具有通信约束的反馈辅助PD型量化迭代学习控制

本文针对网络线性系统, 研究了具有通信约束的反馈辅助PD型迭代学习控制问题. 信号从远程设备传输到 迭代学习控制器过程中, 存在数据量化与数据包丢失的情况. 将数据包丢失模型描述为具有已知概率的伯努利二 进制序列, 采用扇形界方法处理数据量化误差, 提出了一种反馈辅助PD型迭代学习控制算法. 采用压缩映射法分析 证明了在存在数据量化和丢失的情况下, 所提控制算法依然可以保证跟踪误差渐近收敛到零. 并进一步对存在初 始状态偏移时所提算法的鲁棒性进行了讨论. 最后, 通过仿真示例, 对比验证了理论结果的有效性和优越性.     

Nonlinear iterative learning control with applications to lithographic machinery

An experimental demonstration is given of (nonlinear) iterative learning control applied to a reticle stage of a lithographic wafer scanner. To limit the presence of noise in the learned forces, a nonlinear amplitude-dependent learning gain is proposed. With this gain, high-amplitude signal contents is separated from low-amplitude noise, the former being compensated by the learning algorithm. Contrary to the underlying linear design, the continuously varying trade-off between high-gain convergence rates and low-gain noise transmission demonstrates a significant improvement of the nonlinear design in achieving performance.     

一种新型的迭代学习控制器设计研究

针对一般连续系统的迭代学习控制问题进行了讨论,通过对常用的P型迭代学习控制算法的分析,在分析比较P型、PD型迭代学习控制律存在问题的基础上,提出了一种新型的迭代学习控制算法,利用误差信号以及相邻两次误差的差值信号对系统控制律进行逐次修正,既能避免PD型迭代算法由于微分作用而出现的不良影响,又可以充分地利用了系统已保存的有效信息,从而实现良好的跟踪效果以及较快的跟踪收敛速度,最后通过对一非线性连续系统的仿真,结果验证了算法相对于传统P算法的有效性与优越性.     

机械臂带角度修正的开闭环迭代学习轨迹跟踪控制

在迭代学习控制研究中, 通常的一个假设是: 系统每次迭代初态与期望初态一致或迭代初态固定. 针对迭代学习控制律在迭代初态的限制下难以应用到机械臂轨迹跟踪控制中的问题, 本文对机械臂系统模型降阶变换, 将其转化为低阶系统. 对于变换设计后的机械臂系统模型, 提出一种带有角度修正的开闭环迭代学习控制算法, 该算法利用误差信号及相邻两次误差的偏差信号对系统控制律进行逐次修正, 与常规P型算法相比, 充分利用了系统已存的和当前的有效信息, 与常规PD型算法相比, 避免了由于微分作用而带来的不稳定影响. 同时, 用输出向量的角度关系作为评估控制输入好坏的标准对所设计的迭代学习律的变化趋势进行“奖-惩”, 从而实现了良好的跟踪效果并具有较快的收敛速度. 本文还针对机械臂系统存在关节转角限位的情况对控制算法进行改进, 以使机械臂在实际运作中真正实时地完成指定工作任务. 仿真结果表明了所提控制策略的有效性.     

Performance of convergence-based variable-gain control of optical storage drives

In this paper, a method for the performance assessment of a variable-gain control design for optical storage drives is proposed. The variable-gain strategy is used to overcome well-known linear control design trade-offs between low-frequency tracking properties and high-frequency noise sensitivity. A convergence-based control design is proposed that guarantees stability of the closed-loop system and a unique bounded steady-state response for any bounded disturbance. These favourable properties, guaranteed by virtue of convergence, allow for a unique performance evaluation of the control system. Moreover, technical conditions for convergence are derived for the variable-gain controlled system and a quantitative performance measure, taking into account both low-frequency tracking properties and high-frequency measurement noise sensitivity, is proposed. The convergence conditions together with the performance measure jointly constitute a design tool for tuning the parameters of the variable-gain controller. The resulting design is shown to outperform linear control designs.     

