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Sparse Deep Neural Network for Nonlinear Partial Differential Equations

Numerical Mathematics(Theory,Methods and Applications) 2023年第1期16卷 58-78页

作者： Yuesheng Xu Taishan Zeng Department of Mathematics and Statistics Old Dominion UniversityNorfolkVirginia 23529USA School of Mathematical Science South China Normal UniversityGuangzhou 510631China Guangdong Key Laboratory of Big Data Analysis and Processing Guangzhou 510006China

More competent learning models are demanded for data processing due to increasingly greater amounts of data available in *** that we encounter often have certain embedded sparsity *** is,if they are represented in an appropriate basis,their energies can concentrate on a small number of basis *** paper is devoted to a numerical study of adaptive approximation of solutions of nonlinear partial differential equations whose solutions may have singularities,by deep neural networks(DNNs)with a sparse regularization with multiple *** that DNNs have an intrinsic multi-scale structure which is favorable for adaptive representation of functions,by employing a penalty with multiple parameters,we develop DNNs with a multi-scale sparse regularization(SDNN)for effectively representing functions having certain *** then apply the proposed SDNN to numerical solutions of the Burgers equation and the Schrödinger *** examples confirm that solutions generated by the proposed SDNN are sparse and accurate.

关键词： Sparse approximation deep learning nonlinear partial differential equations sparse regularization adaptive approximation

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Backstepping sliding mode tracking control of quad-rotor under input saturation

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International Journal of Intelligent Computing and Cybernetics 2012年第4期5卷 515-532页

作者： Xun Gong Yue Bai Zhicheng Hou Changjun Zhao Yantao Tian Qiang Sun School of Telecommunication Engineering Jilin UniversityChangchunChina Chang Chun Institute of Optics Fine Mechanics and Physics Chinese Academy of SciencesChangchunChina

Purpose–The quad-rotor is an under-actuation,strong coupled nonlinear system with parameters uncertainty,unmodeled disturbance and drive capability *** purpose of the paper is to design a flight control system to regulate the aircraft track the desired trajectory and keep the attitude angles stable on account of these ***/methodology/approach–Considering the dynamics of a quad-rotor,the closed-loop flight control system is divided into two nested loops:the translational outer-loop and the attitude *** the outer-loop,the translational controller,which exports the desired attitude angles to the inner-loop,is designed based on bounded control *** consideration of the influence of uncertain rotational inertia and external disturbance,the backstepping sliding mode approach with adaptive gains is used in the *** switching control strategy based on the sign functions of sliding surface is introduced into the design procedure with respect to the input ***–The validity of the proposed flight control system was verified through numerical simulation and prototype flight experiment in this ***,with relation to the flying,the motor speed is kept in the predetermined ***/value–This article introduces a new flight control system designed for a quad-rotor.

关键词： Quad-rotor Double-loops Backstepping algorithm adaptive approximation Bounded control Prototype experiment Genetic algorithms Flight control

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Actuator and sensor fault isolation in a class of nonlinear dynamical systems

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Journal of Automation and Intelligence 2024年第2期3卷 57-72页

作者： Hamed Tirandaz Christodoulos Keliris Marios M.Polycarpou KIOS Research Center for Intelligent Systems and Networks and the Department of Electrical and Computer EngineeringUniversity of CyprusNicosia 1678Cyprus

Fault isolation in dynamical systems is a challenging task due to modeling uncertainty and measurement noise,interactive effects of multiple faults and fault *** paper proposes a unified approach for isolation of multiple actuator or sensor faults in a class of nonlinear uncertain dynamical *** and sensor fault isolation are accomplished in two independent modules,that monitor the system and are able to isolate the potential faulty actuator(s)or sensor(s).For the sensor fault isolation(SFI)case,a module is designed which monitors the system and utilizes an adaptive isolation threshold on the output residuals computed via a nonlinear estimation scheme that allows the isolation of single/multiple faulty sensor(s).For the actuator fault isolation(AFI)case,a second module is designed,which utilizes a learning-based scheme for adaptive approximation of faulty actuator(s)and,based on a reasoning decision logic and suitably designed AFI thresholds,the faulty actuator(s)set can be *** effectiveness of the proposed fault isolation approach developed in this paper is demonstrated through a simulation example.

关键词： Actuator and sensor fault isolation adaptive approximation Observer-based fault diagnosis Reasoning-based decision logic

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