Newton method based iterative learning control for discrete non-linear systems

Significant progress has been achieved in terms of both theory and industrial applications of iterative learning control (ILC) in the past decade. However, the techniques of solving non-linear ILC problems are still under development. The main result of this paper is a novel non-linear ILC algorithm that utilizes the capability of the Newton method. By setting up links between non-linear ILC problems and non-linear multivariable equations, the Newton method is introduced into the ILC framework. The implementation of the new algorithm allows one to decompose a nonlinear ILC problem into a sequence of linear time-varying ILC problems. Simulations on a discrete non-linear system and a manipulator model display its advantages. Conditions for its semi-local convergence are analysed. Links of ILC with existing non-linear topics are pointed out as ways to construct new non-linear ILC schemes. Potential improvements are discussed for future work.     

Robot visual servoing with iterative learning control

This paper presents an iterative learning scheme for vision-guided robot trajectory tracking. First, a stability criterion for designing iterative learning controller is proposed. It can be used for a system with initial resetting error. By using the criterion, one can convert the design problem into finding a positive definite discrete matrix kernel and a more general form of learning control can be obtained. Then, a three-dimensional (3D) trajectory tracking system with a single static camera to realize robot movement imitation is presented based on this criterion.     

Convergence characteristics of PD-type iterative learning control in discrete frequency domain

On the basis that a Dirichlet-type signal over a finite time period can be expanded in a Fourier series consisting of fundamental-frequency sinusoidal and cosine waves plus a sequence of higher-frequency harmonic waves, this paper investigates the convergence characteristics of the first- and second-order proportional-derivative-type iterative learning control schemes for repetitive linear time-invariant systems in discrete spectrum. By deriving the properties of the Fourier coefficients in a complex form with respect to the linear time-invariant dynamics and adopting Parseval's Energy Equality, the average energy of the tracking error signal over the finite operation time interval is converted into a quarter of a summation of the fundamental spectrum plus the harmonic spectrums. By means of analyzing the feature of discrete frequency-wise spectrum of the tracking error, sufficient and necessary conditions for monotone convergence with respect to the first-order iterative learning control scheme is deduced together with convergence of the second-order learning scheme is discussed. Numerical simulations manifest the validity and the effectiveness.     

Navigation function-based visual servo control

In this paper, the mapping between the desired camera feature vector and the desired camera pose (i.e., the position and orientation) is investigated to develop a measurable image Jacobian-like matrix. An image-space path planner is then proposed to generate a desired image trajectory based on this measurable image Jacobian-like matrix and an image-space navigation function (NF) (i.e., a special potential field function) while satisfying rigid body constraints. An adaptive, homography-based visual servo tracking controller is then developed to navigate the position and orientation of a camera held by the end-effector of a robot manipulator to a goal position and orientation along the desired image-space trajectory while ensuring the target points remain visible (i.e., the target points avoid self-occlusion and remain in the field-of-view (FOV)) under certain technical restrictions. Due to the inherent nonlinear nature of the problem and the lack of depth information from a monocular system, a Lyapunov-based analysis is used to analyze the path planner and the adaptive controller. Simulation results are provided to illustrate the performance of the proposed approach.     

Iterative learning control for two-dimensional linear discrete systems with Fornasini-Marchesini model

International Journal of Control, Automation and Systems - Almost all existing iterative learning control (ILC) algorithms have focused on one-dimensional (1-D) dynamical systems, and seldom were...     

Adaptive iterative learning control for robot manipulators

In this paper, we propose some adaptive iterative learning control (ILC) schemes for trajectory tracking of rigid robot manipulators, with unknown parameters, performing repetitive tasks. The proposed control schemes are based upon the use of a proportional-derivative (PD) feedback structure, for which an iterative term is added to cope with the unknown parameters and disturbances. The control design is very simple in the sense that the only requirement on the PD and learning gains is the positive definiteness condition and the bounds of the robot parameters are not needed. In contrast to classical ILC schemes where the number of iterative variables is generally equal to the number of control inputs, the second controller proposed in this paper uses just two iterative variables, which is an interesting fact from a practical point of view since it contributes considerably to memory space saving in real-time implementations. We also show that it is possible to use a single iterative variable in the control scheme if some bounds of the system parameters are known. Furthermore, the resetting condition is relaxed to a certain extent for a certain class of reference trajectories. Finally, simulation results are provided to illustrate the effectiveness of the proposed controllers.     

A pseudoinverse-based iterative learning control

Learning control is a very effective approach for tracking control in processes occurring repetitively over a fixed interval of time. In this paper, an iterative learning control (ILC) algorithm is proposed to accommodate a general class of nonlinear, nonminimum-phase plants with disturbances and initialization errors. The algorithm requires the computation of an approximate inverse of the linearized plant rather than the exact inverse. An advantage of this approach is that the output of the plant need not be differentiated. A bound on the asymptotic trajectory error is exhibited via a concise proof and is shown to grow continuously with a bound on the disturbances. The structure of the controller is such that the low frequency components of the trajectory converge faster than the high frequency components     

基于模糊辨识的非线性连续系统的迭代学习控制

基于非线性连续动态的模型辨识算法，给出了非线性连续系统的一种非常有效的迭代学习控制方案。该控制方案不要求非线性连续系统中具体的非线性关系，并且容许系统初始误差的存在。     

LMI-based robust iterative learning controller design for discrete linear uncertain systems

This paper addresses the design problem of robust iterative learning controllers for a class of linear discrete-time systems with norm-bounded parameter uncertainties. An iterative learning algorithm with current cycle feedback is proposed to achieve both robust convergence and robust stability. The synthesis problem of the proposed iterative learmng control （ILC） system is reformulated as a γ-suboptimal H-infinity control problem via the linear fractional transformation （LFT）. A sufficient condition for the convergence of the ILC algorithm is presented in terms of linear matrix inequalities （LMIs）. Furthermore, the linear wansfer operators of the ILC algorithm with high convergence speed are obtained by using existing convex optimization techniques. The simulation results demonstrate the effectiveness of the proposed method.     

