Stability of Iterative Learning Control with Data Dropouts via Asynchronous Dynamical System

In this paper, the stability of iterative learning control with data dropouts is discussed. By the super vector formulation, an iterative learning control （ILC） system with data dropouts can be modeled as an asynchronous dynamical system with rate constraints on events in the iteration domain. The stability condition is provided in the form of linear matrix inequalities （LMIS） depending on the stability of asynchronous dynamical systems. The analysis is supported by simulations.

Adaptive adjustment of iterative learning control gain matrix in harsh noise environment

For the robustness problem of open-loop P-type iterative learning control under the influence of measurement noise which is inevitable in actual systems, an adaptive adjustment algorithm of iterative learning nonlinear gain matrix based on error amplitude is proposed and two nonlinear gain functions are given. Then with the help of Bellman-Gronwall lemma, the robustness proof is derived. At last, an example is simulated and analyzed. The results show that when there exists measurement noise, the proposed learning law adjusts the learning gain matrix on line based on error amplitude, thus can make a compromise between learning convergence rate and convergence accuracy to some extent： the fast convergence rate is achieved with high gain in initial learning stage, the strong robustness and high convergence accuracy are achieved at the same time with small gain in the end learning stage, thus better learning results are obtained.

Iterative Learning Control for homing guidance design of missiles

This paper presents an Iterative Learning Control design applied to homing guidance of missiles against maneuvering targets. According to numerical experiments, although an increase of the control energies is appreciated with respect to a previous published base controller for comparison, this strategy, which is simple to realize, is able to reduce the time to reach the head-on condition to target destruction. This fact is important to minimize the missile lateral force-level to fulfill engaging in hyper-sonic target persecutions.

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 MittagLeffler 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.

Compensation of hysteresis in piezoelectric actuator with iterative learning control

This paper presents the application of iterative learning control (ILC) to compensate hysteresis in a piezoelectric actuator. The proposed controller is a hybrid of proportional-integral-differential (PID) control, whose main function is for trajectory tracking, and a chatter-based ILC, whose main function is for hysteresis compensation. Stability analysis of the proposed ILC is presented, with the PID included in the dynamic of the piezoelectric actuator. The performance of the proposed controller is analysed through simulation and verified with experiment with a piezoelectric actuator.

Robust Optimization-Based Iterative Learning Control for Nonlinear Systems With Nonrepetitive Uncertainties

This paper aims to solve the robust iterative learning control(ILC)problems for nonlinear time-varying systems in the presence of nonrepetitive uncertainties.A new optimization-based method is proposed to design and analyze adaptive ILC,for which robust convergence analysis via a contraction mapping approach is realized by leveraging properties of substochastic matrices.It is shown that robust tracking tasks can be realized for optimization-based adaptive ILC,where the boundedness of system trajectories and estimated parameters can be ensured,regardless of unknown time-varying nonlinearities and nonrepetitive uncertainties.Two simulation tests,especially implemented for an injection molding process,demonstrate the effectiveness of our robust optimization-based ILC results.

Iterative Learning Control With Incomplete Information： A Survey

This paper conducts a survey on iterative learning control(ILC) with incomplete information and associated control system design, which is a frontier of the ILC field.The incomplete information, including passive and active types,can cause data loss or fragment due to various factors. Passive incomplete information refers to incomplete data and information caused by practical system limitations during data collection,storage, transmission, and processing, such as data dropouts,delays, disordering, and limited transmission bandwidth. Active incomplete information refers to incomplete data and information caused by man-made reduction of data quantity and quality on the premise that the given objective is satisfied, such as sampling and quantization. This survey emphasizes two aspects:the first one is how to guarantee good learning performance and tracking performance with passive incomplete data, and the second is how to balance the control performance index and data demand by active means. The promising research directions along this topic are also addressed, where data robustness is highly emphasized. This survey is expected to improve understanding of the restrictive relationship and trade-off between incomplete data and tracking performance, quantitatively, and promote further developments of ILC theory.

