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Discontinuous Galerkin Finite Element Methods for Linear Port-Hamiltonian Dynamical systems

Journal of Scientific Computing 2025年第1期104卷 1-47页

作者： Cheng, Xiaoyu van der Vegt, J.J.W. Xu, Yan Zwart, H.J. School of Mathematics University of Science and Technology of China Anhui Hefei 230026 China Department of Applied Mathematics Mathematics of Computational Science Group University of Twente P.O. Box 217 Enschede 7500 AE Netherlands Department of Applied Mathematics Mathematics of Systems Theory Group University of Twente P.O. Box 217 Enschede 7500 AE Netherlands Department of Mechanical Engineering Dynamics and Control Group Eindhoven University of Technology P.O. Box 513 Eindhoven 5600 MB Netherlands

In this paper, we present discontinuous Galerkin (DG) finite element discretizations for a class of linear hyperbolic port-Hamiltonian dynamical systems. The key point in constructing a port-Hamiltonian system is a Stokes-Dirac structure. Instead of following the traditional approach of defining the strong form of the Dirac structure, we define a Dirac structure in weak form, specifically in the input-state-output form. This is implemented within broken Sobolev spaces on a tessellation with polyhedral elements. After that, we state the weak port-Hamiltonian formulation and prove that it relates to a Poisson bracket. In our work, a crucial aspect of constructing the above-mentioned Dirac structure is that we provide a conservative relation between the boundary ports. Next, we state DG discretizations of the port-Hamiltonian system by using the weak form of the Dirac structure and broken polynomial spaces of differential forms, and we provide a priori error estimates for the structure-preserving port-Hamiltonian discontinuous Galerkin (PHDG) discretizations. The accuracy and capability of the methods developed in this paper are demonstrated by presenting several numerical experiments. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

关键词： Dirac structure Discontinuous Galerkin methods Exterior calculus Port-Hamiltonian systems

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Locomotion Optimization and Manipulation Planning of a Tetrahedron-Based Mobile Mechanism with Binary control

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Chinese Journal of Mechanical Engineering 2018年第1期31卷 78-99页

作者： Ran Liu Yan-An Yao Wan Ding Xiao-Ping Liu School of Mechanical Electronic and Control EngineeringBeijing Jiaotong University Department of Mechanism Theory and Dynamics of Machines RWTH Aachen University Department of Systems and Computer Engineering Carleton University

Locomotion and manipulation optimization is essential for the performance of tetrahedron-based mobile mechanism. Most of current optimization methods are constrained to the continuous actuated system with limited degree of freedom(DOF), which is infeasible to the optimization of binary control multi-DOF system. A novel optimization method using for the locomotion and manipulation of an 18 DOFs tetrahedron-based mechanism called 5-TET is proposed. The optimization objective is to realize the required locomotion by executing the least number of *** control strategy is adopted, and forward kinematic and tipping dynamic analyses are performed, *** on a developed genetic algorithm(GA), the optimal number of alternative struts between two adjacent steps is obtained as 5. Finally, a potential manipulation function is proposed, and the energy consumption comparison between optimal 5-TET and the traditional wheeled robot is carried out. The presented locomotion optimization and manipulation planning enrich the research of tetrahedron-based mechanisms and provide the instruction to the successive locomotion and operation planning of multi-DOF mechanisms.

关键词： Tetrahedron-based mobile mechanism Binary control GA Locomotion optimization Manipulation planning

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Synchronization in multiplex systems with simplex interactions beyond all-to-all coupling 6

Synchronization in multiplex systems with simplex interactio...

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6th International Conference "Neurotechnologies and Neurointerfaces", CNN 2024

作者： Laptyeva, Tetyana Ivanchenko, Mikhail Department of Control Theory and Dynamics of Systems Lobachevsky University Nizhny Novgorod Russia Department of Applied Mathematics Lobachevsky University Nizhny Novgorod Russia

ISBN: (纸本)9798350390926

We investigate syncrhonization transitions in the networks with higher-order symplectic interactions beyond the paradigm of global coupling. In particular, we consider sparse random pairwise and triadic coupling in phase oscillator networks, and additionally address the effect of multiplexing to the layer with the regular grid architecture. We demonstrate the persistence of the first order transition to synchronization in the case of sparse coupling, and find that the regular grid can induce such transition even when the pairwise coupling strength is insufficient. Surprisingly, we also find temporary desynchronization that becomes possible also due to multiplexing to the grid of oscillators. ©2024 IEEE.

