Performance deterioration of optimal regulators incorporating state estimators

In this paper, the performance deterioration of optimal regulators caused by the introduction of deterministic state-estimators such as Kalman estimators and Luenberger observers is investigated. It is shown that, in the case of Kalman estimators, the performance deterioration cannot be made arbitrarily small unless the optimal control law can be implemented by direct output feedback. In the case of Luenberger observers with minimum order, a necessary and sufficient condition for the performance deterioration to be made arbitrarily small is derived.     

Observer-based adaptive iterative learning control for nonlinear systems with time-varying delays

An observer-based adaptive iterative learning control (AILC) scheme is developed for a class of nonlinear systems with unknown time-varying parameters and unknown time-varying delays. The linear matrix inequality (LMI) method is employed to design the nonlinear observer. The designed controller contains a proportional-integral-derivative (PID) feedback term in time domain. The learning law of unknown constant parameter is differential-difference-type, and the learning law of unknown time-varying parameter is difference-type. It is assumed that the unknown delay-dependent uncertainty is nonlinearly parameterized. By constructing a Lyapunov-Krasovskii-like composite energy function (CEF), we prove the boundedness of all closed-loop signals and the convergence of tracking error. A simulation example is provided to illustrate the effectiveness of the control algorithm proposed in this paper.     

执行器饱和多智能体系统的自适应学习一致性算法

针对一类受到执行器饱和高阶多智能体系统在有限时间区间[0,T]上的精确一致性问题,利用自适应迭代学习控制的方法,设计了具有全饱和差分型自适应更新律的时变增益.通过构造适当的复合能量函数,严格证明了一致性误差向量随着迭代次数趋于无穷而一致趋于零,得到了不依赖于网络通信拓扑矩阵特征值的自适应学习一致性算法.最后,给出一个仿真例子,仿真结果说明了所提算法的有效性.     

未知时变时滞非线性参数化系统自适应迭代学习控制

针对含有未知时变参数和时变时滞的非线性参数化系统,提出了一种新的自适应迭代学习控制方法.该方法将参数分离技术与信号置换思想相结合,可以处理含有时变参数和时滞相关不确定性的非线性系统.设计了一种自适应控制策略,使跟踪误差的平方在一个有限区间上的积分渐近收敛于零.通过构造Lyapunov-Krasovskii型复合能量函数,给出了闭环系统收敛的一个充分条件.给出两个仿真例子验证了控制方法的有效性.     

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.     

一类不确定运动系统的空间迭代学习控制

本文讨论了一类在有限空间区间内重复运行的不确定运动系统的跟踪控制问题.通过引入空间状态微分算子和空间复合能量函数,提出了一种空间周期的自适应迭代学习控制算法.首先利用空间状态微分算子,将系统从时间域转化到空间域形式.然后基于空间复合能量函数设计了控制器,利用含限幅作用的参数自适应律逼近系统中的不确定性,同时引入鲁棒项共同抑制非参数不确定性的影响.通过严格的数学分析,证明了在标准初始条件和随机有界初始误差两种情况下的跟踪误差收敛性.最后通过列车仿真进一步验证了该算法的有效性.     

一类不确定系统的自适应滑模迭代学习控制

本文针对一类在有限时间内执行重复任务的不确定非线性系统状态跟踪问题,提出一种自适应滑模迭代学习控制方法,在存在初始偏移的情况下也能实现对参考轨迹的完全收敛.本文通过设计全饱和自适应迭代学习更新律,估计参数和非参数不确定性以及未知期望控制输入,并将估计值限制在指定界内,避免估计值的正向累加.文章设计的自适应滑模迭代学习控制方法对系统模型的信息需求少,在对系统非参数不确定性的上界估计时不需要Lipschitz界函数已知.本文给出严格的理论分析,证明闭环系统所有信号的一致有界性以及跟踪误差的一致收敛性,并通过仿真验证所提控制方法的有效性.     

