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.     

The robust adaptive control of chaotic systems with unknown parameters and external disturbance via a scalar input

This paper investigates the control of chaotic systems in the presence of unknown parameters, model uncertainties, and external disturbance. We first discuss the control of a class of chaotic systems and then investigate the control of general chaotic systems. Based on the adaptive control scheme, some novel criteria are proposed via a backstepping‐like procedure. As an example, the control of the Zhang hyperchaotic system is investigated via a single input. Some numerical simulations are given to demonstrate the robustness and efficiency of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Adaptive actuator failure compensation design for unknown chaotic multi‐input systems

In this paper, an adaptive control approach is designed for compensating the faults in the actuators of chaotic systems and maintaining the acceptable system stability. We propose a state‐feedback model reference adaptive control scheme for unknown chaotic multi‐input systems. Only the dimensions of the chaotic systems are required to be known. Based on Lyapunov stability theory, new adaptive control laws are synthesized to accommodate actuator failures and system nonlinearities. An illustrative example is studied. The simulation results show the effectiveness of the design method. Copyright © 2014 John Wiley & Sons, Ltd.     

Composite learning fuzzy synchronization for incommensurate fractional‐order chaotic systems with time‐varying delays

This paper presents a composite learning fuzzy control to synchronize two different uncertain incommensurate fractional‐order time‐varying delayed chaotic systems with unknown external disturbances and mismatched parametric uncertainties via the Takagi‐Sugeno fuzzy method. An adaptive controller together with fractional‐order composite learning laws is designed based on both a parallel distributed compensation technology and a fractional Lyapunov criterion. The boundedness of all variables in the closed‐loop system and the Mittag‐Leffler stability of tracking error can be guaranteed. T‐S fuzzy systems are provided to tackle unknown nonlinear functions. The distinctive features of the proposed approach consist in the following: (1) a supervisory control law is designed to compensate the lumped disturbances; (2) both the prediction error and the tracking error are used to estimate the unknown fuzzy system parameters; (3) parameter convergence can be ensured by an interval excitation condition. Finally, the feasibility of the proposed control strategy is demonstrated throughout an illustrative example.     

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.     

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.     

An adaptive nonlinear output feedback controller using dynamic bounding with an aircraft control application

An adaptive output feedback control scheme is developed for a class of nonlinear systems with uncertain nonlinearities, which are bounded by both static and dynamic functions of the system output, and with actuator failures whose failure time instants, patterns and values are unknown, as motivated from an aircraft flight control application. An adaptive backstepping control law using dynamic bounding is constructed to deal with unknown actuator failures as well as system parameter and dynamics uncertainties to guarantee desired system performance. Complete stability and performance analysis and illustrative simulation results of an application to aircraft flight control are presented. Copyright © 2008 John Wiley & Sons, Ltd.     

Fixed-time fault-tolerant control of uncertain MIMO switched interconnected systems subject to state delay,unknown control directions,and quantized nonlinear inputs

This paper investigates design of an adaptive fixed-time fault-tolerant decentralized controller for a class of uncertain multi-input multi-output (MIMO) switched large-scale non-strict interconnected systems under arbitrary switching subject to unknown control directions, quantized nonlinear inputs, actuator failures unknown external disturbances, and unmodeled dynamics. In addition to interconnected terms, time-varying delayed interconnected terms have been considered in the system model which makes it more general than previous works in the literature. The proposed controller can handle switched systems with unknown switching signal and different types of input nonlinearities including, saturation, backlash, and dead-zone. The singularity problem in designing the fixed time controller has been solved. The quantizer and actuators fault parameters are assumed to be unknown. The Razumikhin lemma has been used to deal with the delayed interconnected terms. To cope with the system unknown dynamics, neural networks (NNs) have been applied and by updating the maximum norms of the networks weight vectors the computational load has been reduced. The explosion of complexity occurring in the traditional back-stepping technique has been avoided by applying dynamic surface control (DSC). Finally, by defining an appropriate common Lyapunov function (CLF), fixed-time convergence of system outputs and the closed-loop system stability have been established. The effectiveness of the proposed controller has been shown via simulation study.     

Adaptive control of pure-feedback nonlinear systems with full-state time-varying constraints and unmodeled dynamics

This paper focuses on the problem of adaptive control for a class of pure-feedback nonlinear systems with full-state time-varying constraints and unmodeled dynamics. By introducing a one-to-one nonlinear mapping, the constrained pure-feedback nonlinear system with state and input unmodeled dynamics is transformed into unconstrained pure-feedback system. The controller design based on the transformed novel system is proposed by using a modified dynamic surface control method. Dynamic signal and normalization signal are designed to handle dynamical uncertain terms and input unmodeled dynamics, respectively. By adding nonnegative normalization signal into the whole Lyapunov function and using the introducing compact set in the stability analysis, all signals in the whole system are proved to be semiglobally uniformly ultimately bounded, and all states can obey the time-varying constraint conditions. A numerical example is provided to demonstrate the effectiveness of the proposed approach.     

