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Article

Structure Preserving Uncertainty Modelling and Robustness Analysis for Spatially Distributed Dissipative Dynamical Systems

Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Ivana Lučića 5, 10000 Zagreb, Croatia
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Academic Editors: Dragan Pamucar, Dragan Marinkovic and Samarjit Kar
Mathematics 2022, 10(12), 2125; https://doi.org/10.3390/math10122125
Received: 29 April 2022 / Revised: 14 June 2022 / Accepted: 15 June 2022 / Published: 18 June 2022
(This article belongs to the Special Issue Dynamics under Uncertainty: Modeling Simulation and Complexity II)
The paper deals with uncertainty modelling, robust stability and performance analysis of multi-input multi-output (MIMO) reduced order spatially distributed dissipative dynamical systems. While researching the topic of modern robust control of such systems, two key findings were discovered: (i) systematic modelling of the uncertainty and model order reduction (MOR) at the level of a subsystem gives both modelling freedom and the ability for obtaining less conservative uncertainties on the level of a subsystem; (ii) for a special class of interconnected dissipative dynamical systems, uncertainty conservatism at the subsystem level can be reduced—a novel, structure preserving algorithm employing subsystem partitioning and subsystem MOR by means of balanced truncation method (BTM) is used to obtain low-order robustly stable interconnected systems. Such systems are suitable for practical decentralized and distributed robust controller synthesis. Built upon a powerful framework of integral quadratic constraints (IQCs), this approach gives uncertainty modelling flexibility to perform robustness analysis of real world interconnected systems that are usually affected by multiple types of uncertainties at once. The proposed uncertainty modelling procedure and its practical application are presented on the numerical example. A spatially discretized vibration dynamical system comprised of a series of simply supported Euler beams mutually interconnected by springs and dampers is examined. Spatial discretization of the mathematical model is carried out using the finite element method (FEM). View Full-Text
Keywords: uncertainty modelling; structure preserving; model order reduction; integral quadratic constraints; dissipative dynamical systems uncertainty modelling; structure preserving; model order reduction; integral quadratic constraints; dissipative dynamical systems
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MDPI and ACS Style

Dogančić, B.; Jokić, M.; Alujević, N.; Wolf, H. Structure Preserving Uncertainty Modelling and Robustness Analysis for Spatially Distributed Dissipative Dynamical Systems. Mathematics 2022, 10, 2125. https://doi.org/10.3390/math10122125

AMA Style

Dogančić B, Jokić M, Alujević N, Wolf H. Structure Preserving Uncertainty Modelling and Robustness Analysis for Spatially Distributed Dissipative Dynamical Systems. Mathematics. 2022; 10(12):2125. https://doi.org/10.3390/math10122125

Chicago/Turabian Style

Dogančić, Bruno, Marko Jokić, Neven Alujević, and Hinko Wolf. 2022. "Structure Preserving Uncertainty Modelling and Robustness Analysis for Spatially Distributed Dissipative Dynamical Systems" Mathematics 10, no. 12: 2125. https://doi.org/10.3390/math10122125

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