Adaptive iterative learning control for switched nonlinear continuous-time systems

In this paper, an adaptive iterative learning control (ILC) method is proposed for switched nonlinear continuous-time systems with time-varying parametric uncertainties. First, an iterative learning controller is constructed with a state feedback term in the time domain and an adaptive learning term in the iteration domain. Then a switched nonlinear continuous-discrete two-dimensional (2D) system is built to describe the adaptive ILC system. Multiple 2D Lyapunov functions-based analysis ensures that the 2D system is exponentially stable, and the tracking error will converge to zero in the iteration domain. The design method of the iterative learning controller is obtained by solving a linear matrix inequality. Finally, the efficacy of the proposed controller is demonstrated by the simulation results.     

输入增益未知非参数不确定系统的准最优学习控制

为解决一类非参数不确定系统在任意初态且输入增益未知情形下的轨迹跟踪问题, 提出准最优误差跟踪学习控制方法.该方法综合准最优控制和迭代学习控制两种技术设计控制器, 在构造期望误差轨迹的基础上, 根据控制Lyapunov函数及Sontag公式给出标称系统的优化控制, 以鲁棒方法和学习方法相结合的策略处理非参数不确定性.闭环系统经过足够次迭代运行后, 经由实现系统误差对期望误差轨迹在整个作业区间上的精确跟踪, 获得系统状态对参考信号在预设的部分作业区间上的精确跟踪.仿真结果表明所设计学习系统在收敛速度方面快于非优化设计.     

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.     

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.

     

基于改进粒子群算法的毫米波大规模MIMO混合预编码方案

针对毫米波大规模多输入多输出（MIMO）系统中基于传统粒子群优化（PSO）算法的混合预编码方案,在迭代后期收敛速度较慢以及容易陷入局部最优值的问题,提出了一种基于改进PSO算法的混合预编码方案。首先,随机初始化粒子的位置矢量和速度矢量,并以最大化系统和速率为目标求解初始群体最优位置矢量;其次,更新位置矢量和速度矢量,并随机地选择更新后的两个粒子的个体历史最优位置矢量进行加权求和作为新的个体历史最优位置矢量,从中挑选出若干个使系统和速率最大的粒子,将其个体历史最优位置矢量的加权平均值作为新的群体最优位置矢量,并与之前的群体最优位置矢量比较,经过多次迭代形成最终的群体最优位置矢量即为所求的最佳混合预编码矢量,并对其进行归一化;最后,根据归一化后的混合预编码矢量设计最终的模拟预编码矩阵和数字预编码矩阵。仿真结果表明,与基于传统PSO算法的混合预编码方案相比,所提改进方案在收敛速度与和速率上都得到优化;其收敛速度提高约100%,且性能可以达到全数字预编码方案的90%,因此,该改进方案能够有效提升系统性能且加快收敛。     

Iterative Learning Control Via Weighted Local-Symmetrical-Integration

A new iterative learning control (ILC) updating law is proposed for tracking control of continuous linear system over a finite time interval. The ILC is applied as a feedforward controller to the existing feedback controller. By using the weighted local symmetrical integral (WLSI) of feedback control signal of previous iteration, the ILC updating law takes a simple form with only two design parameters: the learning gain and the range of local integration. Convergence analysis is presented together with a design procedure. A set of experimental results are presented to illustrate the effectiveness of the proposed WLSI-ILC scheme.     

A guaranteed monotonically convergent iterative learning control

This paper presents a new iterative learning control (ILC) scheme for linear discrete time systems. In this scheme, the input of the controlled system is modified by applying a semi‐sliding window algorithm, with a maximum length of n + 1, on the tracking errors obtained from the previous iteration (n is the order of the controlled system). The convergence of the presented ILC is analyzed. It is shown that, if its learning gains are chosen proportional to the denominator coefficients of the system transfer function, then its monotonic convergence condition is independent of the time duration of the iterations and depends only on the numerator coefficients of the system transfer function. The application of the presented ILC to control second‐order systems is described in detail. Numerical examples are added to illustrate the results. Copyright © 2011 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

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.     

