Learning Law Research Articles

Neural Network-Based Cooperative Identification for a Class of Unknown Nonlinear Systems via Event-Triggered Communication

In this paper, a neural network (NN)-based distributed cooperative identification strategy with event-triggered communication is studied for a group of coupled identical nonlinear systems. We develop a distributed cooperative learning law in the context of event-triggered communication, where an agent will transmit its NN weights to its neighbors only when its weight trigger error norm exceeds an exponentially decreasing threshold. It is proven that the estimated weights of all radial basis function NNs converge to a small neighborhood of their optimal values. Therefore, the unknown nonlinear function is approximated along the union of all the system trajectories. It is further proven that there exists a positive minimum interevent interval and Zeno behavior can be avoided. Finally, we give a simulation example to demonstrate these features.

Iterative Learning Scheme Based Sensor Fault Estimation for Nonlinear Repetitive System

Iterative learning scheme is proposed with the aim to achieve perfect tracking of a prescribed reference trajectory for systems that operate repetitively. In this paper, a sensor fault estimation framework is proposed for nonlinear repetitive system. First, the problem of sensor fault estimation is converted to actuator fault estimation via state redefinition. Afterward, state observer is designed for state reconstruction while iterative learning law is presented for fault estimation. Thus, the information in the previous period can be utilized to improve the fault estimating performance in current iterative trial. Avoiding the uncertainty caused by the norm optimal theory, the uniform convergence of error extended system is guaranteed by asymptotic stability and optimal function. Finally, the efficiency and merits of the proposed scheme are illustrated by numerical examples.

Improved Learning Experience Memristor Model and Application as Neural Network Synapse

This paper proposes a memristor model, named learning experience memristor (LEM), for using as synapse in the associative neural network. The properties of LEM are discussed under different external voltages. And then, we design a new feedback learning rule, all input feedback (AIF). An associative neural network-based the AIF law and LEM synapse is constructed and analyzed, and the associative neural network incorporates learning experience behavior, forgetting, and threshold functions. The properties of LEM are also verified through PSpice simulation. The associative neural network circuit based on AIF law and LEM are constructed and simulated using PSpice, the simulation results are analyzed sufficiently. Finally, different memristors are used as synapses in the associative neural network, and we analyze and compare the simulation results. All simulation results show that the associative neural network incorporating LEM synapses and AIF learning law exhibits good performance, mimicking biological neural networks, and self-learning behavior.

Adaptive Finite-Time Synchronization for Complex Dynamical Network with Different Dimensions of Nodes and Time-Varying Outer Coupling Structures

In this paper, we investigate finite-time synchronization problems of complex dynamical networks with different dimensions of nodes, which contain unknown periodically coupling structures and bounded time-varying delay. Based on finite-time stability theory, the inequality techniques, and the properties of Kronecker production of matrices, some useful finite-time synchronization criteria for complex dynamical network with unknown periodical couplings have been obtained. In addition, with proper adaptive periodical learning law designed, the unknown periodical couplings have been estimated successfully. Finally, some simulation examples are performed to verify the theoretical findings.

Stabilization and Synchronization of Uncertain Zhang System by Means of Robust Adaptive Control

Standard adaptive control is the preferred approach for stabilization and synchronization of chaotic systems when the structure of such systems is a priori known but the parameters are unknown. However, in the presence of unmodeled dynamics and/or disturbance, this approach is not effective anymore due to the drift of the parameter estimations, which eventually causes the instability of the closed-loop system. In this paper, a robustifying term, which consists of a saturation function, is used to avoid this problem. The robustifying term is added to the adaptive control law. Consequently, the learning law is also modified. The boundedness of the states and the parameter estimations is rigorously and thoroughly proven by means of Lyapunov like analysis based on Barbalat’s lemma. On these new conditions, the convergence to zero cannot be achieved due to the presence of unmodeled dynamics and/or disturbance. However, it is still possible to guarantee the asymptotic convergence to a bounded zone around zero. The width of this zone can be adjusted by the designer. The performance of this robust approach is verified by numerical simulations. Although, for simplicity, this strategy is only applied to the stabilization and synchronization of Zhang system, the procedure can easily be generalized to a broad class of chaotic systems.