Robust Iterative Learning Controller for the Non-zero Initial Error Problem on Robot Manipulator

Industrial robot system is a kind of dynamic system w ith strong nonlinear coupling and high position precision. A lot of control ways , such as nonlinear feedbackdecomposition motion and adaptive control and so o n, have been used to control this kind of system, but there are some deficiencie s in those methods: some need accurate and some need complicated operation and e tc. In recent years, in need of controlling the industrial robots, aiming at com pletely tracking the ideal input for the controlled subject with repetitive character, a new research area, ILC (iterative learning control), has been devel oped in the control technology and theory. The iterative learning control method can make the controlled subject operate as desired in a definite time span, merely making use of the prior control experie nce of the system and searching for the desired control signal according to the practical and desired output signal. The process of searching is equal to that o f learning, during which we only need to measure the output signal to amend the control signal, not like the adaptive control strategy, which on line assesses t he complex parameters of the system. Besides, since the iterative learning contr ol relies little on the prior message of the subject, it has been well used in a lot of areas, especially the dynamic systems with strong non-linear coupling a nd high repetitive position precision and the control system with batch producti on. Since robot manipulator has the above-mentioned character, ILC can be very well used in robot manipulator. In the ILC, since the operation always begins with a certain initial state, init ial condition has been required in almost all convergence verification. Therefor e, in designing the controller, the initial state has to be restricted with some condition to guarantee the convergence of the algorithm. The settle of initial condition problem has long been pursued in the ILC. There are commonly two kinds of initial condition problems: one is zero initial error problem, another is non-zero initial error problem. In practice, the repe titive operation will invariably produce excursion of the iterative initial stat e from the desired initial state. As a result, the research on the second in itial problem has more practical meaning. In this paper, for the non-zero initial error problem, one novel robust ILC alg orithms, respectively combining PD type iterative learning control algorithm wit h the robust feedback control algorithm, has been presented. This novel robust ILC algorithm contain two parts: feedforward ILC algorithm and robust feedback algorithm, which can be used to restrain disturbance from param eter variation, mechanical nonlinearities and unmodeled dynamics and to achieve good performance as well. The feedforward ILC algorithm can be used to improve the tracking error and perf ormance of the system through iteratively learning from the previous operation, thus performing the tracking task very fast. The robust feedback algorithm could mainly be applied to make the real output of the system not deviate too much fr om the desired tracking trajectory, and guarantee the system’s robustness w hen there are exterior noises and variations of the system parameter. In this paper, in order to analyze the convergence of the algorithm, Lyapunov st ability theory has been used through properly selecting the Lyapunov function. T he result of the verification shows the feasibility of the novel robust iterativ e learning control in theory. Finally, aiming at the two-freedom rate robot, simulation has been made with th e MATLAB software. Furthermore, two groups of parameters are selected to validat e the robustness of the algorithm.

Discounted Iterative Adaptive Critic Designs With Novel Stability Analysis for Tracking Control

The core task of tracking control is to make the controlled plant track a desired trajectory.The traditional performance index used in previous studies cannot eliminate completely the tracking error as the number of time steps increases.In this paper,a new cost function is introduced to develop the value-iteration-based adaptive critic framework to solve the tracking control problem.Unlike the regulator problem,the iterative value function of tracking control problem cannot be regarded as a Lyapunov function.A novel stability analysis method is developed to guarantee that the tracking error converges to zero.The discounted iterative scheme under the new cost function for the special case of linear systems is elaborated.Finally,the tracking performance of the present scheme is demonstrated by numerical results and compared with those of the traditional approaches.

