Xiao-Dong Li

2-D system theory based iterative learning control for linear continuous systems with time delays

This paper presents two-dimensional (2-D) system theory based iterative learning control (ILC) methods for linear continuous multivariable systems with time delays in state or with time delays in input. Necessary and sufficient conditions are given for convergence of the proposed ILC rules. In this paper, we demonstrate that the 2-D linear continuous-discrete Roessers model can be applied to describe the ILC process of linear continuous time-delay systems. Three numerical examples are used to illustrate the effectiveness of the proposed ILC methods.

Approximation of dynamical time-variant systems by continuous-time recurrent neural networks

This paper studies the approximation ability of continuous-time recurrent neural networks to dynamical time-variant systems. It proves that any finite time trajectory of a given dynamical time-variant system can be approximated by the internal state of a continuous-time recurrent neural network. Given several special forms of dynamical time-variant systems or trajectories, this paper shows that they can all be approximately realized by the internal state of a simple recurrent neural network.

A real-time learning control approach for nonlinear continuous-time system using recurrent neural networks

In this paper, a real-time iterative learning control (ILC) approach for a nonlinear continuous-time system using recurrent neural networks (RNNs) with time-varying weights is presented. Two RNNs are utilized in the ILC system. One is used to approximate the nonlinear system and another is used to mimic the desired system response. The ILC rule is obtained by combining the two RNNs to form a neural network control system. Also, a kind of iterative RNNs training algorithm is developed based on the two-dimensional (2-D) system theory. An RNN using the proposed 2-D training algorithm is able to approximate any trajectory to a very high degree of accuracy. Simulation results show that the proposed ILC approach is very efficient. The newly developed 2-D RNNs training algorithms provides a new dimension to the application of RNNs in a nonlinear continuous-time system.

Modeling of continuous time dynamical systems with input by recurrent neural networks

This paper proves that any finite time trajectory of a given n-dimensional dynamical continuous system with input can be approximated by the internal state of the output units of a continuous time recurrent neural network (RNN). The proof is based on the idea of embedding the n-dimensional dynamical system into a higher dimensional one. As a result, we are able to confirm that any continuous dynamical system can be modeled by an RNN.

Iterative learning control for a class of nonlinear discrete-time systems with multiple input delays

This article, addresses the robust iterative learning control (ILC) problem for nonlinear discrete time-delay systems. The derivation of convergence and robustness for the proposed ILC rule is based on two-dimensional (2D) linear inequalities. For a class of nonlinear discrete-time systems with multiple input delays, it is shown that the ILC tracking errors are bounded in the presence of state, output disturbances and initial state uncertainty. As these disturbances and uncertainty satisfy required conditions, the ILC tracking errors even can be driven to zero. Two numerical examples are used to validate the proposed ILC method.

Adaptive iterative learning control of non-linear MIMO continuous systems with iteration-varying initial error and reference trajectory

In this article, an adaptive iterative learning control (ILC) approach is presented to deal with a class of non-linear multi-input multi-output (MIMO) continuous systems with parametric uncertainty. Unlike general ILC techniques, the proposed adaptive ILC approach allows that both the initial error and the reference trajectory are iteration-varying in the ILC process. The designed ILC tracking strategy is to set out a very small initial time interval, and track the iteration-varying reference trajectory beyond the initial time interval. The reference trajectory tracking error beyond the initial time interval can be driven to zero. While the proposed adaptive ILC technique is applied to the repetitive learning control of non-linear MIMO continuous systems, a complete reference trajectory tracking over the whole time interval can be achieved.

Repetitive Learning Control of Nonlinear Continuous-Time Systems Using Quasi-Sliding Mode

In this brief, a quasi-sliding mode (QSM)-based repetitive learning control (RLC) method is proposed for tackling multi-input multi-output nonlinear continuous-time systems with matching perturbations. The proposed RLC method is able to perform rejection of periodic exogenous disturbances as well as tracking of periodic reference trajectories. It ensures a robust system stability when it is subject to nonperiodic uncertainties and disturbances. In this brief, an application to a robotic manipulator is used to illustrate the performance of the proposed QSM-based RLC method. A comparative study with the conventional variable structure control (VSC) technique is also included

Double-regularization approach for blind restoration of multichannel imagery

In this paper, a double-regularization (DR) approach is proposed to perform blind multichannel imagery restoration. The proposed DR approach effectively utilizes the smoothness property of image planes and blur operators. The correlations between different image planes are considered in the blind restoration process. The proposed approach minimizes a cost function that consists of a restoration error measure about each image plane and two regularization terms. The conjugate gradient type alternative-minimization (AM) strategy is derived to minimize the cost function. The developed AM strategy is simple and effective. Excellent results were obtained. The proposed approach provides a new dimension for the blind restoration of the multichannel imagery.

Further results on iterative learning control with convergence conditions for linear time-variant discrete systems

This article is concerned with some further results on iterative learning control (ILC) algorithms with convergence conditions for linear time-variant discrete systems. By converting two-Dimensional (2-D) ILC process of the linear time-variant discrete systems into 1-D linear time-invariant discrete systems, this article presents convergent ILC algorithms with necessary and sufficient conditions for two classes of linear time-variant discrete systems. Main results in (Li, X.-D., Ho, J.K.L., and Chow, T.W.S. (2005), ‘Iterative Learning Control for Linear Time-variant Discrete Systems Based on 2-D System Theory’, IEE Proceedings, Control Theory and Applications, 152, 13–18 and Huang, S.N., Tan, K.K., and Lee, T.H. (2002), ‘Necessary and Sufficient Condition for Convergence of Iterative Learning Algorithm’, Automatica 38, 1257–1260) are extended and generalised.

Brief paper: Quasi-sliding mode based repetitive control for nonlinear continuous-time systems with rejection of periodic disturbances

A Quasi-Sliding Mode (QSM) based tracking control method for tackling Multiple-Input Multiple-Output (MIMO) nonlinear continuous-time systems with un-matching system uncertainties and exogenous disturbances is proposed. The presented Repetitive Control (RC) scheme ensures robust system stability when the system is subject to non-periodic uncertainties and exogenous disturbances. The complete rejection of periodic exogenous disturbances and a perfect tracking of non-periodic reference trajectories are achievable. In this paper, a practical application to a mass-spring-damper system is used to illustrate the validity of the proposed QSM based RC method.