Varying trail lengths-based iterative learning control for linear discrete-time systems with vector relative degree

In this article, to tackle with the iteration-varying trail lengths and random initial state shifts, an average operator-based PD-type iterative learning control (ILC) law is firstly presented for linear discrete-time multiple-input multiple-output (MIMO) systems with vector relative degree. The proposed PD-type ILC law includes an initial rectifying action against initial state shifts, and pursues the reference trajectory tracking beyond the initial time points. As special cases of the PD-type ILC law, P-type and D-type ILC laws are then introduced. It is proved that for linear discrete-time MIMO systems with vector relative degree, the three proposed ILC laws can drive the varying trail lengths-based ILC tracking errors to zero in mathematical expectation beyond the initial time points. A numerical example is used to illustrate the effectiveness of the proposed ILC laws.     

Iterative Path Tracking of an Omni-Directional Mobile Robot

We propose a path-tracking algorithm that is developed using an iterative learning control (ILC) technique and use the algorithm to control an omni-directional mobile robot. The proposed algorithm can be categorized as an open–closed PD-type ILC; it generates robot velocity commands by a PD-type ILC update rule using both previous and current information. When applied to the omni-directional mobile robot, it can decrease position errors and track the desired trajectory. Under the general problem setting that includes a mobile robot, we show that the proposed algorithm guarantees that the system states, outputs and control inputs converge to within small error bounds around the desired ones even under state disturbances, measurement noises and initial state errors. By using simulation and experimental tests, we demonstrate that the proposed algorithm converges fast to the desired path, and results in small root-mean-square (r.m.s.) position error under various surface conditions. The proposed algorithm shows better path-tracking performance than the conventional PID algorithm and achieves faster convergence and lower r.m.s. error than the existing two ILC algorithms.     

线性时不变系统PID–型迭代学习控制律的单调收敛形态

传统的迭代学习控制机理中, 积分补偿是典型的策略之一, 但其跟踪效用并不明确. 本文针对连续线性时 不变系统, 对传统的PD–型迭代学习控制律嵌入积分补偿, 利用分部积分法和推广的卷积Young不等式, 在Lebesgue- p范数意义下, 理论分析一阶和二阶PID–型迭代学习控制律的收敛性态. 结果表明, 当比例、积分和导数学习增益满 足适当条件时, 一阶PID–型迭代学习控制律是单调收敛的, 二阶PID–型迭代学习控制律是双迭代单调收敛的. 数值 仿真验证了积分补偿可有效地提高系统的跟踪性能.     

基于强化迭代学习的四旋翼无人机轨迹控制

为进一步提升在未知环境下四旋翼无人机轨迹的跟踪精度,提出了一种在传统反馈控制架构上增加迭代学习前馈控制器的控制方法。针对迭代学习控制（ILC）中存在的学习参数整定困难的问题,提出了一种利用强化学习（RL）对迭代学习控制器的学习参数进行整定优化的方法。首先,利用RL对迭代学习控制器的学习参数进行优化,筛选出当前环境及任务下最优的学习参数以保证迭代学习控制器的控制效果最优;其次,利用迭代学习控制器的学习能力不断迭代优化前馈输入,直至实现完美跟踪;最后,在有随机噪声存在的仿真环境中把所提出的强化迭代学习控制（RL-ILC）算法与未经参数优化的ILC方法、滑模变结构控制（SMC）方法以及比例-积分-微分（PID）控制方法进行对比实验。实验结果表明,所提算法在经过2次迭代后,总误差缩减为初始误差的0.2%,实现了快速收敛;并且与SMC控制方法及PID控制方法相比,RL-ILC算法在算法收敛后不会受噪声影响产生轨迹波动。由此可见,所提算法能够有效提高无人机轨迹跟踪的准确性和鲁棒性。     

随机变批次长度的反馈辅助PD型量化迭代学习控制

针对离散线性系统,研究批次长度随机变化的反馈辅助PD型量化迭代学习控制问题.考虑系统信号经量化后传输到控制器或执行器的情况,给出两种量化方案:跟踪误差信号量化和控制输入信号量化.基于两种不同的量化信号,在批次长度和初始条件随机变化前提下设计反馈辅助PD型迭代学习控制算法.采用扇形界的处理方法和堆积系统框架,推导数学期望下的学习收敛条件:在误差信号量化情况下,所提出控制算法可以保证跟踪误差渐近收敛到零;在控制输入信号量化情况下,所提出控制算法能够保证跟踪误差有界收敛.仿真示例对比验证了两种量化方案下所提出方法的有效性和优越性.     