Iterative learning control for position tracking of a pneumatic actuated X–Y table

The iterative learning control (ILC) obtains the unknown information from repeated control operations. Meanwhile, the tracking error from previous stages is used as the correction factor for the next control action. Therefore, the ILC controller can make the system tracking error converge to a small region within a limited number of iterations. This study builds a proportional-valve-controlled pneumatic X–Y table system for performing position tracking control experiments. The experiments involve implementing the ILC controllers and comparing the results. The P-type updating law with delay parameters is used for both the x- and y-axes in the repetitive trajectory tracking control. Experimental results demonstrate that the ILC controller can effectively control the system and track the desired circular trajectory at different speeds. The control parameters are varied to investigate their effects on the ILC convergence.     

Iterative Learning Control for a Class of Fractional Order Distributed Parameter Systems

This paper concerns a second‐order P‐type iterative learning control (ILC) scheme for a class of fractional order linear distributed parameter systems. First, by analyzing of the control and learning processes, a discrete system for P‐type ILC is established and the ILC design problem is then converted to a stability problem for such a discrete system. Next, a sufficient condition for the convergence of the control input and the tracking errors is obtained by using generalized Gronwall inequality, which is less conservative than the existing one. By incorporating the convergent condition obtained into the original system, the ILC scheme is derived. Finally, the validity of the proposed method is verified by a numerical example.     

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.     

A Practical Iterative Learning Path‐Following Control Of An Omni‐Directional Vehicle

A new practical iterative learning control (ILC) updating law is proposed to improve the path following accuracy for an omni‐directional autonomous mobile robot. The ILC scheme is applied as a feedforward controller to the existing feedback controller. By using the local symmetrical double‐integral of the feedback control signal of the previous iteration, the ILC updating law takes a simple form with only two design parameters: the learning gain and the range of local integration. Convergence analysis is presented together with a design procedure. Simulation results on a difficult maneuver are presented to illustrate the effectiveness of the proposed simple and yet practical scheme. The simulation is based on the model of a novel robotic platform, the Utah State University (USU) Omni‐Directional Vehicle (ODV), which uses multiple “smart wheels,” whose speed and direction can be independently controlled through dedicated processors for each wheel.     

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。     

Iterative learning control design with high‐order internal model for discrete‐time nonlinear systems

In this paper, a high‐order internal model (HOIM)‐based iterative learning control (ILC) scheme is proposed for discrete‐time nonlinear systems to tackle the tracking problem under iteration‐varying desired trajectories. By incorporating the HOIM that is utilized to describe the variation of desired trajectories in the iteration domain into the ILC design, it is shown that the system output can converge to the desired trajectory along the iteration axis within arbitrarily small error. Furthermore, the learning property in the presence of state disturbances and output noise is discussed under HOIM‐based ILC with an integrator in the iteration axis. Two simulation examples are given to demonstrate the effectiveness of the proposed control method. Copyright © 2016 John Wiley & Sons, Ltd.     

融合迭代学习与干扰观测器的压电微动平台精密运动控制

针对运动系统中常见的重复参考轨迹,尽管迭代学习控制（iterative learning control,ILC）可以通过迭代有效消除重复误差,但其对于非重复性干扰十分敏感．为实现在非重复干扰环境下压电微动平台的精密运动,提出了融合ILC与干扰观测器（disturbance observer,DOB）的控制策略．为避免复杂的迟滞建模,将迟滞非线性视为迭代过程中的重复性输入干扰．为保证控制策略的稳定性,推导其收敛条件并分析对非重复性干扰的抑制作用从而降低收敛误差．最后在压电微动平台进行了对比实验,结果表明：所提控制策略可以在无迟滞模型的前提下有效补偿迟滞非线性．针对理想环境下的5Hz、10Hz、20Hz三角波跟踪,其跟踪误差的均方根在行程的0.4%以内;而在非重复干扰环境下,跟踪误差的均方根为10.24nm,与内置的控制器、单独的反馈控制器、ILC相比,分别降低了98.73%、98.67%与88.24%．而且在干扰环境下,所提控制策略加快了ILC的收敛速度．实验结果充分验证了所提控制策略的有效性,实现了压电微动平台的精密运动．     

