Adaptive saturation compensation for strict-feedback systems with unknown control coefficient and input saturation

This work presents an adaptive saturation compensation scheme for the strict-feedback uncertain systems with unknown control coefficient and input saturation. An adaptive saturation dynamic filter that does not require the a priori information of the completely unknown control coefficient is incorporated to correct position errors online to reduce the saturation effect. A Nussbaum-type function is employed to handle the unknown control coefficient and avoid the control singularity. The adaptive command-filtered backstepping is employed to derive the adaptive controller. The repeated differential operations of stabilizing functions required in the traditional backstepping are obviated due to command filters. It is analyzed that the designed adaptive controller achieves the system output tracking and the closed-loop uniform ultimate stability. A simulation example is provided to validate the scheme.     

Adaptive multi-dimensional Taylor network funnel control of a class of nonlinear systems with asymmetric input saturation

In view of the result and performance of control are affected by the existence of input constraints and requirements, adaptive multi-dimensional Taylor network (MTN) funnel control problem is studied for a class of nonlinear systems with asymmetric input saturation in this paper. Firstly, the effect of asymmetric input saturation can overcome by introducing the Gaussian error function, namely, the asymmetric saturation model is represented as a simple linear model with a bounded disturbance. Secondly, MTNs are employed to approximate the unknown functions in the controller design. Then, an adaptive MTN tracking controller is developed by blends the idea of funnel control into backstepping, which can guarantee that the tracking error always meets the given prescribed performance regarding the transient and steady state responses as well as the output of system tracks the give continuous reference signal. Finally, the effectiveness of the proposed control is demonstrated using two examples.     

Integral barrier Lyapunov function-based adaptive fuzzy output feedback control for nonlinear delayed systems with time-varying full-state constraints

In this article, an adaptive fuzzy output feedback control method is presented for nonlinear time-delay systems with time-varying full state constraints and input saturation. To overcome the problem of time-varying constraints, the integral barrier Lyapunov functions (IBLFs) integrating with dynamic surface control (DSC) are applied for the first time to keep the state from violating constraints. The effects of unknown time delays can be removed by using designed Lyapunov-Krasovskii functions (LKFs). An auxiliary design system is introduced to solve the problem of input saturation. The unknown nonlinear functions are approximated by the fuzzy logic systems (FLS), and the unmeasured states are estimated by a designed fuzzy observer. The novel controller can guarantee that all signals remain semiglobally uniformly ultimately bounded and satisfactory tracking performance is achieved. Finally, two simulation examples illustrate the effectiveness of the presented control methods.     

Sliding mode disturbance observer‐based adaptive control for uncertain MIMO nonlinear systems with dead‐zone

In this paper, an adaptive integral sliding mode control (ISMC) scheme is developed for a class of uncertain multi‐input and multi‐output nonlinear systems with unknown external disturbance, system uncertainty, and dead‐zone. The research is motivated by the fact that the ISMC scheme against unknown external disturbance and system uncertainty is very important for multi‐input and multi‐output nonlinear systems. The system uncertainty, the unknown external disturbance, and the effect of dead‐zone are integrated as a compounded disturbance, which is well estimated using a sliding mode disturbance observer (SMDO). Then, the adaptive ISMC based on the designed SMDO is presented to guarantee the satisfactory tracking performance in the presence of system uncertainty, external disturbance, and dead‐zone. Finally, the designed adaptive ISMC strategy based on SMDO is applied to the attitude control of the near space vehicle, and simulation results are presented to illustrate the effectiveness of the proposed adaptive ISMC scheme using the SMDO. Copyright © 2016 John Wiley & Sons, Ltd.     

Decentralized prescribed performance adaptive tracking control for Markovian jump uncertain nonlinear systems with input saturation

A decentralized prescribed performance adaptive tracking control problem is investigated for Markovian jump uncertain nonlinear interconnected large‐scale systems. The considered interconnected large‐scale systems contain unknown nonlinear uncertainties, unknown control gains, actuator saturation, and Markovian jump signals, and the Markovian jump subsystems are in the form of triangular structure. First, by defining a novel state transformation with the performance function, the prescribed performance control problem is transformed to stabilization problem. Then, introducing an intermediate control signal into the control design, employing neural network to approximate the unknown composite nonlinear function, and based on the framework of the backstepping control design and adaptive estimation method, a corresponding decentralized prescribed performance adaptive tracking controller is designed. It is proved that all the signals in the closed‐loop system are bounded, and the prescribed tracking performances are guaranteed. A numerical example is provided to illustrate the effectiveness of the proposed control strategy. Copyright © 2016 John Wiley & Sons, Ltd.     