Model free adaptive control design for a tilt trirotor unmanned aerial vehicle with quaternion feedback: Theory and implementation

This article focuses on the attitude and altitude tracking control of the tilt trirotor unmanned aerial vehicle (UAV) which is subject to modeling uncertainties and unknown external disturbances. A novel model free adaptive controller is designed to achieve asymptotic tracking control of the UAV attitude and altitude channels. The control scheme is based on the data driven strategy, and relies on the input/output data to estimate the system dynamics online. Furthermore, the discrete sliding mode algorithm is combined to enhance the system robustness, and the quaternion feedback is employed to avoid the singularity associated with the attitude control design. The stability of closed-loop system and the convergence of the tracking errors are proved. And real time flight experiments are preformed on a tilt trirotor UAV control testbed. The experimental results verify the effectiveness of the proposed control scheme and achieve a strong robustness with respect to the modeling uncertainties and unknown external disturbances.     

执行器非线性超低空空投航迹倾角自适应控制

针对超低空空投下滑阶段执行器非线性、外界不确定性大气扰动以及模型存在未知非线性等因素干扰轨迹精确跟踪问题,提出一种鲁棒自适应神经网络动态面跟踪控制方法。建立了含执行器输入非线性的超低空空投载机纵向非线性模型,采用神经网络逼近模型中未知非线性函数,引入非线性鲁棒补偿项消除了执行器非线性建模误差和外界扰动。应用Lyapunov稳定性理论证明了闭环系统所有信号均是有界收敛的。仿真验证了所提方法既保证了轨迹跟踪的精确性又具有较强的鲁棒性。     

Direct adaptive neural control of nonlinear strict‐feedback systems with unmodeled dynamics using small‐gain approach

In this paper, a novel direct adaptive neural control approach is presented for a class of single‐input and single‐output strict‐feedback nonlinear systems with nonlinear uncertainties, unmodeled dynamics, and dynamic disturbances. Radial basis function neural networks are used to approximate the unknown and desired control signals, and a direct adaptive neural controller is constructed by combining the backstepping technique and the property of hyperbolic tangent function. It is shown that the proposed control scheme can guarantee that all signals in the closed‐loop system are semi‐globally uniformly ultimately bounded in mean square. The main advantage of this paper is that a novel adaptive neural control scheme with only one adaptive law is developed for uncertain strict‐feedback nonlinear systems with unmodeled dynamics. Simulation results are provided to illustrate the effectiveness of the proposed scheme. Copyright © 2015 John Wiley & Sons, Ltd.     

非线性系统自适应控制及其在电力系统中的应用

电力系统中存在众多不确定的参数,所面临的运行条件和外界扰动复杂多变,有必要引入自适应控制理论来处理这些不确定因素。非线性系统的自适应控制与线性系统相比,在研究方法等方面都有着很大的不同,目前处在继续发展的阶段。文章首先对近十几年来非线性系统的参数自适应控制、鲁棒自适应以及智能化自适应控制做了简明的归纳,然后介绍了其中一些研究成果在电力系统稳定与控制研究中的应用,最后对全文做了总结和展望。     

Fixed time synchronization of delayed chaotic neural networks by using active adaptive control

This article aims to investigate the fixed time synchronization of a class of chaotic neural systems by way of adaptive control method. Using Lyapunov stability theory, a new fixed time stability theorem which plays an important role on the synchronization scheme is presented at first. Then, combining the fixed time stability theorem and adaptive control technique, an adaptive control scheme has been developed to achieve the fixed time synchronization of chaotic neural systems. The proposed controllers assure the global convergence of the error dynamics in fixed-time based on the Lyapunov stability theory. Furthermore, the proposed control strategy cannot only provide a fast convergence rate, but also afford a bounded convergence time which is unrelated to the initial values and easy to work out by using the simple time calculation formula. Finally, numerical simulations are presented by taking a typical two-order chaotic neural system as an example to verify and demonstrate the effectiveness of the proposed scheme.     