Robust design of feedback feed-forward iterative learning control based on 2D system theory for linear uncertain systems

For a class of linear discrete-time uncertain systems, a feedback feed-forward iterative learning control (ILC) scheme is proposed, which is comprised of an iterative learning controller and two current iteration feedback controllers. The iterative learning controller is used to improve the performance along the iteration direction and the feedback controllers are used to improve the performance along the time direction. First of all, the uncertain feedback feed-forward ILC system is presented by an uncertain two-dimensional Roesser model system. Then, two robust control schemes are proposed. One can ensure that the feedback feed-forward ILC system is bounded-input bounded-output stable along time direction, and the other can ensure that the feedback feed-forward ILC system is asymptotically stable along time direction. Both schemes can guarantee the system is robust monotonically convergent along the iteration direction. Third, the robust convergent sufficient conditions are given, which contains a linear matrix inequality (LMI). Moreover, the LMI can be used to determine the gain matrix of the feedback feed-forward iterative learning controller. Finally, the simulation results are presented to demonstrate the effectiveness of the proposed schemes.     

Robust design of integrated feedback and iterative learning control of a batch process based on a 2D Roesser system

To improve stability and convergence, feedback control is often incorporated with iterative learning control (ILC), resulting in feedback feed-forward ILC (FFILC). In this paper, a general form of FFILC is studied, comprising of two feedback controllers, a state feedback controller and a tracking error compensator, for the robustness and convergence along time direction, and an ILC for performance along the cycle direction. The integrated design of this FFILC scheme is transformed into a robust control problem of an uncertain 2D Roesser system. To describe the stability and convergence quantitatively along the time and the cycle direction, the concepts of robust stability and convergence along the two axes are introduced. A series of algorithms are established for the FFILC design. These algorithms allow the designer to balance and choose optimization objectives to meet the FFILC performance requirements. The applications to injection molding velocity control show the good effectiveness and feasibility of the proposed design methods.     

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.     

Sampled‐data iterative learning control for continuous‐time nonlinear systems with iteration‐varying lengths

In this work, sampled‐data iterative learning control (ILC) method is extended to a class of continuous‐time nonlinear systems with iteration‐varying trial lengths. In order to propose a unified ILC algorithm, the tracking errors will be redefined when the trial length is shorter or longer than the desired one. Based on the modified tracking errors, 2 sampled‐data ILC schemes are proposed to handle the randomly varying trial lengths. Sufficient conditions are derived rigorously to guarantee the convergence of the nonlinear system at each sampling instant. To verify the effectiveness of the proposed ILC laws, simulations for a nonlinear system are performed. The simulation results show that if the sampling period is set to be small enough, the convergence of the learning algorithms can be achieved as the iteration number increases.     

Quasi-Newton-type optimized iterative learning control for discrete linear time invariant systems

In this paper, a quasi-Newton-type optimized iterative learning control (ILC) algorithm is investigated for a class of discrete linear time-invariant systems. The proposed learning algorithm is to update the learning gain matrix by a quasi-Newton-type matrix instead of the inversion of the plant. By means of the mathematical inductive method, the monotone convergence of the proposed algorithm is analyzed, which shows that the tracking error monotonously converges to zero after a finite number of iterations. Compared with the existing optimized ILC algorithms, due to the superlinear convergence of quasi-Newton method, the proposed learning law operates with a faster convergent rate and is robust to the ill-condition of the system model, and thus owns a wide range of applications. Numerical simulations demonstrate the validity and effectiveness.