Finite-time adaptive fuzzy control for a class of output constrained nonlinear systems with dead-zone

The article investigates the finite-time adaptive fuzzy control for a class of nonlinear systems with output constraint and input dead-zone. First, by skillfully combining the barrier Lyapunov function, backstepping design method, and finite-time control theory, a novel adaptive state-feedback tracking controller is constructed, and the output constraint of the nonlinear system is not violated. Second, the fuzzy logic system is used to approximate unknown function in the nonlinear system. Third, the finite-time command filter is introduced to avoid the problem of “complexity explosion” caused by repeated differentiations of the virtual control signal in conventional backstepping control schemes. Meanwhile, a new saturation function is added in the compensating signal for filter error to improve control accuracy. Finally, based on Lyapunov stability analysis, all the signals of the closed-loop are proved to be semi-globally uniformly ultimately bounded, and the tracking error converges to a small neighborhood region of the origin in a finite time. A simulation example is presented to demonstrate the effectiveness for the proposed control scheme.     

基于自适应模糊滑模控制的机器人轨迹跟踪算法

针对控制参数的不确定性以及存在未知外部扰动情况下移动机器人的轨迹跟踪问题,提出一种基于光滑非线性饱和函数的自适应模糊滑模轨迹跟踪控制算法。通过建立不确定非线性移动机器人运动控制模型,利用自适应模糊逻辑系统构建自适应模糊滑模控制器。为了增强轨迹跟踪控制算法对随机不确定外部扰动适应能力的同时削弱滑模控制算法中的输入抖振现象,利用有界输入有界输出(BIBO)稳定的方法,通过带有自适应调节算法的模糊系统对滑模控制律中非线性函数项进行自适应逼近,并设计了模糊系统中可调参数的自适应控制律,保证了控制系统的稳定与收敛。实验结果表明,所设计的控制器对系统参数不确定性和外界扰动均具有较强的轨迹跟踪性能和鲁棒性。与传统的滑模控制算法相比,该算法不仅能有效减小输入抖振而且轨迹跟踪控制精度提高了18.89%。     

Extended-state-observer-based dynamic surface control of flexible-joint robot systems with input saturation

This article presents an extended-state-observer-based dynamic surface control approach for flexible-joint robot systems with asymmetric input saturation and large unknown dynamic knowledge. Traditional controllers for flexible-joint robot systems usually use approximation technology to deal with unknown dynamics knowledge. Unlike the traditional control algorithm, this article utilizes an extended state observer to estimate the unknown dynamics. For the closed-loop system, the delay strategy handles the time-scale separation issue, the filtering system overcomes the “explosion of differentiation” caused by the repeated differentiation of auxiliary control signals, and the mean-value-theorem solves the input saturation problem of the actuator. The stability analysis implies that estimation errors of extended state observers (ESOs) and other state variables are semiglobally uniformly ultimately bounded. Compared with fuzzy control algorithms, the novel ESO-based dynamic surface control approach not only omits online learning time but also uses only a few control parameters to obtain satisfactory tracking performance. Finally, a comparison simulation experiment is provided to illustrate the effectiveness of the gained conclusions.     

Adaptive output feedback control of uncertain nonlinear systems with input delay and output constraint

This paper proposes an adaptive neural‐network control design for a class of output‐feedback nonlinear systems with input delay and unmodeled dynamics under the condition of an output constraint. A coordinate transformation with an input integral term and a Nussbaum function are combined to solve the problem of the input possessing both time delay and unknown control gain. By utilizing a barrier Lyapunov function and designing tuning functions, the adjustment of multiparameters is handled with a single adaptive law. The uncertainty of the system is approximated by dynamic signal and radial basis function neural networks (RBFNNs). Based on Lyapunov stability theory, an adaptive tracking control scheme is developed to guarantee all the signals of the closed‐loop systems are semiglobally uniformly ultimately bounded, and the output constraint is not violated.     