Modeling of the temperature distribution of a greenhouse using finite element differential neural networks

Most of the existing works in the literature related to greenhouse modeling treat the temperature within a greenhouse as homogeneous. However, experimental data show that there exists a temperature spatial distribution within a greenhouse, and this gradient can produce different negative effects on the crop. Thus, the modeling of this distribution will allow to study the influence of particular climate conditions on the crop and to propose new temperature control schemes that take into account the spatial distribution of the temperature. In this work, a Finite Element Differential Neural Network (FE-DNN) is proposed to model a distributed parameter system with a measurable disturbance input. The learning laws for the FE-DNN are derived by means of Lyapunov's stability analysis and a bound for the identification error is obtained. The proposed neuro identifier is then employed to model the temperature distribution of a greenhouse prototype using data measured inside the greenhouse, and showing good results.

The case study in learning law

The present study is a reflection on the method of case study in learning law. To achieve this purpose we will discuss the traditional method and its limitations to the challenges of law in the era of globalization. We will emphasize the urgent need to implement the case study method in Portuguese law schools, as an instrument that enhances the active participation of the student, protagonist in the process of learning and knowledge acquisition. This study is justified today, especially the challenges triggered by the Bologna process, including the implication in the teaching, learning and assessment. The teacher is assumed as a supervisor of the learning process, calling for the autonomy of the student. It is intended that students develop critical thinking and be able to reflect on their own learning process. Therefore, the need to revise the traditional methodology here rooted in the teaching of law. A review of the literature will be carried out, which will seek to contextualize, at present, the reflexivity with the pedagogical objective. Use shall be a deductive reasoning, based on the general reality of teaching to learning the law, underlining the importance of the case study method for the development of didactic and pedagogical dimension. At the end of this tour we will be able to discern the extent of the right learning, seeking a methodological model capable of mobilizing students for their new role, participatory and critical. The current model of education should focus on learning and the use of teaching methods that are not limited to the learning, particularly the most active. The student should be able to participate and discuss the acquired knowledge in concrete contexts of social life.
 Keywords: education; teaching; case; method.

Output-based modeling of catalytic ozonation by differential neural networks with discontinuous learning law

The aim of this study was to develop an adaptive state estimator with discontinuous parameter adjustment law for the catalytic ozonation system. A nonlinear transformation defined an equivalent system presented in chain-of-integrators form with uncertain structure in the dynamics of the last state. A step-by-step state estimator using a sequence of super-twisting algorithms (STAs) estimated the unmeasured states of the uncertain system. A class of differential neural network (DNN) with discontinuous learning law served to estimate the uncertain section of the catalytic process. The learning method was developed by implementing a strong lower-semi-continuous Lyapunov function. The method used to generate the laws that adjusted the weights, also yields the estimation of the parameters included in the catalytic ozonation system. A set of numerical simulations demonstrated the application of the DNN-based state observer to solve the estimation of the non-measurable information in the catalytic ozonation system. The available output signal was the concentration of the ozone gas at the output of the reactor. This was the only information used by the observer. The state estimator with discontinuous learning laws was also evaluated with experimental information obtained by a catalytic ozonation system using NiO as catalyst and phtalic acid as model contaminant. The effect of aggregating the DNN in the observer structure was compared with the observer using only the sequence of STA. The superior performance of the observer developed in this study was confirmed by evaluating the mean square error of the identification error.

Iterative learning control for linear generalized distributed parameter system

In this paper, we use the iterative learning control algorithm to deal with generalized distributed parameter system with parabolic type which described by generalized partial differential equation. Because of the particularity of the generalized system, we usually need generalized value decomposition, but the algorithm we proposed in this paper does not need to consider the impulsive solution of the generalized system, so it can simplify the calculation process. A novel generalized theoretical result is presented by using the PD-type learning law under some assumptions. The convergence conditions of algorithm are established. By the basic generalized theory, matrix theory and mapping principle, the paper gives rigorous convergence proof of the algorithm to ensure the tracking error is convergent in L2 norm. Finally, we use an example to verify the validity of the new proposed algorithm. Through this paper, we can do further study and discuss the iterative learning algorithm for generalized distributer parameter system in the future.

