Multivariable norm optimal iterative learning control with auxiliary optimisation

The paper describes a substantial extension of norm optimal iterative learning control (NOILC) that permits tracking of a class of finite dimensional reference signals whilst simultaneously converging to the solution of a constrained quadratic optimisation problem. The theory is presented in a general functional analytical framework using operators between chosen real Hilbert spaces. This is applied to solve problems in continuous time where tracking is only required at selected intermediate points of the time interval but, simultaneously, the solution is required to minimise a specified quadratic objective function of the input signals and chosen auxiliary (state) variables. Applications to the discrete time case, including the case of multi-rate sampling, are also summarised. The algorithms are motivated by practical need and provide a methodology for reducing undesirable effects such as payload spillage, vibration tendencies and actuator wear whilst maintaining the desired tracking accuracy necessary for task completion. Solutions in terms of NOILC methodologies involving both feedforward and feedback components offer the possibilities of greater robustness than purely feedforward actions. Results describing the inherent robustness of the feedforward implementation are presented and the work is illustrated by experimental results from a robotic manipulator.     

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.     

An iterative approach to the optimal co-design of linear control systems

This paper investigates the optimal co-design of both physical plants and control policies for a class of continuous-time linear control systems. The optimal co-design of a specific linear control system is commonly formulated as a nonlinear non-convex optimisation problem (NNOP), and solved by using iterative techniques, where the plant parameters and the control policy are updated iteratively and alternately. This paper proposes a novel iterative approach to solve the NNOP, where the plant parameters are updated by solving a standard semi-definite programming problem, with non-convexity no longer involved. The proposed system design is generally less conservative in terms of the system performance compared to the conventional system-equivalence-based design, albeit the range of applicability is slightly reduced. A practical optimisation algorithm is proposed to compute a sub-optimal solution ensuring the system stability, and the convergence of the algorithm is established. The effectiveness of the proposed algorithm is illustrated by its application to the optimal co-design of a physical load positioning system.     

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.     

A computationally efficient norm optimal iterative learning control approach for LTV systems

This paper proposes a computationally efficient iterative learning control (ILC) approach termed non-lifted norm optimal ILC (N-NOILC). The objective is to remove the computational complexity issues of previous 2-norm optimal ILC approaches, which are based on lifted system techniques, while retaining the iteration domain convergence properties. The computational complexity needed to implement the proposed method scales linearly with the trial length. Therefore, the approach can be implemented on controlled processes having long trial durations and high sampling rates. Robustness is accomplished by adding a penalty term on the control input in the cost function. Simulations are presented to verify and validate the features of the proposed method.     

Basis functions and parameter optimisation in high-order iterative learning control

In this paper a new parameter-optimal high-order Iterative Learning Control (ILC) algorithms is proposed to extend the work of Owens and Feng [Parameter optimisation in iterative learning control. International Journal of Control 14(11), 1059-1069]. If the original plant is positive, this new algorithm will result in convergent learning where the convergence is monotonic to zero tracking error. If the original plant is not positive, it can be shown that by adding a suitable set of basis functions into the algorithm, the tracking error will again converge monotonically to zero. This provides a considerable improvement to earlier work on parameter-optimal ILC as it opens up the possibility of globally convergent algorithms for any linear plant G. The number of parameters needed to ensure convergence could, however, become large. The paper shows that the use of low-order parameterisations is capable of achieving much of the benefit achieved in the ‘ideal’ case.     

Accelerated norm-optimal iterative learning control algorithms using successive projection

This article proposes a novel technique for accelerating the convergence of the previously published norm-optimal iterative learning control (NOILC) methodology. The basis of the results is a formal proof of an observation made by D.H. Owens, namely that the NOILC algorithm is equivalent to a successive projection algorithm between linear varieties in a suitable product Hilbert space. This leads to two proposed accelerated algorithms together with well-defined convergence properties. The results show that the proposed accelerated algorithms are capable of ensuring monotonic error norm reductions and can outperform NOILC by more rapid reductions in error norm from iteration to iteration. In particular, examples indicate that the approach can improve the performance of NOILC for the problematic case of non-minimum phase systems. Realisation of the algorithms is discussed and numerical simulations are provided for comparative purposes and to demonstrate the numerical performance and effectiveness of the proposed methods.     

迭代学习在PID控制中的应用

利用迭代学习过程记忆的期望控制、期望轨迹以及跟踪误差,提出了拟合控制系统的PID控制器参数的方法。用这种方法实现的PID控制器结构简单,作用于系统可获得较佳的动态特性和较强的鲁棒性。仿真实例表明了这种方法具有很好的可行性和实用性。     

Neural network control of multivariable processes with a fast optimisation algorithm

A radial basis function (RBF) neural network model based predictive control scheme is developed for multivariable nonlinear systems in this paper. A fast convergence algorithm is proposed and employed in multidimensional optimisation in the control scheme to reduce the computing time and save required computer memory. The scheme is applied to a simulated two-input two-output nonlinear process for set-point tracking control. Simulation results demonstrate the effectiveness of the control strategy and the fast learning algorithm for multivariable non-linear processes. Comparison of the performance with PID control is included.     