不确定性机器人系统自适应鲁棒迭代学习控制

利用Lyapunov方法, 提出了一种不确定性机器人系统的自适应鲁棒迭代学习控制策略, 整个系统在迭代域里是全局渐近稳定的. 所考虑的机器人系统同时包含了结构和非结构不确定性. 在设计时, 系统的不确定性被分解成可重复性和非重复性两部分, 并考虑了系统的标称模型. 在所提出的控制策略中, 自适应策略用来估算做法确定性的界, 界的修正与迭代学习控制量一样的迭代域得以实现的. 计算机仿真表明本文提出的控制策略是有效的.     

Adaptive iterative learning control for coordination of second‐order multi‐agent systems

In this paper, an efficient framework is proposed to the consensus and formation control of distributed multi‐agent systems with second‐order dynamics and unknown time‐varying parameters, by means of an adaptive iterative learning control approach. Under the assumption that the acceleration of the leader is unknown to any follower agents, a new adaptive auxiliary control and the distributed adaptive iterative learning protocols are designed. Then, all follower agents track the leader uniformly on [0,T] for consensus problem and keep the desired distance from the leader and achieve velocity consensus uniformly on [0,T] for the formation problem, respectively. The distributed multi‐agent coordinations performance is analyzed based on the Lyapunov stability theory. Finally, simulation examples are given to illustrate the effectiveness of the proposed protocols in this paper.Copyright © 2013 John Wiley & Sons, Ltd.     

一类未知非线性系统的智能迭代学习控制

从自适应的角度设计迭代学习控制，将神经网络引入迭代学习控制中。学习控制与自适应控制相结合，使得对网络权值的学习和跟踪控制同时进行，克服 了经典迭代学习控制的一些缺陷。基于Lyapunov直接方法，证明了整个控制系统的稳定并实现了任意精度的跟踪。实例仿真结果说明了算法 的有效性及其所具有的优点。     

基于未知高频增益的非线性系统自适应迭代学习控制

针对一类单输入单输出不确定非线性重复跟踪系统,提出一种基于完全未知高频反馈增益的自适应迭代学习控制.与普通迭代学习控制需要学习增益稳定性前提条件不同,自适应迭代学习控制通过不断修改Nussbaum形式的高频学习增益达到收敛.经证明当迭代次数i→∞时,重复跟踪误差可一致收敛到任意小界δ.仿真结果表明了该控制方法的有效性.     

An Exploration on Adaptive Iterative Learning Control for a Class of Commensurate High-order Uncertain Nonlinear Fractional Order Systems

This paper explores the adaptive iterative learning control method in the control of fractional order systems for the first time. An adaptive iterative learning control (AILC) scheme is presented for a class of commensurate high-order uncertain nonlinear fractional order systems in the presence of disturbance. To facilitate the controller design, a sliding mode surface of tracking errors is designed by using sufficient conditions of linear fractional order systems. To relax the assumption of the identical initial condition in iterative learning control (ILC), a new boundary layer function is proposed by employing Mittag-Leffler function. The uncertainty in the system is compensated for by utilizing radial basis function neural network. Fractional order differential type updating laws and difference type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. The hyperbolic tangent function and a convergent series sequence are used to design robust control term for neural network approximation error and bounded disturbance, simultaneously guaranteeing the learning convergence along iteration. The system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapnov-like composite energy function (CEF) containing new integral type Lyapunov function, while keeping all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.      

输入具有齿隙非线性特性的周期系统的自适应控制

针对一类输入含齿隙非线性动态特性的周期时变系统, 在周期不确定性可时变参数化的条件下设计自适应控制器. 对周期时变参数进行傅里叶级数展开, 并采用微分自适应律估计未知傅里叶系数和齿隙动态特性参数, 通过鲁棒方法消除截断误差和齿隙模型的有界误差项对系统性能的影响. 采用双曲函数替代符号函数确保控制器可微, 同时能有效抑制颤振. 引入Δ函数, 避免参数估计发散, 并保证系统输出渐近跟踪理想轨迹. 理论分析与仿真结果表明, 闭环系统所有信号有界.     

时变参数化非线性系统自适应迭代学习控制器设计

针对一类时变参数化非线性系统的控制问题进行深入研究,提出一种新的迭代神经网络估计器,并证明了其逼近引理,实现了对时变不确定性的逼近.在用迭代神经网络对时变不确定性进行估计的同时,以Lyapunov稳定性理论为基础,综合运用Backstepping和自适应控制技术,设计了自适应迭代学习控制器,并进行了稳定性分析,得到了稳定性定理,解决了这类时变非线性系统的控制问题.最后的仿真实验验证了所提出设计方法的正确性.     