关键词： Synchronization

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Consensus analysis of systems with time-varying interactions : An event-triggered approach

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IFAC-PapersOnLine 2017年第1期50卷 9349-9354页

作者： Arun Kumar S. Chowdhury N.R. Srikant S. Raisch J. Department of Systems and Control Engineering Indian Institute of Technology Bombay Mumbai 400076 India Fachgebiet Regelungssysteme Technische Universität Berlin Berlin 10587 Germany Systems and Control Theory Group Max Planck Institute for Dynamics of Complex Technical Systems Germany

We present consensus analysis of systems with single integrator dynamics interacting via time-varying graphs under the event-triggered control paradigm. Event-triggered control sparsifies the control applied, thus reducing the control effort expended. Initially, we consider a multi-agent system with persistently exciting interactions and study the behaviour under the application of event-triggered control with two types of trigger functions- static and dynamic trigger. We show that while in the case of static trigger, the edge-states converge to a ball around the origin, the dynamic trigger function forces the states to reach consensus exponentially. Finally, we extend these results to a more general setting where we consider switching topologies. We show that similar results can be obtained for agents interacting via switching topologies and validate our results by means of simulations. © 2017

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Stabilization of Multi-AUV formation with digital control

Stabilization of Multi-AUV formation with digital control

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International Convention on Information and Communication Technology, Electronics and Microelectronics

作者： S. A. Ul'yanov N. N. Maximkin Institute for System Dynamics and Control Theory / Department of Information Control Systems Irkutsk Russia

ISBN: (纸本)9781509025435

Formation stability problem for a team of autonomous underwater vehicles (AUV) with digital control is investigated. A leader-follower formation control algorithm for multi-AUV system is proposed. Feedback control signal for the follower, which is piecewise constant, is computed on the basis of discrete measurements of the distance and the bearing angle to the leader. A discrete observer for estimation of the derivatives of the distance and the bearing angle are used to improve the control performance. The parameters of the controller and observer are synthesized using a digital control system design method based on the vector Lyapunov functions that allows one to take into account the uncertainties of the plant, measurement errors, and control constraints. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control scheme.

关键词： Observers Digital control Vehicle dynamics Stability analysis Feedback control Lyapunov methods

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Constructing Strong Differential control Models with a Minimum Operator Norm. I

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Cybernetics and systems Analysis 2004年第1期40卷 120-125页

作者： Daneev, A. V. Rusanov, V. A. Technical State University Irkutsk Institute of Systems Dynamics and Control Theory Siberian Department of the Russian Academy of Sciences Irkutsk Russia

In terms of constructions of a formal identification process, the problems are analysed of existence and construction of strong differential (A, B)-models with minimum operator norm in the space of ξ-models.

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PD controllers to solve single-input, index-1 DAE based LQR problems

PD controllers to solve single-input, index-1 DAE based LQR ...

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European control Conference (ECC)

作者： Chayan Bhawal Jan Heiland Peter Benner Department of Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg

ISBN: (数字)9783907144022

ISBN: (纸本)9781728188133

In this paper, we present a method to compute the optimal trajectories of a linear quadratic regulator (LQR) problem corresponding to a single input, index-1 constant coefficient DAE system. Further, we also show that using a suitably designed proportional-derivative (PD) state-feedback controller one can force the trajectories of the corresponding DAE system to its optimal trajectories. Unlike the results present in the literature, the results in this paper are applicable for any arbitrary initial condition of the system.