Robust reinforcement learning with UUB guarantee for safe motion control of autonomous robots

This paper addresses the issue of safety in reinforcement learning(RL)with disturbances and its application in the safety-constrained motion control of autonomous robots.To tackle this problem,a robust Lyapunov value function(rLVF)is proposed.The rLVF is obtained by introducing a data-based LVF under the worst-case disturbance of the observed state.Using the rLVF,a uniformly ultimate boundedness criterion is established.This criterion is desired to ensure that the cost function,which serves as a safety criterion,ultimately converges to a range via the policy to be designed.Moreover,to mitigate the drastic variation of the rLVF caused by differences in states,a smoothing regularization of the rLVF is introduced.To train policies with safety guarantees under the worst disturbances of the observed states,an off-policy robust RL algorithm is proposed.The proposed algorithm is applied to motion control tasks of an autonomous vehicle and a cartpole,which involve external disturbances and variations of the model parameters,respectively.The experimental results demonstrate the effectiveness of the theoretical findings and the advantages of the proposed algorithm in terms of robustness and safety.

膝-踝-趾动力型假肢解耦控制研究

针对膝-踝-趾动力型假肢系统的强耦合性,导致系统控制效果不理想等问题,本文设计控制法则分解法解耦器对系统进行解耦,降低耦合度,提高控制效果。利用拉格朗日方程建立了膝-踝-趾动力型假肢系统支撑末期的动力学模型,此模型的耦合度为1.22,耦合性较强,需要进行解耦;基于控制法则分解法设计模型解耦器,以此简化假肢系统,将耦合度强的系统简化为膝、踝、趾独立控制的模型;基于自适应迭代学习设计控制器,对解耦前后三自由度假肢系统的各关节进行控制。结果表明:此解耦器可以将假肢模型简化为3个单输入、单输出的系统,同时降低关节间的耦合度,加快系统的收敛速度,与解耦前的控制效果相比,解耦后系统收敛误差明显减小。本文为多关节假肢系统提供了模型简化方法,为实物样机控制提供理论验证。

Robust Iterative Learning Control of Single-phase Grid-connected Inverter

For the single phase inductance-capacitance-inductance(LCL) grid-connected inverter in micro-grid, a kind of robust iterative learning controller is designed. Based on the output power droop characteristics of inverter, the current sharing among the inverters is achieved. Iterative learning strategy is suitable for repeated tracking control and inhibiting periodic disturbance, and is designed using robust performance index, so that it has the ability to overcome the uncertainty of system parameters. Compared with the repetitive control, the robust iterative learning control can get high precision output waveform, and enhance the tracking ability for waveform, and the distortion problem of the output signal can be solved effectively.

An Advanced FMRL Controller for FACTS Devices to Enhance Dynamic Performance of Power Systems

The parameters of power system slowly change with time due to environmental effects or may change rapidly due to faults. It is preferable that the control technique in this system possesses robustness for various fault conditions and disturbances. The used flexible alternating current transmission system （FACTS） in this paper is an advanced super-conducting magnetic energy storage （ASMES）. Many control techniques that use ASMES to improve power system stability have been proposed. While fuzzy controller has proven its value in some applications, the researches applying fuzzy controller with ASMES have been actively reported. However, it is sometimes very difficult to specify the rule base for some plants, when the parameters change. To solve this problem, a fuzzy model reference learning controller （FMRLC） is proposed in this paper, which investigates multi-input multi-output FMRLC for time-variant nonlinear system. This control method provides the motivation for adaptive fuzzy control, where the focus is on the automatic online synthesis and tuning of fuzzy controller parameters （i.e., using online data to continually learn the fuzzy controller that will ensure that the performance objectives are met）. Simulation results show that the proposed robust controller is able to work with nonlinear and nonstationary power system （i.e., single machine-infinite bus （SMIB） system）, under various fault conditions and disturbances.