Tracking Control of Join-Free Timed Continuous Petri Net Systems under Infinite Servers Semantics

A new low-and-high gain algorithm is presented for tracking control of a subclass of timed continuous Petri Net (contPN) systems working under infinite servers semantics. The inherent properties of timed contPN determine that the control signals must be non-negative and upper bounded by functions of system states. In the proposed control approach, LQ theory is first used to design a low-gain controller such that the control signals satisfy the input constraints. Based on the low-gain controller, a high-gain term is further added to fully employ available control energy, and control performance can be improved consequently. In order to guarantee global tracking convergence and smoothness on the tracking target, a mixed trajectory (state step and ramp) is used instead of a pure step reference signal. The new tracking target is designed to ensure the existence of the low-gain controller and possible fast system response concurrently. Rigorous proof based on Lyapunov function is provided to guarantee that for a conservative and strongly connected Join-Free (JF) timed contPN system, the proposed algorithm can ensure the global asymptotical convergence of both system states and control signals.

数据丢失对迭代学习控制的影响分析

针对一类线性系统,分析数据丢失对迭代学习控制算法的影响.首先基于lifting方法给出跟踪误差渐近收敛和单调收敛的条件,并分析收敛速度与数据丢失率的关系,结果表明收敛速度随着数据丢失程度的增加而变慢.其次,为抑制迭代变化扰动的影响,给出一种存在数据丢失时的鲁棒迭代学习控制器设计方法,并将控制器设计问题转化为求取线性矩阵不等式的可行解.仿真示例验证了理论分析的结果以及鲁棒迭代学习控制算法的有效性.

     

基于向量图分析的一种迭代学习控制算法及其鲁棒性

为了增强迭代学习控制的鲁棒性,加快学习过程的收敛速度,而又不过多地依赖于系统内部信息,本文基于向量图分析思路,利用输入空间的向量构造三角形修正结构,得到了一种新的迭代学习控制算法．该算法根据跟踪误差的大小,调节输入控制量在三角形的一条边上滑动,在跟踪误差较大时,算法能找到控制期望的大致位置并加速收敛,在跟踪误差较小时,能将控制量稳定在其期望的很小邻域内,理论上证明了该邻域直径大小为跟踪误差的二阶无穷小．数值仿真结果说明了它的有效性和优越性．     

Iterative Learning Control for Distributed Parameter Systems Based on Non-Collocated Sensors and Actuators

In this paper, an open-loop PD-type iterative learning control (ILC) scheme is first proposed for two kinds of distributed parameter systems (DPSs) which are described by parabolic partial differential equations using non-collocated sensors and actuators. Then, a closed-loop PD-type ILC algorithm is extended to a class of distributed parameter systems with a non-collocated single sensor and m actuators when the initial states of the system exist some errors. Under some given assumptions, the convergence conditions of output errors for the systems can be obtained. Finally, one numerical example for a distributed parameter system with a single sensor and two actuators is presented to illustrate the effectiveness of the proposed ILC schemes.      

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.     

Robotic Manipulators State Observation Via One-Time Gain Switching

High-gain Luenberger-like state observation would provide the best possible tracking error of nonlinear systems at the expense of higher transient variance and slower convergence to the real state. Conversely, low-gain Luenberger-like observation usually provides lower transient variance of the error system, but might lead to nonzero or nonconvergent steady tracking error. This paper presents new switching-gain observer designs that capitalize on the benefits of low-gain, high-gain, and sliding mode observations. Switching and non-switching observer designs are both considered. Since adaptive observers are often of complex structures and might be difficult to implement, a simpler adaptation form is presented using one-time switching between two predetermined solutions. A nonlinear coordinate transformation is applied to obtain a linear observable system with nonlinear perturbation terms characterized by a Lipschitz constant and/or a finite bound on the norm. Sufficient conditions are derived for the existence of sliding mode, asymptotic stability of the error system, and the independence of the reconstruction error system from the perturbation inputs during the sliding mode. The new observer designs are applied to flexible-joint manipulators in order to explore their performance capabilities. The switching-gain observer was shown to be a reasonable compromise that is easy to be implemented.     