关键词： Trajectory Indexes Matrix converters PD control Optimal control Regulators controllability

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Development of a VTOL mini UAV for multi-tasking missions

Development of a VTOL mini UAV for multi-tasking missions

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作者： Bataillé, B. Poinsot, D. Moschetta, J.-M. Bérard, C. Piquereau, A. ISAE France ONERA DCSD ISAE France BP54032 FR-31055 Toulouse Cedex 4 France Department of Flight Dynamics and Systems Control ONERA-DCSD BP 74025 FR-31055 Toulouse Codex 4 France Department of Mathematics Computer Science and Control Theory ISAE BP54032 FR-31055 Toulouse Codex 4 France Department of Flight Dynamics and Systems Control ONERA-DCSD BP 74025 FR-31055 Toulouse Cedex 4 France

Recent developments in the field of Mini-UAVs lead to successful designs in both hovering rotorcraft and fixed wing aircraft. However, a polyvalent MAV capable of stable hovering and fast forward flight is still expected. A promising candidate for such versatile missions consists of a tilt-body tail-sitter configuration. That concept is studied in this paper both from the flight mechanics and control points of view. Developments are based on an existing prototype called Vertigo. It consists of a tail sitter fixed-wing mini-UAV equipped with a contra-rotating pair of propellers in tractor configuration. A wind-tunnel campaign was carried out to extract experimental results from the Vertigo aerodynamic characteristics. A 6-component sting balance was fitted in the powered model enabling excursion in angles of attack and sideslip angles up to 90. Thus, a detailed understanding of the transition mechanism could be obtained. An analytical model including propwash effects was derived from experimental results. The analytical model was used to compute stability modes for specific flight conditions. This allowed an appropriate design of the autopilot capable of stabilisation and control over the whole flight envelope. A gain sequencing technique was chosen to ensure stability while minimising control loop execution time. A MATLAB-based flight simulator including an analytical model for the propeller slipstream has been developed in order to test the validity of airborne control loops. Simulation results are presented in the paper including hover flight, forward flight and transitions. Flight tests lead to successful inbound and outbound transitions of the Vertigo.

关键词： Analytical models

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AFast Solver for an H_(1) Regularized PDE-Constrained Optimization Problem

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Communications in Computational Physics 2016年第1期19卷 143-167页

作者： Andrew T.Barker Tyrone Rees Martin Stoll Center for Applied Scientific Computing Lawrence Livermore National LaboratoryMail Stop L-561LivermoreCA 94551USA Numerical Analysis Group Scientific Computing DepartmentRutherford Appleton LaboratoryChiltonDidcotOxfordshireOX110QXUnited Kingdom Computational Methods in Systems and Control Theory Max Planck Institute for Dynamics of Complex Technical SystemsSandtorstr.139106MagdeburgGermany

In this paperwe consider PDE-constrained optimization problemswhich incorporate an H_(1)regularization control *** focus on a time-dependent PDE,and consider both distributed and boundary *** problems we consider include bound constraints on the state,and we use a Moreau-Yosida penalty function to handle *** propose Krylov solvers and Schur complement preconditioning strategies for the different problems and illustrate their performance with numerical examples.

关键词： Preconditioning Krylov methods PDE-constrained optimization optimal control of PDEs

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Analysis of different crystalliser configurations to perform preferential crystallisation

Analysis of different crystalliser configurations to perform...

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作者： Elsner, M.P. Muslera, E. Alonso Angelov, I. Fernaśndez Menéndez, D. Lorenz, H. Polenske, D. Vollmer, U. Raisch, J. Seidel-Morgenstern, A. Max Planck Institute for Dynamics of Complex Technical Systems Physical and Chemical Foundations of Process Engineering Sandtorstr. 1 39106 Magdeburg Germany Max Planck Institute for Dynamics of Complex Technical Systems Systems and Control Theory Group Sandtorstr. 1 39106 Magdeburg Germany Otto von Guericke University Department of Chemical Engineering Universitätsplatz 2 39106 Magdeburg Germany Otto von Guericke University Department of System Theory of Process Engineering PO Box 4120 39106 Magdeburg Germany

The intention of this paper is the analysis of general concepts for preferential crystallisation with the focus on aspects of quantification. In this preliminary examination, the amino acid threonine was used as a model system. The use of on-line polarimetry in combination with on-line densimetry as well as microscopic investigation enables to obtain some indispensable information about the crystallisation kinetics. Taking these estimated values into consideration a simplified mathematical description as a first approach including a population balance model was established for the simulation of the time changes of liquid phase composition during the preferential crystallisation process. Based on this simplified model different crystalliser configurations were investtigated.

关键词： Crystallization

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