Precise Tracking for Continuous‐Time Non‐Minimum Phase Systems

Stable inversion based precise tracking for continuous‐time square or nonsquare non‐minimum phase systems is studied. However, high precision trajectory tracking of non‐minimum phase systems can be obtained by the stable inversion method but requiring large enough extended time interval. In order to solve this problem of large extended time restriction, a novel approach to precise trajectory tracking of non‐minimum phase systems is proposed, it is called the improved stable inversion (ISI) method, using an optimal integration of the pre‐actuation and the optimal state transition (OST) techniques. The ISI method can obtain precise trajectory tracking with a smaller extended time interval as compared to the stable inversion method. The proposed method achieves better validation through numerical simulations for the non‐minimum phase system.     

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.     

Improved D‐Type Anticipatory Iterative Learning Control for a Class of Inhomogeneous Heat Equations

This paper aims at providing a practical iterative learning control (ILC) scheme for a wide class of heat transfer systems in the sense that it avoids high‐gain learning of ILC, thus a potential non‐monotonic convergence issue, and the risk of violating the hardware limitation of input profile in implementation. Meanwhile, the ILC scheme guarantees the identical initial condition of heat process. As a result, the output tracking precision may be improved while not reducing the anticipatory step size as in 1 . All the benefits of the proposed ILC scheme are achieved by applying a heuristic selection algorithm for the anticipatory step size and rectifying the output reference simultaneously.     

ILC for non-minimum phase system

In this paper we propose a design method of an iterative learning controller (ILC) for a non-minimum phase (NMP) system by model-matching theory. The ILC consists of two learning filters acting on both the previous input signal and the previous error signal. To design the learning filters, we convert the convergence condition of the ILC into the model-matching problem and get the stable and proper learning filter by solving the Nevanlinna's algorithm. To show the usefulness of the proposed algorithm, some design examples are included.     

A homotopy method for exact output tracking of some non‐minimum phase nonlinear control systems

This paper presents a method for non‐causal exact dynamic inversion for a class of non‐minimum phase nonlinear systems, which seems to be an alternative to those existing in the literature. This method is based on a homotopy procedure that allows to find a ‘small’ periodic solution of a desired equation by a continuous deformation of a known periodic solution of a simpler auxiliary system. This method allows to face the exact output tracking problem for some non‐minimum phase systems that are well known in the literature, such as the inverted pendulum, the motorcycle and the CTOL aircraft. Copyright © 2008 John Wiley & Sons, Ltd.     

Formation control for multi‐agent systems through an iterative learning design approach

This paper deals with formation control problems for multi‐agent systems by using iterative learning control (ILC) design approaches. Distributed formation ILC algorithms are presented to enable all agents in directed graphs to achieve the desired relative formations perfectly over a finite‐time interval. It is shown that not only asymptotic stability but also monotonic convergence of multi‐agent formation ILC can be accomplished, and the convergence conditions in terms of linear matrix inequalities can be simultaneously established. The derived results are also applicable to multi‐agent systems that are subject to stochastic disturbances and model uncertainties. Furthermore, the feasibility of convergence conditions and the effect of communication delays are discussed for the proposed multi‐agent formation ILC algorithms. Simulation results are given for uncertain multi‐agent systems to verify the theoretical study. Copyright © 2012 John Wiley & Sons, Ltd.     

Identification based adaptive iterative learning controller

In recent years, more research in the control field has been in the area of self‐learning and adaptable systems, such as a robot that can teach itself to improve its performance. One of the more promising algorithms for self‐learning control systems is Iterative Learning Control (ILC), which is an algorithm capable of tracking a desired trajectory within a specified error limit. Conventional ILC algorithms have the problem of relatively slow convergence rate and adaptability. This paper suggests a novel approach by combining system identification techniques with the proposed ILC approach to overcome the aforementioned problems. The ensuing design procedure is explained and results are accrued from a number of simulation examples. A key point in the proposed scheme is the computation of gain matrices using the steepest descent approach. It has been found that the learning rule can be guaranteed to converge if certain conditions are satisfied. Copyright © 2010 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

基于稳定逆的非最小相位系统的迭代学习控制

针对迭代学习控制在非最小相位系统上应用效果差的缺点,根据最优化性能指标和非因果的稳定逆理论,提出了一种基于稳定逆的最优开闭环综合迭代学习控制,分析了学习律的收敛性并给出了此种非因果的学习律在实际应用中的运用方式.     

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     

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.     

非最小相位系统的基函数型自适应迭代学习控制

针对重复运行的未知非最小相位系统的轨迹跟踪问题, 结合时域稳定逆特点, 提出了一种新的基函数型自适应迭代学习控制(Basis function based adaptive iterative learning control, BFAILC)算法. 该算法在迭代控制过程中应用自适应迭代学习辨识算法估计基函数模型, 采用伪逆型学习律逼近系统的稳定逆, 保证了迭代学习控制的收敛性和鲁棒性. 以傅里叶基函数为例, 通过在非最小相位系统上的控制仿真, 验证了算法的有效性.     

