Adaptive iterative learning control for a class of non-linearly parameterised systems with input saturations

In this paper, an adaptive iterative learning control scheme is proposed for a class of non-linearly parameterised systems with unknown time-varying parameters and input saturations. By incorporating a saturation function, a new iterative learning control mechanism is presented which includes a feedback term and a parameter updating term. Through the use of parameter separation technique, the non-linear parameters are separated from the non-linear function and then a saturated difference updating law is designed in iteration domain by combining the unknown parametric term of the local Lipschitz continuous function and the unknown time-varying gain into an unknown time-varying function. The analysis of convergence is based on a time-weighted Lyapunov–Krasovskii-like composite energy function which consists of time-weighted input, state and parameter estimation information. The proposed learning control mechanism warrants a L²_{[0, T]} convergence of the tracking error sequence along the iteration axis. Simulation results are provided to illustrate the effectiveness of the adaptive iterative learning control scheme.     

Learning control for discrete-time nonlinear systems with sensor saturation and measurement noises

The iterative learning control (ILC) is investigated for a class of nonlinear systems with measurement noises where the output is subject to sensor saturation. An ILC algorithm is introduced based on the measured output information rather than the actual output signal. A decreasing sequence is also incorporated into the learning algorithm to ensure a stable convergence under stochastic noises. It is strictly proved with the help of the stochastic approximation technique that the input sequence converges to the desired input almost surely along the iteration axis. Illustrative simulations are exploited to verify the effectiveness of the proposed algorithm.     

Convergence properties of two networked iterative learning control schemes for discrete-time systems with random packet dropout

This paper addresses convergence issue of two networked iterative learning control (NILC) schemes for a class of discrete-time nonlinear systems with random packet dropout occurred in input and output channels and modelled as 0–1 Bernoulli-type random variable. In the two NILC schemes, the dropped control input of the current iteration is substituted by the synchronous input used at the previous iteration, whilst for the dropped system output, the first replacement strategy is to replace it by the synchronous pre-given desired trajectory and the second one is to substitute it by the synchronous output used at the previous iteration. By the stochastic analysis technique, we analyse the convergence properties of two NILC schemes. It is shown that under appropriate constraints on learning gain and packet dropout probabilities, the tracking errors driven by the two schemes are convergent to zero in the expectation sense along iteration direction, respectively. Finally, illustrative simulations are carried out to manifest the validity and effectiveness of the results.     

非线性非仿射离散时间系统的两阶段最优迭代学习控制

On the basis of a new dynamic linearization technology along the iteration axis,a dual-stage optimal iterative learning control is presented for nonlinear and non-affine discrete-time systems.Dual-stage indicates that two optimal learning stages are designed respectively to improve control input sequence and the learning gain iteratively.The main feature is that the controller design and convergence analysis only depend on the I/O data of the dynamical system.In other words,we can easily select the control parameters without knowing any other knowledge of the system.Simulation study illustrates the geometrical convergence of the presented method along the iteration axis,in which an example of freeway traffic iterative learning control is noteworthy for its intrinsic engineering importance.     

Iterative learning control with input sharing for multi-agent consensus tracking

In this paper, a novel iterative learning control (ILC) scheme with input sharing is presented for multi-agent consensus tracking. In many ILC works for multi-agent coordination problem, each agent maintains its own input learning, and the input signal is corrected by local measurements over iteration domain. If the agents are allowed to share their learned inputs among them, the strategy can improve the learning process as more learning resources are available. In this work, we develop a new type of learning controller by considering the input sharing among agents, which includes the traditional ILC strategy as a special case. The convergence condition is rigorously derived and analyzed as well. Furthermore, the proposed controller is extended to multi-agent systems under iteration-varying graph. It turns out that the developed controller is very robust to communication variations. In the numerical study, three illustrative examples are presented to show the effectiveness of the proposed controller. The learning controller with input sharing demonstrates not only faster convergence but also smooth transient performance.     