Adaptive robust control for free-floating space robot with unknown uncertainty based on neural network

It is difficult to obtain a precise mathematical model of free-floating space robot for the uncertain factors, such as current measurement technology and external disturbance. Hence, a suitable solution would be an adaptive robust control method based on neural network is proposed for free-floating space robot. The dynamic model of free-floating space robot is established; a computed torque controller based on exact model is designed, and the controller can guarantee the stability of the system. However, in practice, the mathematical model of the system cannot be accurately obtained. Therefore, a neural network controller is proposed to approximate the unknown model in the system, so that the controller avoids dependence on mathematical models. The adaptive learning laws of weights are designed to realize online real-time adjustment. The adaptive robust controller is designed to suppress the external disturbance and compensate the approximation error and improve the robustness and control precision of the system. The stability of closed-loop system is proved based on Lyapunov theory. Simulations tests verify the effectiveness of the proposed control method and are of great significance to free-floating space robot.

Power Restoration Prediction Following Extreme Events and Disasters

This article examines electric power restoration following catastrophic damage in modern cities and regions due to extreme events and disasters. Recovery time and non-restoration probability are derived using new data from a comprehensive range of recent massive hurricanes, extensive wildfires, severe snowstorms, and damaging cyclones. Despite their totally disparate origins, over three orders of magnitude severe wildfires and hurricanes have the same non-restoration probability trends, which are of simple exponential form. The results fall into categories that are dependent on and grouped by the degree of damage and social disruption. The implications are discussed for emergency response planning. These new results demonstrate that the scientific laws of probability and human learning, which dominate risk in modern technologies and societies are also applicable to a wide range of disasters and extreme events.

Multi-lagged-input iterative dynamic linearization based data-driven adaptive iterative learning control

This article presents a multi-lagged-input based data-driven adaptive iterative learning control (M-DDAILC) method for nonlinear multiple-input-multiple-output (MIMO) systems by virtue of multi-lagged-input iterative dynamic linearization (IDL). The original nonlinear and non-affine MIMO system is equivalently transformed into a linear input-output incremental counterpart without loss of dynamics. The proposed learning law utilizes the desired trajectory to cancel the influence from iteration-by-iteration variations, as well as additional multi-lagged inputs to improve control performance. The developed iterative estimation law is more effective and also makes estimation of the unknown parameters easier because the dynamics for each parameter to represent are decreased by dividing the system into multiple components in the multi-lagged-input IDL formulation. Moreover, the proposed M-DDAILC does not need an explicit and accurate model. It is proved to be iteratively convergent with rigorous analysis. Both a numerical example and a practical application to a permanent magnet linear motor are provided to verify the validity and applicability of the proposed method.

Composite Energy Function-Based Spatial Iterative Learning Control in Motion Systems

In this brief, a novel spatial iterative learning control (ILC) method is proposed for a class of high-order nonlinear motion systems in the presence of both parametric and nonparametric uncertainties. Since the system performs the tracking task iteratively in the spatial domain and the uncertainties are functions of spatial coordinates, the traditional ILC that updates the control signals in the time domain is not applicable. The proposed spatial ILC aims at improving the system tracking performance by making full use of the spatial periodicity. First, the dynamics of the motion systems are converted from the temporal domain to the spatial domain via feedback linearization. Then, the learning law is designed to tackle the system uncertainties. By utilizing a newly defined space-based barrier composite energy function, the boundedness and the convergence of state tracking error are ensured rigorously. In the end, an illustrative example is shown to demonstrate the efficacy of the proposed ILC scheme.

Composite Learning Control of MIMO Systems With Applications

Considering the unknown dynamics of the multiple-input-multiple-output strict-feedback nonlinear systems, this paper proposed the neural composite learning control using the online recorded data. The control structure follows the back-stepping scheme, while neural networks (NNs) are employed for uncertainty approximation. Through the error dynamics analysis, the critical prediction error is constructed to indicate the performance of intelligent learning over the interval. Furthermore, the novel composite learning law is proposed for NN weights update. The stability of the closed-loop system is analyzed via the Lyapunov approach and the signals are guaranteed to be bounded. Through simulation test of two-input and two-output systems, the proposed controller can achieve better tracking performance, while with the composite learning algorithm, the NNs can efficiently approximate nonlinear functions. Similar conclusions are obtained on the control of the hypersonic reentry vehicle.

The Therapist as Conditioned Stimulus.