An approach to multivariable system identification

Two prototype identifiable structures are presented which make possible the identification via an equation-error model reference adaptive system of linear plants with rational transfer function matrices. The structures include as specialisations many of the particular structures presented hitherto in the literature. Convergence properties are also discussed, and several modes of convergence are distinguished: model output to plant output, model transfer function matrix to plant transfer function matrix, and model parameters to plant parameters. Conditions are presented for exponentially fast convergence in the absence of noise.     

Networked iterative learning control approach for nonlinear systems with random communication delay

This paper constructs a proportional-type networked iterative learning control (NILC) scheme for a class of discrete-time nonlinear systems with the stochastic data communication delay within one operation duration and being subject to Bernoulli-type distribution. In the scheme, the communication delayed data is replaced by successfully captured one at the concurrent sampling moment of the latest iteration. The tracking performance of the addressed NILC algorithm is analysed by statistic technique in virtue of mathematical expectation. The analysis shows that, under certain conditions, the expectation of the tracking error measured in the form of 1-norm is asymptotically convergent to zero. Numerical experiments are carried out to illustrate the validity and effectiveness.     

Robust iterative learning control for linear systems with multiple time-invariant parametric uncertainties

This article presents a novel robust iterative learning control algorithm (ILC) for linear systems in the presence of multiple time-invariant parametric uncertainties.The robust design problem is formulated as a min–max problem with a quadratic performance criterion subject to constraints of the iterative control input update. Then, we propose a new methodology to find a sub-optimal solution of the min–max problem. By finding an upper bound of the worst-case performance, the min–max problem is relaxed to be a minimisation problem. Applying Lagrangian duality to this minimisation problem leads to a dual problem which can be reformulated as a convex optimisation problem over linear matrix inequalities (LMIs). An LMI-based ILC algorithm is given afterward and the convergence of the control input as well as the system error are proved. Finally, we apply the proposed ILC to a generic example and a distillation column. The numerical results reveal the effectiveness of the LMI-based algorithm.     

迭代学习控制的研究现状

迭代学习控制经历了二十多年的发展历程,已经取得了很多研究成果,现已成为智能控制的一个重要研究方向,并得到越来越广泛的应用.本文对迭代学习控制的基本原理和主要研究问题从发展的角度作了详细阐述,并对其应用作了细致介绍.     

基于未知高频增益的非线性系统自适应迭代学习控制

针对一类单输入单输出不确定非线性重复跟踪系统,提出一种基于完全未知高频反馈增益的自适应迭代学习控制.与普通迭代学习控制需要学习增益稳定性前提条件不同,自适应迭代学习控制通过不断修改Nussbaum形式的高频学习增益达到收敛.经证明当迭代次数i→∞时,重复跟踪误差可一致收敛到任意小界δ.仿真结果表明了该控制方法的有效性.     

基于混合灵敏度设计的鲁棒迭代学习控制

提出一种鲁棒迭代学习控制的设计方法．利用混合灵敏度设计方法,控制器满足一定鲁棒性条件时就可以直接获得收敛更新规则．此外,只要学习滤波函数满足一定条件,系统跟踪误差将显著降低．仿真结果表明该方法有效性较高．     

Robustification of iterative learning control and repetitive control by averaging

This paper describes a recently developed averaging technique to robustify iterative learning and repetitive controllers. The robustified controllers are found by minimising cost functions that are averaged over either multiple analytical time-domain models or experimental frequency-domain data. The aim is to produce a technique that is simple and general, and can be applied to any iterative learning control (ILC) or repetitive control (RC) design that involves the minimisation of a cost function. Substantial improvement in convergence to zero tracking error in the presence of model uncertainties has been observed for both ILC and RC by this averaging technique.     

Control of a pneumatic power active lower-limb orthosis with filter-based iterative learning control

A filter-based iterative learning control (FILC) scheme is developed in this paper, which consists in a proportional–derivative (PD) feedback controller and a feedforward filter. Moreover, based on two-dimensional system theory, the stability of the FILC system is proven. The design criteria for a wavelet transform filter (WTF) – chosen as the feedforward filter – and the PD feedback controller are also given. Finally, using a pneumatic power active lower-limb orthosis (PPALO) as the controlled plant, the wavelet-based iterative learning control (WILC) implementation and the orchestration of a trajectory tracking control simulation are given in detail and the overall tracking performance is validated.     

Analysis of boundary effects in iterative learning control

Boundary effects in iterative learning control (ILC) algorithms are considered in this article. ILC algorithms involve filtering of input and error signals over finite-time intervals, often using non-causal filters, and it is important that the boundary effects of the filtering operations are handled in an appropriate way. The topic is studied using both a proposed theoretical framework and simulations, and it is shown that the method for handling the boundary effects has impact on the stability and convergence properties of the ILC algorithm.     

Constrained point-to-point iterative learning control with experimental verification

Iterative learning control is a methodology applicable to systems which repeatedly track a specified reference trajectory defined over a finite time duration. Here the methodology is instead applied to the point-to-point motion control problem in which the output is only specified at a subset of time instants. The iterative learning framework is expanded to address this case, and conditions for convergence to zero point-to-point tracking error are derived. It is shown how the extra design freedom the point-to-point set-up brings allows additional input, output and state constraints to be simultaneously addressed, hence providing a powerful design framework of wide practical utility. Experimental results confirm the performance and accuracy that can be achieved, and the improvements gained over the standard ILC framework.