Set-point-related Indirect Iterative Learning Control for Multi-input Multi-output Systems

A form of iterative learning control (ILC) is used to update the set-point for the local controller. It is referred to as set-point-related (SPR) indirect ILC. SPR indirect ILC has shown excellent performance: as a supervision module for the local controller, ILC can improve the tracking performance of the closed-loop system along the batch direction. In this study, an ILC-based P-type controller is proposed for multi-input multi-output (MIMO) linear batch processes, where a P-type controller is used to design the control signal directly and an ILC module is used to update the set-point for the P-type controller. Under the proposed ILC-based P-type controller, the closed-loop system can be transformed to a 2-dimensional (2D) Roesser s system. Based on the 2D system framework, a sufficient condition for asymptotic stability of the closed-loop system is derived in this paper. In terms of the average tracking error (ATE), the closed-loop control performance under the proposed algorithm can be improved from batch to batch, even though there are repetitive disturbances. A numerical example is used to validate the proposed results.

A novel D-type iterative learning control design for antilinear systems

In this paper,a novel D-type iterative learning control(ILC)law is proposed for discrete-time antilinear systems.This D-type control law is different from the previous linear(nonlinear)D-type ILC law.The main feature is that we take the conjugate of the(t+1)-th error to construct the proposed controller.The convergence proofs are given for their corresponding ILC schemes.

基于迭代学习的工业机械臂抗干扰控制方法

为了克服工业机械臂的未知负载力矩和摩擦等干扰因素的影响,采用迭代学习算法设计了滑模控制律。首先建立了工业机械臂数学模型,然后设计了二阶非奇异快速终端滑模面,同时提出了滑模控制律,最后利用迭代学习方法来改善滑模控制律的抖振现象,并进行了收敛性分析。仿真结果表明:设计的基于迭代学习的滑模控制律能够有效消除各种干扰因素的影响,实现对工业机械臂运动轨迹的精确控制,最大跟踪误差仅为0.3mm,在实测验证中的最大跟踪误差也仅为0.17mm,平均运行时长仅为1.73s,大幅提升了对工业机械臂的控制精准度。

Deep Reinforcement Learning Enabled Bi-level Robust Parameter Optimization of Hydropower-dominated Systems for Damping Ultra-low Frequency Oscillation

This paper proposes a robust and computationally efficient control method for damping ultra-low frequency oscillations(ULFOs) in hydropower-dominated systems. Unlike the existing robust optimization based control formulation that can only deal with a limited number of operating conditions, the proposed method reformulates the control problem into a bi-level robust parameter optimization model. This allows us to consider a wide range of system operating conditions. To speed up the bi-level optimization process, the deep deterministic policy gradient(DDPG) based deep reinforcement learning algorithm is developed to train an intelligent agent. This agent can provide very fast lower-level decision variables for the upper-level model, significantly enhancing its computational efficiency. Simulation results demonstrate that the proposed method can achieve much better damping control performance than other alternatives with slightly degraded dynamic response performance of the governor under various types of operating conditions.

The Learning Control and Learning Adaptive Control of General Nonlinear Systems：MIMO Case

The learning control law for the general MIMO nonlinear systems with white noise distrubance is presented in the paper,it has extremely simple, recursive, incremental form,and strong robustness,it can also deal with the ill-conditioned systems.The new adaptive control scheme is presented when the parameters of the MIMO nonlinear systems are unknown.The convergence,BIBO stability,and robustness of learning adaptive control scheme are also discussed in this paper.

永磁直线同步电动机的自适应学习控制

由于没有传动机构,使永磁直线交流同步电机(PMLSM)控制器设计较为复杂。PMLSM对模型不确定性和外扰更加敏感;推力波动等非线性因素对运动精度影响很大。针对上述问题,用自适应学习方法改善PMLSM的轨迹跟踪性能,并对迭代模式和单次运行模式下算法的收敛性进行了证明,通过实验进行了算法验证。该控制方法基于迭代学习,控制器分为两个部分,通过执行重复任务自适应学习项补偿系统的非线性;另一项用于增强系统的鲁棒性,保证系统在单次运动模式下稳定。实验结果表明,这种控制方法可以有效提高PMLSM轨迹跟踪精度。