This manuscript is part of a special issue to commemorate professor Paul Eelen, who passed away on August 21, 2016. Paul was a clinically oriented scientist, for whom learning principles (Pavlovian or operant) were more than salivary responses and lever presses. His expertise in learning psychology and his enthusiasm to translate this knowledge to clinical practice inspired many inside and outside academia. Several of his original writings were in the Dutch language. Instead of editing a special issue with contributions of colleagues and friends, we decided to translate a selection of his manuscripts to English to allow wide access to his original insights and opinions. Even though the manuscripts were written more than two decades ago, their content is surprisingly contemporary. This manuscript was originally published in 1989 as part of an edited book on the therapeutic relation. In this chapter, Paul Eelen takes a critical position against the dominance of the client-centered approach. He presents the therapeutic relation as a behavioural interaction between the patient and his therapist which is subject to laws of learning. This is exemplified by an in-depth analysis of the therapist as a conditioned stimulus.First published as: Eelen, P., Depreeuw, E., & Van den Bergh, O. (1989). De therapeut als geconditioneerde stimulus. In H. Vertommen, G. Cluckers, & G. Lietaer (Eds.), De relatie in therapie (pp. 147–165). Leuven: Universitaire Pers Leuven.1

The world at their fingertips? The mental wellbeing of online distance-based law students

ABSTRACTIn recent years there has been an increased interest in student mental wellbeing within higher education. In terms of legal education, much of this has been focused upon the United States (US) and Australia, with a lack of United Kingdom (UK)-based empirical data available. Although there is now extensive provision of online distance learning options available to UK (and other) law students, there is a notable lack of research into the possible challenges which are specific to this form of tertiary offering. This paper seeks to contribute to the development of research in this area by reporting upon, and analysing, preliminary data gathered from an empirical study of the mental wellbeing of online distance learning law students.

Variable Gain Iterative Learning Control with Forgetting Factor

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.

Analysis of Regularity of Daily Performance and Final Grade

Grade is an important index to evaluate students' learning quality. It is very instructive to study the logical relation and regularity of daily performance, final grade and total grade for grasping student learning dynamics and determining the learning crowd of different levels. This paper uses the data of cloud class of financial management through regression analysis method to study the learning law of the three levels of people and gets a conclusion that students whose score less than 70 need to use cloud teaching platform for process learning and students whose score above 90 should improve the content and means of activities.

Pavlovian conditioning of social exploration in adult female rats

Social conditioned place preference (SCPP) studies show that the reward value of social interaction is amenable to the laws of associative learning, such that it becomes associated with the physical properties of the context. However, social interaction can be initiated and maintained by a variety of motivations, such as the exploration of a novel conspecific, aggression, mutual grooming and mating-like actions. In order to study whether social exploration is rewarding, we used a conventional Pavlovian conditioning procedure in which access to a restrained same-sex rat served as a reward. Three dependent variables in two experiments showed that the reward value of social exploration becomes conditioned to a transient cue, and it is also subject to extinction and spontaneous recovery. The results may help to elucidate the mixed results obtained with SCPP procedures.

The Need for Diversity in Teaching Law

Teaching law is normally depicted with students seated in a largelecture theatre with the professor in law who lectures in the traditionallecture method feeding students with the content of law. This content isfaithfully taken down by students as notes while trying to make sense ofthe professor’s lectures. This was the norm of teaching law some 20 yearsback during the author’s student time and still is the practice because thelecture method is the most efficient means to cover the vast subject contentof law. Furthermore, it is opined that it is easier to expound one’s viewsthan to ask penetrating questions which rarely provoke the activity oforiginal thinking. As such, law students are inundated with substantive andprocedural law. Little thought is given to the learning process. The corpusof learning the law becomes less significant. Emphasis is on teaching thelaw. The traditional teaching norm of lecture method is so innate that thetraditional method of teaching law is perpetuated, dragging the studentsinto a dry and boring journey of studying law. Even though the study oflaw is daunted as a serious one, but equal significance should be givento provoke the cognitive thinking of the students. Law students should betaught to think like a lawyer. Additionally, some form of creativity can bean added value in teaching law which makes learning law more vibrant.This article laments that the traditional pedagogy of teaching law merelyimparts knowledge, whereas law students should be taught to learn the law,stimulate critical thinking and ignite their cognitive skills.
 Keywords: law, diversity, teaching pedagogy