Zhang Neural Networks for Online Solution of Time-Varying Linear Inequalities

In this chapter, a special type of recurrent neural networks termed “Zhang neural network” (ZNN) is presented and studied for online solution of time-varying linear (matrix-vector and matrix) inequalities. Specifically, focusing on solving the time-varying linear matrix-vector inequality (LMVI), we develop and investigate two different ZNN models based on two different Zhang functions (ZFs). Then, being an extension, by defining another two different ZFs, another two ZNN models are developed and investigated to solve the time-varying linear matrix inequality (LMI). For such ZNN models, theoretical results and analyses are presented as well to show their computational performances. Simulation results with two illustrative examples further substantiate the efficacy of the presented ZNN models for time-varying LMVI and LMI solving

Design and analysis of three nonlinearly activated ZNN models for solving time-varying linear matrix inequalities in finite time

To obtain the superiority property of solving time-varying linear matrix inequalities (LMIs), three novel finite-time convergence zeroing neural network (FTCZNN) models are designed and analyzed in this paper. First, to make the Matlab toolbox calculation processing more conveniently, the matrix vectorization technique is used to transform matrix-valued FTCZNN models into vector-valued FTCZNN models. Then, considering the importance of nonlinear activation functions on the conventional zeroing neural network (ZNN), the sign-bi-power activation function (AF), the improved sign-bi-power AF and the tunable sign-bi-power AF are explored to establish the FTCZNN models. Theoretical analysis shows that the FTCZNN models not only can accelerate the convergence speed, but also can achieve finite-time convergence. Computer numerical results ulteriorly confirm the effectiveness and advantages of the FTCZNN models for finding the solution set of time-varying LMIs

AI based Robot Safe Learning and Control

Introduction This open access book mainly focuses on the safe control of robot manipulators. The control schemes are mainly developed based on dynamic neural network, which is an important theoretical branch of deep reinforcement learning. In order to enhance the safety performance of robot systems, the control strategies include adaptive tracking control for robots with model uncertainties, compliance control in uncertain environments, obstacle avoidance in dynamic workspace. The idea for this book on solving safe control of robot arms was conceived during the industrial applications and the research discussion in the laboratory. Most of the materials in this book are derived from the authors’ papers published in journals, such as IEEE Transactions on Industrial Electronics, neurocomputing, etc. This book can be used as a reference book for researcher and designer of the robotic systems and AI based controllers, and can also be used as a reference book for senior undergraduate and graduate students in colleges and universities

Adaptive control for time-varying systems: congelation and interconnection

This thesis investigates the adaptive control problem for systems with time-varying parameters. Two concepts are developed and exploited throughout the thesis: the congelation of variables, and the active nodes. The thesis first revisits the classical adaptive schemes and explains the challenges brought by the presence of time-varying parameters. Then, the concept of congelation of variables is introduced and its use in combinations with passivity-based, immersion-and-invariant, and identification-based adaptive schemes are discussed. As the congelation of variables method introduces additional interconnection in the closed-loop system, a framework for small-gain-like control synthesis for interconnected systems is needed.\vspace{2ex} To this end, the thesis proceeds by introducing the notion of active nodes. This is instrumental to show that as long as a class of node systems that possess adjustable damping parameters, that is the active nodes, satisfy certain graph-theoretic conditions, the desired small-gain-like property for the overall system can be enforced via tuning these adjustable parameters. Such conditions for interconnected systems with quadratic, nonlinear, and linearly parametrized supply rates, respectively, are elaborated from the analysis and control synthesis perspectives. The placement and the computation/adaptation of the damping parameters are also discussed. Following the introduction of these two fundamental tools, the thesis proceeds by discussing state-feedback designs for a class of lower-triangular nonlinear systems. The backstepping technique and the congelation of variables method are combined for passivity-based, immersion-and-invariance, and identification-based schemes. The notion of active nodes is exploited to yield simple and systematic proofs. Based on the results established for lower-triangular systems, the thesis continues to investigate output-feedback adaptive control problems. An immersion-and-invariance scheme for single-input single-output linear systems and a passivity-based scheme for nonlinear systems in observer form are proposed. The proof and interpretation of these results are also based on the notion of active nodes. The simulation results show that the adaptive control schemes proposed in the thesis have superior performance when compared with the classical schemes in the presence of time-varying parameters. Finally, the thesis studies two applications of the theoretical results proposed. The servo control problem for serial elastic actuators, and the disease control problem for interconnected settlements. The discussions show that these problems can be solved efficiently using the framework provided by the thesis.Open Acces

Fractional Calculus Operators and the Mittag-Leffler Function

This book focuses on applications of the theory of fractional calculus in numerical analysis and various fields of physics and engineering. Inequalities involving fractional calculus operators containing the Mittag–Leffler function in their kernels are of particular interest. Special attention is given to dynamical models, magnetization, hypergeometric series, initial and boundary value problems, and fractional differential equations, among others