Frequency-domain iterative learning control of a marine vibrator

To the purpose of marine seismic acquisition, new acoustic sources have been developed to reduce the environmental impact. The use of marine vibrators makes it possible to define emission frequency ranges, consequently allowing limitation of the frequencies that disturb marine animal life. Constructing marine vibrators with high efficiency and linear dynamics is however difficult, and the vibrators suffer from both friction, backlash and high-order harmonics. These nonlinear effects, in combination with drifting dynamics, make the required control a crucial and challenging problem. This paper presents a model-based iterative learning control solution, performed in the frequency-domain. Additionally, an adaptive reidentification algorithm is developed to cope with drifting dynamics. The proposed solutions are successfully evaluated in experiments with a marine vibrator.     

Image based visual servo control for a class of aerial robotic systems

An image-based strategy for visual servo control of a class of dynamic systems is proposed. The class of systems considered includes dynamic models of unmanned aerial vehicles capable of quasi-stationary flight (hover and near hover flight). The control strategy exploits passivity-like properties of the dynamic model to derive a Lyapunov control algorithm using backstepping techniques. The paper extends earlier work (Hamel, T., & Mahony, R. (2002). Visual servoing of an under-actuated dynamic rigid-body system: An image based approach. IEEE Transactions on Robotics and Automation, 18(2), 187-198) where partial pose information was used in the construction of the visual error. In this paper the visual error is defined purely in terms of the image features derived from the camera input. Local exponential stability of the system is proved. An estimate of the basin of attraction for the closed-loop system is provided.     

倒立摆的可变增益迭代学习控制算法

对倒立摆系统的平衡控制问题进行研究。在建立系统数学模型的基础上,提出指数变增益迭代学习控制律,并设计了控制器。通过系统仿真实验,结果表明：与常规迭代学习控制律相比较,本文采用的方法收敛速度大大加快,系统动态性能得到很大改善。     

Noise tolerant iterative learning control for a class of continuous-time systems

The paper proposes a noise tolerant iterative learning control (ILC) for a class of linear continuous-time systems, which achieves high-precision tracking for uncertain plants by iteration of trials in the presence of heavy measurement noise. The robustness against measurement noise is achieved through (i) projection of continuous-time I/O signals onto a finite-dimensional parameter space, (ii) using error data of all past iterations via an integral operation in the learning law and (iii) noise reduction by H² optimization subject to a specified convergence speed of the ILC.     

Homography-based visual servo tracking control of a wheeled mobile robot

A visual servo tracking controller is developed in this paper for a monocular camera system mounted on an underactuated wheeled mobile robot (WMR) subject to nonholonomic motion constraints (i.e., the camera-in-hand problem). A prerecorded image sequence (e.g., a video) of three target points is used to define a desired trajectory for the WMR. By comparing the target points from a stationary reference image with the corresponding target points in the live image and the prerecorded sequence of images, projective geometric relationships are exploited to construct Euclidean homographies. The information obtained by decomposing the Euclidean homography is used to develop a kinematic controller. A Lyapunov-based analysis is used to develop an adaptive update law to actively compensate for the lack of depth information required for the translation error system. Experimental results are provided to demonstrate the control design.     

All-pass filtering in iterative learning control

In iterative learning control (ILC), it is highly desirable to have a learning compensator with a unit-gain for all frequencies, in order to avoid noise amplification and learning speed degradation during the learning process. In this paper, we show that the realization of a unit-gain compensator is straightforward in ILC, using both forward and backward filtering. As an illustrative example, a unit-gain derivative is proposed to overcome the drawbacks of the conventional derivative. The proposed scheme is equivalent to an all-pass unit-gain phase shifter; the forward filtering uses a 0.5-order derivative and the backward filtering employs a 0.5-order integral. The all-pass phase shifter is deployed in a unit-gain D-type ILC. The advantages of the unit-gain feature are demonstrated by some experimental results on a robot manipulator.     

Parameter optimization in iterative learning control

In this paper parameter optimization through a quadratic performance index is introduced as a method to establish a new iterative learning control law. With this new algorithm, monotonic convergence of the error to zero is guaranteed if the original system is a discrete-time LTI system and it satisfies a positivity condition. If the original system is not positive, two methods are derived to make the system positive. The effect of the choice of weighting parameters in the performance index on convergence rate is analysed. As a result adaptive weights are introduced as a method to improve the convergence properties of the algorithm. A high-order version of the algorithm is also derived and its convergence analysed. The theoretical findings in this paper are highlighted with simulations.     

高阶无模型自适应迭代学习控制

针对一类非线性非仿射离散时间系统,提出了高阶无模型自适应迭代学习控制方案.控制器的设计和分析仅依赖于系统的输入/输出(I/O)数据,不需要已知任何其他知识.该方法采用了高阶学习律,可利用更多以前重复过程中的控制信息提高系统收敛性,且学习增益可通过"拟伪偏导数"更新律迭代调节.仿真结果验证了所提出算法的有效性.     

An optimal method for nonlinear iterative learning control systems with constraint and model uncertainty

Clonal selection algorithm is improved and proposed as a method to implement nonlinear optimal iterative learning control algorithm. In the method, more priori information was coded in a clonal selection algorithm to decrease the size of the search space and to deal with constraint on input. Another clonal selection algorithm is used as a model modifying device to cope with uncertainty in the plant model. Finally, simulations show that the convergence speed is satisfactory regardless of the nature of the plant and whether or not the plant model is precise.