非线性非仿射离散时间系统的两阶段最优迭代学习控制

针对非仿射非线性离散时间系统, 基于一种新的沿迭代轴的动态线性化技术, 提出了双层最优迭代学习控制算法. 双层意味着分别设计了两个最优学习层, 迭代的改进控制输入序列和学习增益. 其主要特点是控制器的设计和收敛性分析只依赖于动态系统的 I/O 数据. 换句话说, 不需要知道系统的任何其他信息就可以很容易的选取控制器参数. 仿真研究表明了提出的算法沿迭代轴具有几何收敛性, 这一特点在快速路交通迭代学习控制中具有重要的工程意义.     

基于BDI框架的多Agent动态协作模型与应用研究

近年来，多Agent学习已经成为人工智能和机器学习研究方向发展最迅速的领域之一．将强化学习和BDI思维状态模型相结合，形成针对多Agent的动态协作模型．在此模型中，个体最优化概念失去其意义，因为每个Agent的回报，不仅取决于自身，而且取决于其它Agent的选择．模型采用AFS神经网络对输入状态空间进行压缩，提高强化学习的收敛速度．与此同时，利用模拟退火算法启发性地指明动作空间搜索方向，使其跳出局部最小点，避免迭代步数的无限增长．理论分析和在机器人足球领域的成功应用，都证明了基于BDI框架的多Agent动态协作模型的有效性。     

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.     

Iterative learning control of inhomogeneous distributed parameter systems—frequency domain design and analysis

This paper aims to construct a design and analysis framework for iterative learning control of linear inhomogeneous distributed parameter systems (LIDPSs), which may be hyperbolic, parabolic, or elliptic, and include many important physical processes such as diffusion, vibration, heat conduction and wave propagation as special cases. Owing to the system model characteristics, LIDPSs are first reformulated into a matrix form in the Laplace transform domain. Then, through the determination of a fundamental matrix, the transfer function of LIDPS is precisely evaluated in a closed form. The derived transfer function provides the direct input–output relationship of the LIDPS, and thus facilitates the consequent ILC design and convergence analysis in the frequency domain. The proposed control design scheme is able to deal with parametric and non-parametric uncertainties and make full use of the process repetition, while avoid any simplification or discretization for the 3D dynamics of LIDPS in the time, space, and iteration domains. In the end, two illustrative processes are addressed to demonstrate the efficacy of the proposed iterative learning control scheme.     

A P‐type Iterative Learning Controller for Uncertain Robotic Systems with Exponentially Decaying Error Bounds

This paper presents a P‐type iterative learning control (ILC) scheme for uncertain robotic systems that perform the same tasks repetitively. The proposed ILC scheme comprises a linear feedback controller consisting of position error and exponentially weighted velocity error with respect to the number of iterations, and a feedforward learning controller updated by the exponentially weighted velocity error from previous trial. As the learning iteration proceeds, the position and velocity errors converge uniformly to zero within error bounds that decay exponentially through the sequence of iterations with arbitrarily selected convergence rate. Consequently, the proposed ILC scheme enables analysis and tuning of the exponential convergence rate in the iteration domain in contrast to other existing P‐type ILC schemes. © 2003 Wiley Periodicals, Inc.     

A note on causal and CITE iterative learning control algorithms

The convergence properties of causal and current iteration tracking error (CITE) discrete time iterative learning control (ILC) algorithms are studied using time and frequency domain convergence criteria. Of particular interest are conditions for monotone convergence, and these are evaluated using a discrete-time version of Bode's integral theorem.     

离散时间非线性系统的数据驱动无模型自适应迭代学习控制

本文基于迭代域的动态线性化方法,提出了一类单入单出离散时间非线性系统的数据驱动无模型自适应迭代学习控制方案.无模型自适应迭代学习控制本质上属于一种数据驱动控制方法,仅利用被控对象的输入输出数据即可实现控制方案的设计.理论分析表明无模型自适应迭代学习控制方案可以保证最大学习误差的单调收敛性.数值仿真和快速路交通控制应用验证了无模型自适应迭代学习控制方案的有效性.     

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.     

Time and frequency domain convergence properties in iterative learning control

The convergence properties of iterative learning control (ILC) algorithms are considered. The analysis is carried out in a framework using linear iterative systems, which enables several results from the theory of linear systems to be applied. This makes it possible to analyse both first-order and high-order ILC algorithms in both the time and frequency domains. The time and frequency domain results can also be tied together in a clear way. Results are also given for the iterationvariant case, i.e. when the dynamics of the system to be controlled or the ILC algorithm itself changes from iteration to iteration.     