测量数据丢失的一类非线性系统迭代学习控制

迭代学习控制方法应用于网络控制系统时,由于通信网络的约束导致数据包丢失现象经常发生.针对存在输出测量数据丢失的一类非线性系统,研究P型迭代学习控制算法的收敛性问题.将数据丢失描述为一个概率已知的随机伯努利过程,在此基础上给出P型迭代学习控制算法的收敛条件,理论上证明了算法的收敛性,并通过仿真验证理论结果.研究表明,当非线性系统存在输出测量数据丢失时,迭代学习控制算法仍然可以保证跟踪误差的收敛性.     

Global convergence for adaptive one-step-ahead optimal controllers based on input matching

This paper establishes global convergence for adaptive one-step-ahead optimal controllers applied to a class of linear discrete time single-input single-output systems. The class of systems includes all stable systems whether they are minimum phase or not, all minimum phase systems whether they are stable or not, and some unstable nonminimum phase systems. The key substantive assumption is that the one-step-ahead optimal controller designed using the true system parameters leads to a stable closed-loop system. Subject to this natural restriction, it is shown that a simple adaptive control algorithm based on input matching is globally convergent in the sense that the system inputs and outputs remain bounded for all time and the input converges to the one-step-ahead optimal input. Both deterministic and stochastic cases are treated.     

Combined inverse and gradient iterative learning control: performance,monotonicity, robustness and non‐minimum‐phase zeros

Based on recent papers that have demonstrated that robust iterative learning control can be based on parameter optimization using either the inverse plant or gradient concepts, this paper presents a unification of these ideas for discrete‐time systems that not only retains the convergence properties and the robustness properties derived in previous papers but also permits the inclusion of filters in the input update formula and a detailed analysis of the effect of non‐minimum‐phase dynamics on algorithm performance in terms of a ‘plateauing’ or ‘flat‐lining’ effect in the error norm evolution. Although the analysis is in the time domain, the robustness conditions are expressed as frequency domain inequalities. The special case of a version of the inverse algorithm that can be used to construct a robust stable anti‐causal inverse non‐minimum‐phase plant is presented and analysed in detail. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

A non-standard iterative learning control approach to tracking periodic signals in discrete-time non-linear systems

In this paper we use the formalism of iterative learning control (ILC) to solve the repetitive control problem of forcing a system to track a prescribed periodic reference signal. Although the systems we consider operate continuously in time, rather than with trials that have distinct starting and ending times, we use the ILC approach by defining a 'trial' in terms of completion of a single 'period' of the output trajectory, where a period is an interval from the start of the trial until the system returns to its initial state. The ILC scheme we develop does not use the standard assumption of uniform trial length. In the final result the periodic motion is achieved by 'repetition' of the learned ILC input signal for a single period. Analysis of the convergence of the algorithm uses an intermediate convergence result for the typical ILC problem. This intermediate result is based on a multi-loop control interpretation of the signal flow in ILC. The idea is demonstrated on an example and it is noted that it may be possible to generalize the ideas to broader classes of systems and ILC algorithms.     

Adaptive fuzzy ILC of nonlinear discrete-time systems with unknown dead zones and control directions

This paper presents an adaptive fuzzy iterative learning control (ILC) design for non-parametrized nonlinear discrete-time systems with unknown input dead zones and control directions. In the proposed adaptive fuzzy ILC algorithm, a fuzzy logic system (FLS) is used to approximate the desired control signal, and an additional adaptive mechanism is designed to compensate for the unknown input dead zone. In dealing with the unknown control direction of the nonlinear discrete-time system, a discrete Nussbaum gain technique is exploited along the iteration axis and applied to the adaptive fuzzy ILC algorithm. As a result, it is proved that the proposed adaptive fuzzy ILC scheme can drive the ILC tracking errors beyond the initial time instants into a tunable residual set as iteration number goes to infinity, and keep all the system signals bounded in the adaptive ILC process. Finally, a simulation example is used to demonstrate the feasibility and effectiveness of the adaptive fuzzy ILC scheme.     

Adaptive Fault‐Tolerant Control of Uncertain MIMO Systems with Reduced Requirement on Desired Trajectory Under Unknown Control Direction

This paper aims at investigating the tracking control problem for a class of multi‐input multi‐output (MIMO) nonlinear systems with non‐square control gain matrix subject to unknown control direction and uncertain desired trajectory. By using the artificial neural network (NN) reconstructs the target trajectory with actual disguised trajectory, we are able to design a practical and stable tracking control scheme without the need for the unavailable desired trajectory. Nussbaum‐type function is incorporated in the control law to handle the unknown control direction. The remarkable feature of the proposed scheme is that it is robust against modeling uncertainties and tolerant to actuation faults, yet guarantees that the closed‐loop system is stable in the sense of ultimately uniformly bounded (UUB). The effectiveness of the proposed control schemes are illustrated through simulation results.     

非最小相位系统的扩展Laguerre基函数迭代学习控制

针对非最小相位系统的跟踪问题,提出了一种新的基函数迭代学习控制算法.该算法利用新型的非因果Laguerre扩展基函数逼近系统逆传递函数,设计最优迭代学习律使系统输入收敛到系统的稳定逆,保证了控制性能.算法不依赖于系统的先验模型,仅需以基函数信号作为系统输入进行模型辨识,减少了模型不确定性的影响.通过对单连杆柔性机械臂这样的典型非最小相位系统跟踪问题的仿真,验证了该方法的良好效果.     

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.