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A multiscale differential-algebraic neural network-based method for learning dynamical systems

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International Journal of Mechanical System Dynamics 2024年第1期4卷 77-87页

作者： Yin Huang Jieyu Ding College of Computer Science&Technology Qingdao UniversityQingdaoChina School of Mathematics and Statistics Qingdao UniversityQingdaoChina Center for Computational Mechanics and Engineering Simulation Qingdao UniversityQingdaoChina

The objective of dynamical system learning tasks is to forecast the future behavior of a system by leveraging observed ***,such systems can sometimes exhibit rigidity due to significant variations in component parameters or the presence of slow and fast variables,leading to challenges in *** overcome this limitation,we propose a multiscale differential-algebraic neural network(MDANN)method that utilizes Lagrangian mechanics and incorporates multiscale information for dynamical system *** MDANN method consists of two main components:the Lagrangian mechanics module and the multiscale *** Lagrangian mechanics module embeds the system in Cartesian coordinates,adopts a differential-algebraic equation format,and uses Lagrange multipliers to impose constraints explicitly,simplifying the learning *** multiscale module converts high-frequency components into low-frequency components using radial scaling to learn subprocesses with large differences in *** results demonstrate that the proposed MDANN method effectively improves the learning of dynamical systems under rigid conditions.

关键词： dynamical systems learning multibody system dynamics differential-algebraic equation neural networks multiscale structures

The Dynamics and Bifurcation Control of a Singular Biological Economic Model

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维普期刊数据库

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International Journal of Automation and computing 2012年第1期9卷 1-7页

作者： Ning Li Hai-Yi Sun Qing-Ling Zhang Institute of Systems Science Northeastern University Shenyang 110819 PRC College of Science Shenyang Jianzhu University Shenyang 110168 PRC

The objective of this paper is to study systematically the dynamics and control strategy of a singular biological economic model that is described by a differential-algebraic equation. It is shown that when the economic profit passes through zero, this model exhibits the transcritical bifurcation, the Hopf bifurcation, and the limit cycle. In particular, the system undergoes the singularity induced bifurcation at the positive equilibrium, which can result in impulse. Then, state feedback controllers closer to the actual control strategies are designed to eliminate the unexpected singularity induced bifurcation and stabilize the positive equilibrium under the positive profit. Finally, numerical simulations verify the results and illustrate the effectiveness of the controllers. Also, the model with positive economic profit is shown numerically to have different dynamics.

关键词： differential-algebraic equation transcritical bifurcation Hopf bifurcation limit cycle singularity induced bifurcation,bifurcation control.

Implicit Integration with Adjoint Sensitivity Propagation for Optimal Control Problems Involving differential-algebraic equations

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Implicit Integration with Adjoint Sensitivity Propagation fo...

Dynamics of a Predator-Prey Ecological System with Nonlinear Harvesting Rate

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作者： Canghua Jiang Kun Xie Zhiqiang Guo Kok Lay Teo School of Electrical Engineering and Automation Hefei University of Technology Department of Mathematics and Statistics Curtin University

ISBN: (纸本)9781538629185

For the solution of optimal control problem involving an index-1 differential-algebraic equation, an efficient function evaluation algorithm is proposed in this paper. In the evaluation procedure, the state equation is propagated forwards, then,adjoint sensitivity is propagated backwards. Thus, it is computationally more efficient than forward sensitivity propagation when the number of constraints is less than that of optimization variables. In order to reduce Newton iterations, the adjoint sensitivity is derived utilizing the implicit function theorem, and the integration procedure is accelerated by incorporating a predictor-corrector strategy. This algorithm is integrated with a nonlinear programming solver Ipopt to solve sequentially the point-to-point optimal control for a Delta robot with constrained motor torque. Numerical experiments demonstrate the efficiency of this algorithm.

关键词： differential-algebraic equation Implicit Runge-Kutta method Adjoint sensitivity Optimal control Delta robot

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Wuhan University Journal of Natural Sciences 2015年第1期20卷 25-33页

作者： LIU Weiyi LI Biwen FU Chaojin CHEN Boshan Institute of Technology Xianning Vocational Technical College College of Mathematics and Statistics Hubei Normal University College of Arts and Science Hubei Normal University

In this paper, a predator-prey ecological economic system with nonlinear harvesting rate is formulated and studied. This system is described by a differential-algebraic equation. By employing local parameterization method, an equivalent differen- tial system with parameter is obtained. Then by normal form the-ory and bifurcation theory, the complex dynamics of the system are investigated, including the local stability of equilibrium point and Hopf bifurcation. Finally, MATLAB simulation illustrates the effectiveness of our results.

关键词： differential-algebraic equation stability Hopf bifurcation nonlinear harvesting rate

Simulation of electrically driven jet using Chebyshev collocation method

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Theoretical & Applied Mechanics Letters 2011年第3期1卷 18-22页

作者： Yan Liu,~(a)) and Ruojing Zhang~(b)) School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China School of Aerospace Engineering and Applied Mechanics Tongji University Shanghai 200092 China

The model of electrically driven jet is governed by a series of quasi 1D dimensionless partial differential equations(PDEs).Following the method of lines,the Chebyshev collocation method is employed to discretize the PDEs and obtain a system of differential-algebraic equations(DAEs).By differentiating constrains in DAEs twice,the system is transformed into a set of ordinary differential equations(ODEs) with *** the implicit differential equations solver 'ddaskr' is used to solve the ODEs and post-stabilization is executed at the end of each *** show the distributions of radius,linear charge density,stretching ratio and also the horizontal velocity at a time ***,the spiral and expanding projections to X-Y plane of the jet centerline suggest the occurring of bending instability.

关键词： electrically driven jet method of lines Chebyshev collocation method differential-algebraic equation bending instability

Accelerating the Advanced-Step NMPC by a Lifted Implicit Runge-Kutta Integrator for Fast Embedded Applications

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Accelerating the Advanced-Step NMPC by a Lifted Implicit Run...