Computationally‐Light Non‐Lifted Data‐Driven Norm‐Optimal Iterative Learning Control

Computational complexity and model dependence are two significant limitations on lifted norm optimal iterative learning control (NOILC). To overcome these two issues and retain monotonic convergence in iteration, this paper proposes a computationally‐efficient non‐lifted NOILC strategy for nonlinear discrete‐time systems via a data‐driven approach. First, an iteration‐dependent linear representation of the controlled nonlinear process is introduced by using a dynamical linearization method in the iteration direction. The non‐lifted NOILC is then proposed by utilizing the input and output measurements only, instead of relying on an explicit model of the plant. The computational complexity is reduced by avoiding matrix operation in the learning law. This greatly facilitates its practical application potential. The proposed control law executes in real‐time and utilizes more control information at previous time instants within the same iteration, which can help improve the control performance. The effectiveness of the non‐lifted data‐driven NOILC is demonstrated by rigorous analysis along with a simulation on a batch chemical reaction process.     

Anticipatory iterative learning control for nonlinear systems witharbitrary relative degree

In this paper, the anticipatory iterative learning control is extended to a class of nonlinear continuous-time systems without restriction on relative degree. The learning algorithm calculates the required input action for the next operation cycle based on the pair of input action taken and its resultant variables. The tracking error convergence performance is examined under input saturation being taken into account. The learning algorithm is shown effective even if differentiation of any order from the tracking error is not used     

Stochastic Iterative Learning Control With Faded Signals

Stochastic iterative learning control (ILC) is designed for solving the tracking problem of stochastic linear systems through fading channels. Consequently, the signals used in learning control algorithms are faded in the sense that a random variable is multiplied by the original signal. To achieve the tracking objective, a two-dimensional Kalman filtering method is used in this study to derive a learning gain matrix varying along both time and iteration axes. The learning gain matrix minimizes the trace of input error covariance. The asymptotic convergence of the generated input sequence to the desired input value is strictly proved in the mean-square sense. Both output and input fading are accounted for separately in turn, followed by a general formulation that both input and output fading coexists. Illustrative examples are provided to verify the effectiveness of the proposed schemes.      

Effects of network communications on a class of learning controlled non-linear systems†

In this article, an iterative learning control approach is proposed for a class of sampled-data non-linear systems over network communication channels. The effects of constant time delays and stochastic packet loss are discussed and demonstrated by simulation results. The focus of this article is to study the remote control problems when the environment is periodic or repeatable over iterations in a fixed finite interval. Because of the existence of time delays and packet loss in input and output signal transmissions, it is not trivial to accomplish the remote stabilisation task of any system. Moreover, to track a desired trajectory through a remote controller is even more difficult. Previous cycle-based learning method is incorporated into the network-based control for a class of non-linear systems which satisfies a global Lipschitz condition. The convergence property of this approach is proven. Furthermore, the convergence in the iteration domain is also discussed when there exists packet loss in both transmission channels of the system. Finally, one single-link rigid robot is given as an example to show the effectiveness of the proposed approach.     

Convergence Analysis of Wireless Remote Iterative Learning Control Systems with Channel Noise

Channel noise, including sensor‐to‐controller(SC) noise and controller‐to‐actuator(CA) noise, impacts the convergence of wireless remote iterative learning control (ILC) system significantly. In this paper, the relationship between output error, SC noise and CA noise is obtained firstly by super‐vector formulation, and then the norm of output error vector covariance matrix is employed to analyze the convergence of the system in presence of SC noise and CA noise. Upper bound of the norm at any sample time reveals that the SC noise is accumulated only in iteration domain, while the CA noise is accumulated not only in iteration domain but also in time domain. Furthermore, the accumulated effect of the CA noise in time domain is ruled by system matrices, so the values of which determine the effect of the CA noise is greater or less than that of the SC noise on convergence of the system. Finally, some simulation results are given to illustrate correctness of the result.