlinear multi-agent systems with unknown control directions and actuator saturation

This article addresses the event-triggered adaptive consensus control of nonlinear multi-agent systems with unknown control direction and actuator saturation. A new robust adaptive control algorithm based on an event-triggered mechanism is designed. The smooth Lipschitz function approximates the saturated nonlinear function, while the Nussbaum function handles unknown control directions and residual terms. The event-triggered mechanism is designed to determine the time of communication, significantly reducing the communication burden. An additional estimator is utilized to deal with unknown parameters involved in neighbor dynamics and prevent information exchange to consistency errors between connected subsystems. The results show that all the signals of the closed-loop system are uniformly bounded, and the consensus tracking error converges to a bounded set. Meanwhile, Zeno's behavior is eliminated. Simulation results confirm the superiority of the proposed method.     

控制方向未知的全状态约束非线性系统的鲁棒自适应跟踪控制

针对一类控制方向未知的含有时变不确定参数和未知时变有界扰动的全状态约束非线性系统,本文提出了一种基于障碍Lyapunov函数的反步自适应控制方法.障碍Lyapunov函数保证了系统状态在运行过程中始终保持在约束区间内;Nussbaum型函数的引入解决了系统控制方向未知的问题;光滑投影算法确保了不确定时变参数的有界性.障碍Lyapunov函数、Nussbaum型函数及光滑投影算法与反步自适应方法的有效结合首次解决了控制方向未知的全状态约束非线性系统的跟踪控制问题.所设计的自适应鲁棒控制器能在满足状态约束的前提下确保闭环系统的所有信号有界.通过恰当地选取设计参数,系统的跟踪误差将收敛于0的任意小的邻域内.仿真结果表明了控制方案的可行性.     

Adaptive fuzzy backstepping output feedback control of nonlinear time-delay systems with unknown high-frequency gain sign

In this paper, an adaptive fuzzy robust feedback control approach is proposed for a class of single-input and single-output (SISO) strict-feedback nonlinear systems with unknown nonlinear functions, time delays, unknown high-frequency gain sign, and without the measurements of the states. In the backstepping recursive design, fuzzy logic systems are employed to approximate the unknown smooth nonlinear functions, K-filters is designed to estimate the unmeasured states, and Nussbaum gain functions are introduced to solve the problem of unknown sign of high-frequency gain. By combining adaptive fuzzy control theory and adaptive backstepping design, a stable adaptive fuzzy output feedback control scheme is developed. It has been proven that the proposed adaptive fuzzy robust control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded and the tracking error can converge to a small neighborhood of the origin by appropriately choosing design parameters. Simulation results have shown the effectiveness of the proposed method.     

Adaptive fuzzy backstepping output feedback control for strict feedback nonlinear systems with unknown sign of high-frequency gain

In this paper, an adaptive fuzzy robust output feedback control approach is proposed for a class of SISO nonlinear strict-feedback systems with unknown sign of high-frequency gain and the unmeasured states. The nonlinear systems addressed in this paper are assumed to possess the unmodeled dynamics, dynamical disturbances and unknown nonlinear functions, where the unknown nonlinear functions are not linearly parameterized, and no prior knowledge of their bounds is available. In the recursive designing, fuzzy logic systems are used to approximate the unknown nonlinear functions, K-filters are designed to estimate the unmeasured states, and a dynamical signal and Nussbaum gain functions are introduced to handle the unmodeled dynamics and the unknown sign of the high-frequency gain, respectively. Based on Lyapunov function method, a stable adaptive fuzzy output feedback control scheme is developed. It is mathematically proved that the proposed adaptive fuzzy control approach can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded, the output converges to a small neighborhood of the origin. The effectiveness of the proposed approach is illustrated by the simulation examples.     

基于S函数调节的非线性自适应动态面控制

针对一类控制增益未知的多输入多输出（MIMO）非线性系统,提出了一种基于神经网络的鲁棒自适应动态面控制方法．利用动态面控制解决反推法的计算膨胀问题;同时在参数自适应律中引入S（Sigmoid）函数,动态调节神经网络的收敛速度,解决了自适应初始阶段的抖振现象．利用李亚普诺夫稳定性定理,证明了闭环系统所有信号最终有界,系统的跟踪误差最终收敛到有界紧集内．仿真结果表明了该方法的有效性．     

基于不确定逼近的机械手自适应鲁棒预测控制

针对具有参数不确定性和未知外部干扰的机械手轨迹跟踪问题提出了一种多输入多输出自适应鲁棒预测控制方法. 首先根据机械手模型设计非线性鲁棒预测控制律, 并在控制律中引入监督控制项; 然后利用函数逼近的方法逼近控制律中因模型不确定性以及外部干扰引起的未知项. 理论证明了所设计的控制律能够使机械手无静差跟踪期望的关节角轨迹. 仿真验证了本文设计方法的有效性.     

Adaptive quantised fault-tolerant tracking control of uncertain nonlinear systems with unknown control direction and the prescribed accuracy

In this paper, the problem of adaptive fault-tolerant tracking control for a class of uncertain nonlinear systems in the presence of input quantisation and unknown control direction is considered. By choosing a class of particular Nussbaum functions, an adaptive fault-tolerant control scheme is designed to compensate actuator faults and input quantisation while the control direction is unknown. Compared with the existing results, the proposed controller can directly compensate for the nonlinear term caused by actuator faults and the nonlinear decomposition on the quantiser without estimating its bound. Furthermore, via Barhalant's Lemma, it is proven that all the signals of the closed-loop system are globally uniformly bounded and the tracking error converges into a prescribed accuracy in prior. Finally, an illustrative example is used for verifying effectiveness of the proposed approach.