Polynomial deformations of osp(1/2)osp(1/2) and generalized parabosons

We consider the algebra $R$ generated by three elements $A,B,H$ subject to three relations $[H,A]=A$, $[H,B]=-B$ and $\{A,B\}=f(H)$. When $f(H)=H$ this coincides with the Lie superalgebra $osp(1/2)$; when $f$ is a polynomial we speak of polynomial deformations of $osp(1/2)$. Irreducible representations of $R$ are described, and in the case $\deg(f)\leq 2$ we obtain a complete classification, showing some similarities but also some interesting differences with the usual $osp(1/2)$ representations. The relation with deformed oscillator algebras is discussed, leading to the interpretation of $R$ as a generalized paraboson algebra.Comment: 18 pages, LaTeX, TWI-94-X

What is Mindful Leadership?

International audienceIn this article, our aim is to describe an emerging concept in the field of organizational behavior: “Mindfulness”. Mindfulness could be defined as the way to become aware of the body, the mind, the emotions and the spirit. It is often presented as a part of Emotional Intelligence (EI). It comes from ancient oriental traditions. It is far from being a recent concept. Even if it is an old concept, more than thousands of years old, it has emerged in the field of organizational behaviour only three or four years ago, mostly in the USA. It is unfortunate considering that mindfulness is part of the Indian culture, much more than it is of the Western culture. In this paper, we call on scholars for doing intensive research on mindfulness. Four areas of research could be considered. First is effective decision making. We argue that any leader or manager will take better decisions if he/she is centered in a state of mindfulness. The second area concerns team work or relationship management. We argue that a mindful person can better transmit a vision to the team and inspire and motivate them. Because mindfulness leads to emotional stability, we argue that a mindful person is also more effective in dealing with conflicts that appear in the workplace. The third area concerns work-life balance. A mindful person is peaceful and calm, and therefore can effectively manage the stresses arising from work and personal life. The fourth area is eco-centric leadership. We argue that mindfulness helps one recognize the interconnectedness between humans and nature. Therefore, mindful leaders develop eco-centric business models that promote a sustainable lifestyle. In this paper we first describe the concept of mindfulness and trace its origins from Buddhist and Indian perspectives. Then, based on published research, we propose that mindfulness in leaders and managers plays a critical role in developing and nurturing a vision of sustainability that thrives on people-centric and eco-centric approach to business. We conclude by discussing the various avenues of research in this new field

Continual Optimal Adaptive Tracking Of Uncertain Nonlinear Continuous-time Systems Using Multilayer Neural Networks

This study provides a lifelong integral reinforcement learning (LIRL)-based optimal tracking scheme for uncertain nonlinear continuous-time (CT) systems using multilayer neural network (MNN). In this LIRL framework, the optimal control policies are generated by using both the critic neural network (NN) weights and single-layer NN identifier. The critic MNN weight tuning is accomplished using an improved singular value decomposition (SVD) of its activation function gradient. The NN identifier, on the other hand, provides the control coefficient matrix for computing the control policies. An online weight velocity attenuation (WVA)-based consolidation scheme is proposed wherein the significance of weights is derived by using Hamilton-Jacobi-Bellman (HJB) error. This WVA term is incorporated in the critic MNN update law to overcome catastrophic forgetting. Lyapunov stability is employed to demonstrate the uniform ultimate boundedness of the overall closed-loop system. Finally, a numerical example of a two-link robotic manipulator supports the theoretical claims

Optimal Tracking Of Nonlinear Discrete-time Systems Using Zero-Sum Game Formulation And Hybrid Learning

This paper presents a novel hybrid learning-based optimal tracking method to address zero-sum game problems for partially uncertain nonlinear discrete-time systems. An augmented system and its associated discounted cost function are defined to address optimal tracking. Three multi-layer neural networks (NNs) are utilized to approximate the optimal control and the worst-case disturbance inputs, and the value function. The critic weights are tuned using the hybrid technique, whose weights are updated once at the sampling instants and in an iterative manner over finite times within the sampling instants. The proposed hybrid technique helps accelerate the convergence of the approximated value functional to its actual value, which makes the optimal policy attain quicker. A two-layer NN-based actor generates the optimal control input, and its weights are adjusted based on control input errors. Moreover, the concurrent learning method is utilized to ease the requirement of persistent excitation. Further, the Lyapunov method investigates the stability of the closed-loop system. Finally, the proposed method is evaluated on a two-link robot arm and demonstrates promising results

Continual Learning-Based Optimal Output Tracking of Nonlinear Discrete-Time Systems with Constraints: Application to Safe Cargo Transfer

This Paper Addresses a Novel Lifelong Learning (LL)-Based Optimal Output Tracking Control of Uncertain Non-Linear Affine Discrete-Time Systems (DT) with State Constraints. First, to Deal with Optimal Tracking and Reduce the Steady State Error, a Novel Augmented System, Including Tracking Error and its Integral Value and Desired Trajectory, is Proposed. to Guarantee Safety, an Asymmetric Barrier Function (BF) is Incorporated into the Utility Function to Keep the Tracking Error in a Safe Region. Then, an Adaptive Neural Network (NN) Observer is Employed to Estimate the State Vector and the Control Input Matrix of the Uncertain Nonlinear System. Next, an NN-Based Actor-Critic Framework is Utilized to Estimate the Optimal Control Input and the Value Function by using the Estimated State Vector and Control Coefficient Matrix. to Achieve LL for a Multitask Environment in Order to Avoid the Catastrophic Forgetting Issue, the Exponential Weight Velocity Attenuation (EWVA) Scheme is Integrated into the Critic Update Law. Finally, the Proposed Tracker is Applied to a Safe Cargo/ Crew Transfer from a Large Cargo Ship to a Lighter Surface Effect Ship (SES) in Severe Sea Conditions

Lifelong Learning Control of Nonlinear Systems with Constraints using Multilayer Neural Networks with Application to Mobile Robot Tracking

This Paper Presents a Novel Lifelong Multilayer Neural Network (MNN) Tracking Approach for an Uncertain Nonlinear Continuous-Time Strict Feedback System that is Subject to Time-Varying State Constraints. the Proposed Method Uses a Time-Varying Barrier Function to Accommodate the Constraints Leading to the Development of an Efficient Control Scheme. the Unknown Dynamics Are Approximated using a MNN, with Weights Tuned using a Singular Value Decomposition (SVD)-Based Technique. an Online Lifelong Learning (LL) based Elastic Weight Consolidation (EWC) Scheme is Also Incorporated to Alleviate the Issue of Catastrophic Forgetting. the Stability of the overall Closed-Loop System is Analyzed using Lyapunov Analysis. the Effectiveness of the Proposed Method is Demonstrated by using a Quadratic Cost Function through a Numerical Example of Mobile Robot Control Which Demonstrates a 38% Total Cost Reduction When Compared to the Recent Literature and 6% Cost Reduction is Observed When the Proposed Method with LL is Compared to the Proposed Method Without LL