In-situ Data Analytics In Cyber-Physical Systems

Cyber-Physical System (CPS) is an engineered system in which sensing, networking, and computing are tightly coupled with the control of the physical entities. To enable security, scalability and resiliency, new data analytics methodologies are required for computing, monitoring and optimization in CPS. This work investigates the data analytics related challenges in CPS through two study cases: Smart Grid and Seismic Imaging System. For smart grid, this work provides a complete solution for system management based on novel in-situ data analytics designs. We first propose methodologies for two important tasks of power system monitoring: grid topology change and power-line outage detection. To address the issue of low measurement redundancy in topology identification, particularly in the low-level distribution network, we develop a maximum a posterior based mechanism, which is capable of embedding prior information on the breakers status to enhance the identification accuracy. In power-line outage detection, existing approaches suer from high computational complexity and security issues raised from centralized implementation. Instead, this work presents a distributed data analytics framework, which carries out in-network processing and invokes low computational complexity, requiring only simple matrix-vector multiplications. To complete the system functionality, we also propose a new power grid restoration strategy involving data analytics for topology reconfiguration and resource planning after faults or changes. In seismic imaging system, we develop several innovative in-situ seismic imaging schemes in which each sensor node computes the tomography based on its partial information and through gossip with local neighbors. The seismic data are generated in a distributed fashion originally. Dierent from the conventional approach involving data collection and then processing in order, our proposed in-situ data computing methodology is much more ecient. The underlying mechanisms avoid the bottleneck problem on bandwidth since all the data are processed distributed in nature and only limited decisional information is communicated. Furthermore, the proposed algorithms can deliver quicker insights than the state-of-arts in seismic imaging. Hence they are more promising solutions for real-time in-situ data analytics, which is highly demanded in disaster monitoring related applications. Through extensive experiments, we demonstrate that the proposed data computing methods are able to achieve near-optimal high quality seismic tomography, retain low communication cost, and provide real-time seismic data analytics

Power transformer passivity enforcement : pre- and post-processing approaches

Orientador : Prof. Dr. Gustavo Henrique da Costa OliveiraDissertação (mestrado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Engenharia Elétrica. Defesa: Curitiba, 14/09/2015Inclui referências : f. 86-94Resumo: Esta dissertação trata, em bases matemáticas, do estudo das técnicas de aferição e imposição da passividade, uma propriedade qualitativa, geral e fundamental de transformadores. Para esse propósito, são propostas duas novas abordagens: uma de perturbação de dados no domínio da frequência, chamada pré-processamento, bem como um novo procedimento de perturbação de parâmetros no domínio do tempo, denominado pós-processamento. Inicialmente, métodos de aferição da passividade são empregados para distinguir sistemas passivos dos não-passivos bem como caracterizar as violações. Verificadas violações de passividade nos dados, usualmente devidas ao processo de medição, estes mesmos dados são perturbados, configurando o pré-processamento, de modo que todas as violações sejam suprimidas. Tal procedimento envolve encontrar matrizes de perturbação que, em cada frequência, atinjam esse objetivo causando, ao mesmo tempo, e em certo sentido, a menor perturbação possível. Os dados já passivos podem ser identificados e um modelo então obtido. Como dados passivos não garantem a obtenção de um modelo passivo, faz-se mister a imposição da passividade ao modelo obtido. Apesar de conduzir a resultados mais precisos, o pré-processamento de dados não é condição sine qua non para obtenção de modelos passivos. O procedimento de pós-processamento _e que, per se, assegura a passividade, permitindo que este seja empregado de forma independente daquele. Por meio de resultados obtidos com dados experimentais, demonstra-se, de forma individual e conjunta, a validade das técnicas ora propostas. Palavras-chave: Transformadores de Potência, Perturbação de dados, Perturbação de Parâmetros , Passivity-Enforcement, Modelagem, Análise de Transitórios.Abstract: This dissertation addresses the problem concerning the mathematical assessment and enforcement of passivity, a qualitative, general and fundamental property of power transformers. For serving that purpose, two novel approaches are introduced: a pre-processing approach consisting of frequency-domain data perturbation as well as a post-processing one comprising a time-domain parameter perturbation. Initially, passivity assessment methods can be used to distinguish passive systems from non-passive ones and characterize passivity violations. As data can reveal passivity violations owing to the data acquisition process, it is pre-processed so that violations be suppressed. This procedure entails finding a data perturbation matrix that achieves such objective and causes a least possible perturbation, in some sense. Passive data can be identified and a model then extracted. Since passive data does not ensure the extraction of a passive model whatsoever, the employment of passivity enforcement is an indispensable resource for fully guaranteed model passivity. Despite leading to more accurate results, pre-processing is not a sine qua non for obtaining passive models. It is passivity enforcement that per se ensures model passivity, thus allowing post-processing to be used regardless of pre-processing. Underpinned by results achieved upon experimental data, the effectiveness of the methods herein proposed are individually and jointly confirmed. Key-words: Power Transformers, Data Perturbation, Model Parameter Perturbation, Passivity-Enforcement, Modelling, Transient Analysis