Output tracking for nonlinear stochastic systems by iterative learning control

An iterative learning control (ILC) algorithm, which in essence is a stochastic approximation algorithm, is proposed for output tracking for nonlinear stochastic systems with unknown dynamics and unknown noise statistics. The nonlinear function of the system dynamics is allowed to grow up as fast as a polynomial of any degree, but the system is linear with respect to control. It is proved that the ILC generated by the algorithm a.s. converges to the optimal one at each time t/spl isin/[0,1,...,N] and the output tracking error is asymptotically minimized in the mean square sense as the number of iterates tends to infinity, although the convergence rate is rather slow. The only information used in the algorithm is the noisy observation of the system output and the reference signal y/sub d/(t). When the system state equation is free of noise and the system output is realizable, then the exact state tracking is asymptotically achieved and the tracking error is purely due to the observation noise.     

A PD-Type State-Dependent Riccati Equation With Iterative Learning Augmentation for Mechanical Systems

This work proposes a novel proportional-derivative (PD)-type state-dependent Riccati equation (SDRE) approach with iterative learning control (ILC) augmentation. On the one hand, the PD-type control gains could adopt many useful available criteria and tools of conventional PD controllers. On the other hand, the SDRE adds nonlinear and optimality characteristics to the controller, i.e., increasing the stability margins. These advantages with the ILC correction part deliver a precise control law with the capability of error reduction by learning. The SDRE provides a symmetric-positive-definite distributed nonlinear suboptimal gain K(x) for the control input law u = –R–1(x)BT(x)K(x)x. The sub-blocks of the overall gain R–1(x)BT(x)K(x), are not necessarily symmetric positive definite. A new design is proposed to transform the optimal gain into two symmetric-positive-definite gains like PD-type controllers as u = –K_SP(x)e–K_SD(x)?. The new form allows us to analytically prove the stability of the proposed learning-based controller for mechanical systems; and presents guaranteed uniform boundedness in finite-time between learning loops. The symmetric PD-type controller is also developed for the state-dependent differential Riccati equation (SDDRE) to manipulate the final time. The SDDRE expresses a differential equation with a final boundary condition, which imposes a constraint on time that could be used for finite-time control. So, the availability of PD-type finite-time control is an asset for enhancing the conventional classical linear controllers with this tool. The learning rules benefit from the gradient descent method for both regulation and tracking cases. One of the advantages of this approach is a guaranteed-stability even from the first loop of learning. A mechanical manipulator, as an illustrative example, was simulated for both regulation and tracking problems. Successful experimental validation was done to show the capability of the system in practice by the implementation of the proposed method on a variable-pitch rotor benchmark.      

随机分布控制系统的自适应迭代学习控制

介绍输出概率密度函数(PDF)常规的迭代学习控制(ILC)的收敛条件,并利用此条件设计相应的迭代学习律.主要讨论如何解决输出PDF迭代学习控制(ILC)中的过迭代,收敛速度等问题.以离散输出概率密度函教(PDF)控制模型为基础,介绍了直接迭代学习控制算法收敛的必要条件,提出自适应的迭代学习参数调节方法和避免过迭代的迭代结束条件,这些措施能够保证输出PDF的迭代控制收敛且具有较快的收敛速度.仿真结果表明,输出PDF的自适应迭代学习控制具有较快的收敛速度,而学习终止条件能很好地避免过迭代.     

A statistical analysis of certain iterative learning control algorithms

Iterative learning control (ILC) is a technique used to improve the tracking performance of systems carrying out repetitive tasks, which are affected by deterministic disturbances. The achievable performance is greatly degraded, however, when non-repeating, stochastic disturbances are present. This paper aims to compare a number of different ILC algorithms, proposed to be more robust to the presence of these disturbances, first by a statistical analysis and then by simulation results and their application to a linear motor. New expressions for the expected value and variance of the controlled error are developed for each algorithm. The different algorithms are then tested in simulation and finally applied to the linear motor system to test their performance in practice. A filtered ILC algorithm is proposed when the noise and desired output spectra are separated. Otherwise an algorithm with a decreasing gain gives good robustness to noise and achievable precision but at a slower convergence rate.