Adaptive neural finite-time output-feedback tracking control for nonlinear stochastic nonstrict-feedback systems with input saturation

In this paper, an observer-based adaptive neural output-feedback control scheme is developed for a class of nonlinear stochastic nonstrict-feedback systems with input saturation in finite-time interval. The mean value theorem and the property of the smooth function are applied to cope with the difficulties caused by the existence of input saturation. According to the universal approximation capability of the radial basis function neural network, it will be utilized to compensate the unknown nonlinear functions. Based on the state observer, the finite-time Lyapunov stability theorem, we propose an adaptive neural output-feedback control scheme for nonlinear stochastic systems in nonstrict-feedback form. The developed controller guarantees that the system output signal can track the given reference signal trajectory, and all closed-loop signals are semi-globally finite-time stability in probability. The observer errors and the tracking error can converge to a small neighborhood of the origin. Finally, simulation results demonstrate the effectiveness of the developed control scheme.     

A simplified adaptive tracking control for nonlinear pure-feedback systems with input delay and full-state constraints

This article investigated the adaptive backstepping tracking control for a class of pure-feedback systems with input delay and full-state constraints. With the help of mean value theorem, the system is transformed into strict-feedback one. By introducing the Pade approximation method, the effect of input delay was compensated. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. Furthermore, in order to reduce the computational burden by introducing backstepping design technique, dynamic surface control technique was employed. In addition, the number of the adaptive parameters that should be updated online was also reduced. By utilizing the barrier Lyapunov function, the closed-loop nonlinear system is guaranteed to be semi-globally ultimately uniformly bounded. Finally, a numerical simulation example is given to show the effectiveness of the proposed control strategy.     

Robust adaptive steering control for unmanned surface vehicle with unknown control direction and input saturation

A robust adaptive steering control method is proposed to solve the control problem of the unmanned surface vehicle (USV) with uncertainties, unknown control direction, and input saturation. In the controller design process, the adaptive fuzzy system is incorporated into dynamic surface control (DSC) to approximate the uncertainty term induced by external environmental disturbances and model parameters. Then, the Nussbaum function is used to eliminate the requirement for a priori knowledge of the control direction. Besides, to handle the input saturation, the adaptive fuzzy DSC is extended by a second‐order nonlinear filter and antisaturation auxiliary function to compensate for the magnitude and rate saturation of the rudder. All signals of the closed‐loop system are proven to be uniformly ultimately bounded (UUB) by Lyapunov theorem and the Lemma of Nussbaum gain, and the course error can converge to a small neighborhood of zero through choosing design parameters appropriately. Finally, simulation results and comprehensive comparisons are shown for the USV course system, which is demonstrative of the proposed controller's effectiveness and robustness.     

具有输入饱和的不正定关联系统分散控制

针对在实际控制系统中,如果不考虑输入饱和而设计控制器,闭环系统的稳定性无法保证,讨论了具有输入饱和的不确定非线性交联系统的分散控制问题。利用Riccati方程的方法、Lyapunov稳定理论和矩阵理论,研究了一类具有输入饱和的不确定非线性关联大系统的分散鲁棒镇定问题,给出了该类系统可分散鲁棒控制的一个充分条件,并提出了一种分散鲁棒控制器的设计方法。同时,考虑了一类具有输入饱和的不确定非线性相似关联大系统,由于相似系统的结构特点,给出了简洁的分散鲁棒控制条件。     

Adaptive prescribed performance control of nonlinear systems with unknown dead zone

An alternative adaptive control with prescribed performance is proposed to address the output tracking of nonlinear systems with a nonlinear dead zone input. An appropriate function that characterizes the convergence rate, maximum overshoot, and steady‐state error is adopted and incorporated into an output error transformation, and thus the stabilization of the transformed system is sufficient to achieve original tracking control with prescribed performance. The nonlinear dead zone is represented as a time‐varying system and Nussbaum‐type functions are utilized to deal with the unknown control gain dynamics. A novel high‐order neural network with a scalar adaptive weight is developed to approximate unknown nonlinearities, thus the computational costs can be diminished dramatically. Some restrictive assumptions on the system dynamics and the dead‐zone are circumvented. Simulations are included to validate the effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.     

