Iterative Learning Control Analysis Based on Hopfield Neural Networks

This paper presents iterative learning control (ILC) based on two-dimensional (2D) system theory for singular linear continuous-time systems. It is shown that the singular 2D linear continuous-discrete Roesser's model can be applied to describe the ILC process of singular linear continuous-time systems. Necessary and sufficient conditions are given for impulse-free convergence of the proposed ILC rules. Eventually, two numerical examples are given in order to show the results investigated.

This paper is concerned with the variable initial states problem in iterative learning control (ILC) for linear continuous systems. Firstly, the properties of the trajectory of 2-D continuous-discrete Roesser model are analyzed by using Lyapunov's method. Then, for any variable initial states which absolutely converge to the desired initial state, some sufficient conditions in the form of linear matrix inequalities (LMI) are given to ensure the convergence of the PD-type ILC rules. It implies that the ILC rules can be used to achieve the perfect tacking for variable initial states, even if the system dynamic is unknown. Finally, two numerical examples are given to illustrate the perfect tracking performance with exponentially convergent initial states.

The repetitive processing and large quantity of single product represented by 3C products are urgently needed. However, for current processing operations, previous processing data have not been used in the optimization of control input. In order to utilize previous processing data to facilitate the next process and avoid adverse effects caused by repetitive disturbance and noise, the idea of iterative learning was introduced to improve the accuracy of machining. On the control level, since it is difficult to obtain high accuracy by traditional feedback control when faced with complex trajectories, an open-loop iterative learning controller and a position loop feedback controller were introduced, which worked fast with good convergence effects. Aiming at reducing the influence of accidental error, step type iterative learning was put forward. The iteration mechanism was stopped when the accuracy converged to the allowable range so as to reduce computational complexity, store the current iterative part of the control input, and make constant value compensation. However, in simulation and experiment, it was found that after superposition of the iterative learning controller, the phenomenon of partial divergence of the system tracking error occurred. Therefore, the speed and acceleration characteristics of input trajectories in time domain and frequency domain were analyzed. High-frequency noise was introduced in frequency domain, which was found to be the cause of the abovementioned phenomenon, and high-frequency components were filtered to solve the problem. To further improve the accuracy of convergence and avoid filtering effective high-frequency information in some area, a switchable filter based on the analysis of the frequency characteristics of input trajectory was proposed. Through SIMULINK simulation and dSPACE experimental verification, it was proved that the iterative learning controller of modifying controlled quantity and filter based iterative learning control method are effective.

This work presents a two-dimensional (2-D) system theory based iterative learning control (ILC) method for linear continuous-time multivariable systems. We demonstrate that a 2-D continuous-discrete model can be successfully applied to describe both the dynamics of the control system and the behavior of the learning process. We successfully exploited the 2-D continuous-discrete Roesser's linear model by extending the ILC technique from discrete control systems to continuous control systems. Three learning rules for ILC are derived. Necessary and sufficient conditions are given for convergence of the proposed learning rules. Compared to the learning rule suggested by Arimoto et al. (1984), our developed learning rules are less restrictive and have wider applications. The third learning rule proposed ensures the reference output trajectory can be accurately tracked after only one learning trial. Three numerical examples are used to illustrate the proposed control procedures.

Iterative learning control design for linear discrete-time systems with multiple high-order internal models

This paper considers the problem of iterative learning control design for linear systems with data quantization. It is assumed that the control input update signals are quantized before they are transmitted to the iterative learning controller. A logarithmic quantizer is used to decode the signal with a number of quantization levels. Then, a 2‐D Roesser model is established to describe the entire dynamics of the iterative learning control (ILC) system. By using the sector bound method, a sufficient asymptotic stability condition for such a 2‐D system is established and then the ILC design is given simultaneously. The result is also extended to more general cases where the system matrices contain uncertain parameters. The effectiveness of the proposed method is illustrated by a numerical example.

A Robust Iterative Learning Control with Neural Networks for Robot

In order to improve the convergence speed of iterative learning control and reduce the fluctuation of the system error, a class of linear steady-state systems is considered. The convergence of the algorithm and error fluctuations are studied by introducing the variable-gain idea into the D-type iterative learning control algorithm with variable forgetting factor. According to the related properties of the λ norm theory, the convergence of the improved iterative learning algorithm is proved. Compared with iterative learning control with forgetting factor and iterative learning control with variable gain, MATLAB simulation analysis is performed. The simulation results show that the algorithm is effective. The improved iterative learning law not only makes the iterative error smoother, but also improves the convergence speed.