计及时滞影响的水轮发电机调节系统的广域H∞控制

研究了水轮发电机调节系统的广域H∞控制,探讨利用线性矩阵不等式（linear matrix inequality,LMI）进行H∞控制器设计的方法及步骤。除计及时滞影响外,还考虑了外部扰动和建模误差等不确定因素。以联接到远方系统的水轮发电机为例,进行了存在广域测量系统（wide area measurement system,WAMS）时滞影响的水轮发电机调节系统的H∞控制器设计。仿真及分析表明,所设计的控制器在一定范围内具有对时滞的不敏感性,可以抑制外部干扰,保持电力系统的动态稳定。     

风力发电机组独立变桨鲁棒自适应桨距角跟踪控制

在全面考虑风力发电机组桨叶所受各种载荷的情况下,建立了含有时变不确定项、未知载荷干扰的桨叶动力学数学模型,该模型精确描述了桨叶系统的非线性动力学行为。模型存在很多不确定时变参数和未知干扰项,针对这一复杂多变的桨叶模型,采用鲁棒自适应控制方法,成功设计了独立桨距角跟踪控制器。利用李雅普诺夫(Lyapunov)稳定性理论,证明了系统的稳定性。采用Matlab/Simulink仿真软件,建立了风力机组桨叶动力学仿真模型。仿真结果表明,所设计的桨叶桨距角控制器,在系统参数和所受干扰完全未知、不确定且时变的情况下,能够快速跟踪期望的桨距角,表现出良好的鲁棒性。     

Robust nonlinear adaptive backstepping excitation controller design for rejecting external disturbances in multimachine power systems

This paper proposes a new approach to design a robust adaptive backstepping excitation controller for multimachine power systems in order to reject external disturbances. The parameters which significantly affect the stability of power systems (also called stability sensitive parameters) are considered as unknown and the external disturbances are incorporated into the power system model. The proposed excitation controller is designed in such a way that it is adaptive to the unknown parameters and robust to external disturbances. The stability sensitive parameters are estimated through the adaptation laws and the convergences of these adaptation laws are obtained through the negative semi-definiteness of control Lyapunov functions (CLFs). The proposed controller not only provides robustness property against external disturbances but also overcomes the over-parameterization problem of stability sensitive parameters which usually appears in some conventional adaptive methods. Finally, the performance of the proposed controller is tested on a two-area four machine 11-bus power system by considering external disturbances under different scenarios and is compared to that of an existing nonlinear adaptive backstepping controller. Simulation results illustrate the robustness of the proposed controller over an existing one in terms of rejecting external disturbances.     

Adaptive fuzzy finite-time consensus tracking for multiple Euler-Lagrange systems with unknown control directions

In this paper, the problem of adaptive fuzzy finite-time consensus tracking control for multiple Euler-Lagrange systems (ELSs) with uncertain dynamics and unknown control directions (UCDs) is investigated. The computational complexity problem in conventional backstepping is avoided by using finite-time command filter (FTCF), and the error in the filtering process is eliminated through error compensation signals. The fuzzy logic system combined with the adaptive control technique is applied to approximate and estimate the unknown nonlinear dynamics of ELS. The Nussbaum function-based continuous and nonsmooth input control torque is established to eliminate the influence of UCDs, and the proposed control scheme can guarantee the consensus tracking errors converge to the desired neighborhood of the origin within a finite time. Numerical simulation is used to test the effectiveness of the given algorithm.     

Inverse optimal adaptive control for non‐linear uncertain systems with exogenous disturbances

A Lyapunov‐based inverse optimal adaptive control‐system design problem for non‐linear uncertain systems with exogenous ℒ︁₂ disturbances is considered. Specifically, an inverse optimal adaptive non‐linear control framework is developed to explicitly characterize globally stabilizing disturbance rejection adaptive controllers that minimize a nonlinear‐nonquadratic performance functional for non‐linear cascade and block cascade systems with parametric uncertainty. It is shown that the adaptive Lyapunov function guaranteeing closed‐loop stability is a solution to the Hamilton–Jacobi–Isaacs equation for the controlled system and thus guarantees both optimality and robust stability. Additionally, the adaptive Lyapunov function is dissipative with respect to a weighted input–output energy supply rate guaranteeing closed‐loop disturbance rejection. For special integrand structures of the performance functionals considered, the proposed adaptive controllers additionally guarantee robustness to multiplicative input uncertainty. In the case of linear‐quadratic control it is shown that the operations of parameter estimation and controller design are coupled illustrating the breakdown of the certainty equivalence principle for the optimal adaptive control problem. Finally, the proposed framework is used to design adaptive controllers for jet engine compression systems with uncertain system dynamics. Copyright © 2000 John Wiley & Sons, Ltd.     

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%。