基于ACPI的风力发电系统MPPT控制方法

针对直驱永磁同步风力发电系统存在非线性、参数不确定性以及转矩扰动等问题,研究了一种基于自耦PI控制理论的最大功率跟踪控制方法。该方法以转速跟踪为目标,将发电机内部动态与外部输入转矩的不确定性定义为一个总和扰动,从而将非线性不确定系统映射为未知线性系统,并构建了一个在总和扰动反相激励下的受控误差系统。据此设计了基于误差速度因子的自耦PI控制器模型,理论分析了自耦PI闭环控制系统的鲁棒稳定性和抗扰鲁棒性。仿真结果表明了该控制方法能稳定保持最大功率系数,在风力发电系统的最大功率跟踪领域具有良好的应用前景。     

基于观测器的异步电机随机系统模糊反步位置跟踪控制

提出了一种基于观测器的异步电机随机系统模糊反步位置跟踪控制方法:通过构造降维观测器估计转子角速度;采用模糊逻辑系统逼近系统模型中的未知随机非线性函数。利用动态面控制技术解决传统反步设计中存在的"计算爆炸"问题。仿真结果表明:所提出的控制方法可以克服随机扰动的影响,并且确保跟踪误差收敛到足够小的原点邻域内。     

Adaptive switching control of uncertain fractional systems: Application to Chua's circuit

Since the introduction of fractional‐order differential equations, there has been much research interest in synthesis and control of oscillatory, periodic, and chaotic fractional‐order dynamical systems. Therefore, in this article, the problem of stabilization and control of nonlinear three‐dimensional perturbed fractional nonlinear systems is considered. The major novelty of this article is handling partially unknown dynamics of nonlinear fractional‐order systems, as well as coping with input saturation along the existence of model variations and high‐frequency sensor noises via just one control input. The method supposes no known knowledge on the upper bounds of the uncertainties and perturbations. It is assumed that the working region of the input saturation function is also unknown. After the introduction of a simple finite‐time stable nonlinear sliding manifold, an adaptive control technique is used to reach the system variables to the sliding surface. Rigorous stability discussions are adopted to prove the convergence of the developed sliding mode controller. The findings of this research are illustrated using providing computer simulations for the control problem of the chaotic unified system and the fractional Chua's circuit model.     

一类具有高增益观测器的非线性系统的输出调节

针对具有由非线性外部系统产生的未知不确定性函数和未建模动态的非线性不确定系统,研究了其跟踪和干扰抑制问题。首先运用状态变换将输出调节问题转化为非线性系统的镇定问题,接着引入动态信号解决了动态扰动,并设计出高增益的状态观测器去估计不可测的状态。然后根据外系统信息设计自适应的非线性内模,结合自适应控制理论、Backstepping设计方法、模糊控制方法和Lyapunov法给出了输出反馈的自适应模糊控制器和自适应控制律,所提出的输出反馈控制器和自适应律能够实现整个闭环系统的跟踪和干扰抑制,并使得跟踪误差能渐近收敛到给定的任意小的领域内。最后仿真结果验证了所提出的控制器的有效性。     

轨迹跟踪伺服系统的鲁棒复合控制

针对控制输入饱和受限且带有未知扰动的电机伺服系统,提出一种实现曲线轨迹准确跟踪的鲁棒复合控制方案。该方案引入一个参考信号生成器和一个扩展状态观测器,其中参考信号生成器可根据目标轨迹信号构造出对应的状态量,扩展状态观测器用于对系统的状态量和扰动进行估计,采用反馈与前馈相结合构成最终的控制律。利用Lyapunov理论对闭环系统的稳定性进行了严格分析。在MATLAB中进行了仿真研究,随后在一个DSP控制的永磁直线电机二维伺服平台进行了试验验证。结果表明:所提的控制方案能在轨迹跟踪任务中取得优越的瞬态性能和稳态准确性,而且对目标轨迹和扰动的幅值差异具有较好的鲁棒性。