A novel design strategy for iterative learning and repetitive controllers of systems with a high modal density: Theoretical background

While iterative learning control (ILC) and repetitive control (RC) have much ground in common, they fundamentally differ in the initial conditions at each repetition. This difference has lead to distinct analysis techniques, hereby clouding the interrelations between both control strategies. To facilitate the transfer of results, this paper presents a unified approach to ILC and RC. Both control problems are formulated in the trial domain using so-called system lifting. For a given system, the corresponding ILC and RC trial-domain models differ, and a thorough system theoretic analysis and comparison of these models is performed. To illustrate the value of a unified formulation of ILC and RC, the analysis of the most commonly used ILC and RC structures is harmonized. This analysis reveals central differences and similarities between various stability, monotonic convergence and steady-state performance conditions.

In this paper, a new iterative learning algorithm is proposed for repetitive nonlinear systems. The control system employs a combination of state feedback and iterative learning control (ILC) in which the coefficients of states are learned similar to ILC methods. The control system is in a closed loop format both in iteration domain (because of ILC) and in time domain (because of feedback control) which improves the robustness of the conventional ILC. The convergence of the control algorithm is also proved. Finally, simulation results for a 5-DOF manipulator have been presented to illustrate that the proposed algorithm is more robust than a first order P type ILC method at the presence of white Gaussian noise as a nonrepeating disturbance.

This paper addresses the design and experimental characterization of a novel hybrid neural network, in which two distinct classical architectures interact: the Hopfield neural network and the Multi-Layer Perceptron. This hybrid neural system, named MLP+H (from MLP + Hopfield), presents a better performance than each one of the two classical architectures when considered in separate. In addition, it has the ability to deal with different classes of data than that normally allowed by the two conventional architectures. For example, while the Hopfield networks deal with binary patterns and the MLPs with information that always have some analog characteristics (due to the continuous nature of the MLP nodes), the MLP+H deals with analog inputs and purely digital outputs. Moreover, the MLP+H allows reduced training times when compared with the MLP architecture, also presenting compactness and flexibility in dealing with different applications, as implementation of anti-noise filters, an application currently under study.KeywordsConfusion MatrixInput PatternAnalog InputOutput PatternHybrid NetworkThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In 1984 Hopfield showed that the time evolution of a symmetric Hopfield neural networks are a motion in state space that seeks out minima in the energy function (i.e., equilibrium point set of Hopfield neural networks). Because high-order Hopfield neural networks have more extensive applications than Hopfield neural networks, and have been discussed on the convergence of the networks. In practice, a neural network is often subject to environmental noise. It is therefore useful and interesting to find out whether the high-order neural network system still approacher some limit set under stochastic perturbation. In this paper, we will give a number of useful bounds for the noise intensity under which the stochastic high-order neural network will approach its limit set. Our result cancels the requirement of symmetry of the connection weight matrix and includes the classic result on Hopfield neural networks, which is a special case of stochastic high-order Hopfield neural networks. In the end, A example is given to verify the effective of our results.

This work focuses on the model-free iterative learning control (ILC) design with good transient performance and fast convergence rate that is employed for precision control of a wafter stage. First, the experimental setup, the mathematical model, and the desired reference are introduced. Notice that the desired reference and its internal model (IM) are known in advance. Then, based on the internal model principle (IMP), a new ILC scheme, named as 1M-based ILC, is proposed by incorporating the 1M of the reference. The proposed 1M-based ILC is model-free, that is, independent on the system model of the controlled plant. The 1M -based ILC is carefully constructed to track the reference along the time axis while tracking/rejecting repetitive variations along the iteration axis. Precisely because of the tracking capability along the time axis in every iteration, the 1M-based ILC can achieve satisfactory performance even in the 0th iteration and improve the transient performance and the convergence speed. In addition, the 2-D $H_{\infty}$ theory is used to establish the design criterion for the 1M-based ILC. Finally, in the experiments, the efficiency of the 1M-based ILC is illustrated by comparing with a P-type ILC and a model-based one.

The Boolean Satisfiability Problem (BSAT) is one of the most important decision problems in mathematical logic and computational sciences for determining whether or not a solution to a Boolean formula.. Hopfield neural network (HNN) is one of the major type artificial neural network (NN) popularly known for it used in solving various optimization and decision problems based on its energy minimization machinism. The existing models that incorporate standalone network projected non-versatile framework as fundamental Hopfield type of neural network (HNN) employs random search in its training stages and sometimes get trapped at local optimal solution. In this study, Ants Colony Optimzation Algorithm (ACO) as a novel variant of probabilistic metaheuristic algorithm (MA) inspired by the behavior of real Ants, has been incorporated in the training phase of Hopfield types of the neural network (HNN) to accelerate the training process for Random Boolean kSatisfiability reverse analysis (RANkSATRA) based for logic mining. The proposed hybrid model has been evaluated according to robustness and accuracy of the induced logic obtained based on the agricultural soil fertility data set (ASFDS). Based on the experimental simulation results, it reveals that the ACO can effectively work with the Hopfield type of neural network (HNN) for Random 3 Satisfiability Reverse Analysis with 87.5 % classification accuracy