An open-closed-loop iterative learning control approach for nonlinear switched systems with application to freeway traffic control

For nonlinear switched discrete-time systems with input constraints, this paper presents an open-closed-loop iterative learning control (ILC) approach, which includes a feedforward ILC part and a feedback control part. Under a given switching rule, the mathematical induction is used to prove the convergence of ILC tracking error in each subsystem. It is demonstrated that the convergence of ILC tracking error is dependent on the feedforward control gain, but the feedback control can speed up the convergence process of ILC by a suitable selection of feedback control gain. A switched freeway traffic system is used to illustrate the effectiveness of the proposed ILC law.     

Iterative learning control for output‐constrained nonlinear systems with input quantization and actuator faults

In this work, we propose a novel iterative learning control algorithm to deal with a class of nonlinear systems with system output constraint requirements and quantization effects on the system control input. Actuator faults have also been considered, which include multiplicative, additive, and stuck actuator faults. To the best of our knowledge, this is the first reported work in the iterative learning control literature to deal with quantization effects for the control input of nonlinear systems under the effects of actuator faults and system output constraints. Under the proposed scheme, using backstepping design and composite energy function approaches in the analysis, we show that uniform convergence of the state tracking errors can be guaranteed over the iteration domain, and the constraint requirement on the system output will not be violated at all time. In the end, a simulation study on a single‐link robot model is presented to demonstrate the effectiveness of the proposed scheme.     

严格反馈系统约束迭代学习控制

针对一类含有状态约束和任意初态的严格反馈非线性系统,本文提出了基于二次分式型障碍李雅普诺夫函数的误差跟踪学习控制算法.二次分式型障碍李雅普诺夫函数保证了系统跟踪误差在迭代过程中限制于预设的界内,进而保持状态在约束区间内.引入一级数收敛序列用于处理扰动对系统跟踪性能的影响.构造期望误差轨迹解决了系统的初值问题.经迭代学习...     

Adaptive iterative learning control for nonlinear time-delay systems with periodic disturbances using FSE-neural network

An adaptive iterative learning control scheme is presented for a class of strict-feedback nonlinear time-delay systems, with unknown nonlinearly parameterised and time-varying disturbed functions of known periods. Radial basis function neural network and Fourier series expansion (FSE) are combined into a new function approximator to model each suitable disturbed function in systems. The requirement of the traditional iterative learning control algorithm on the nonlinear functions (such as global Lipschitz c...     

Variable-gain PD-type iterative learning control for a class of nonlinear time-varying systems

This paper investigates variable-gain PD-type iterative learning control (ILC) for a class of nonlinear time-varying systems to well balance high-gain convergence rate and low-gain noise transmission. Different from the classic PD-type ILC, the control gains of the proposed method are variable. Each variable-gain consists of an amplitude-dependent term and an iteration-varying term. The amplitude-dependent terms vary with the amplitudes of tracking error and derivative of tracking error, and the iteration-varying terms are increasing along the iteration axis. The proposed ILC achieves a faster convergence rate than low-gain ILC and higher tracking accuracy with limited noise amplification than high-gain ILC. Moreover, the convergence condition of the proposed method in the presence of external noise is provided. Simulation and experimental results demonstrate the effectiveness of the proposed method.     

Neuroadaptive containment control of nonlinear multiagent systems with input saturations

This paper investigates the output containment tracking problem of nonlinear multiagent systems with mismatched uncertain dynamics and input saturations. A neural network–based distributed adaptive command filtered backstepping (CFB) scheme is given, which can guarantee that the containment tracking errors reach to the desired neighborhood of origin and all signals in the closed‐loop system are bounded. Note that error compensation system and virtual control laws established in CFB only use local information, so the given scheme is completely distributed. Moreover, the applied sliding mode differentiator (SMD) can make the outputs of SMD fast approximate the virtual signal and its derivative at each step of backstepping, which can further improve the control quality. Finally, a simulation example is given to show the effectiveness of the proposed scheme.