Parameter dependent reduced order estimators

1997 ◽  
Author(s):  
A. Zlochevsky ◽  
Y. Halevi
Keyword(s):  
Reduced Order ◽  
Parameter Dependent

Optimal Reduced-Order Estimators for Parameter-Dependent Systems

1999 ◽  
Vol 22 (6) ◽  
pp. 846-851
Author(s):  
Alina Zlochevsky ◽  
Yoram Halevi
Keyword(s):  
Reduced Order ◽  
Parameter Dependent

scholarly journals On Distributed Reduced-Order Observer-Based Protocol for Linear Multiagent Consensus under Switching Topology

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yan Zhang ◽  
Lixin Gao ◽  
Changfei Tong
Keyword(s):  
Switching Topology ◽  
Consensus Problem ◽  
Common Lyapunov Function ◽  
Reduced Order ◽  
Reduced Order Observer ◽  
Leader Following ◽  
Multi Agent ◽  
Fixed Topology ◽  
Parameter Dependent ◽  
The Given

We discuss linear multiagent systems consensus problem with distributed reduced-order observer-based protocol under switching topology. We use Jordan decomposition method to prove that the proposed protocols can solve consensus problem under directed fixed topology. By constructing a parameter-dependent common Lyapunov function, we prove that the distributed reduced-order observer-based protocol can also solve the continuous-time multi-agent consensus problem under the undirected switching interconnection topology. Then, we investigate the leader-following consensus problem and propose a reduced-order observer-based protocol for each following agent. By using similar analysis method, we can prove that all following agents can track the leader under a class of directed interaction topologies. Finally, the given simulation example also shows the effectiveness of our obtained result.

scholarly journals Reduced-order modelling of parameter-dependent, linear and nonlinear dynamic partial differential equation models

2017 ◽  
Vol 473 (2200) ◽  
pp. 20160809 ◽  
Author(s):  
A. A. Shah ◽  
W. W. Xing ◽  
V. Triantafyllidis
Keyword(s):  
Dimensional Space ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Problems ◽  
Dynamic Parameter ◽  
Partial Differential ◽  
Reduced Order ◽  
Linear And Nonlinear ◽  
Low Dimensional ◽  
Parameter Dependent ◽  
Parameter Values

In this paper, we develop reduced-order models for dynamic, parameter-dependent, linear and nonlinear partial differential equations using proper orthogonal decomposition (POD). The main challenges are to accurately and efficiently approximate the POD bases for new parameter values and, in the case of nonlinear problems, to efficiently handle the nonlinear terms. We use a Bayesian nonlinear regression approach to learn the snapshots of the solutions and the nonlinearities for new parameter values. Computational efficiency is ensured by using manifold learning to perform the emulation in a low-dimensional space. The accuracy of the method is demonstrated on a linear and a nonlinear example, with comparisons with a global basis approach.

scholarly journals Real-Time Simulation of Parameter-Dependent Fluid Flows through Deep Learning-Based Reduced Order Models

Fluids ◽  
2021 ◽  
Vol 6 (7) ◽  
pp. 259
Author(s):  
Stefania Fresca ◽  
Andrea Manzoni
Keyword(s):  
Deep Learning ◽  
Real Time ◽  
Elastic Beam ◽  
Fluid Flows ◽  
Reduced Order Models ◽  
Fluid Structure ◽  
Reduced Order ◽  
Reduction Strategies ◽  
Pressure Formulation ◽  
Parameter Dependent

Simulating fluid flows in different virtual scenarios is of key importance in engineering applications. However, high-fidelity, full-order models relying, e.g., on the finite element method, are unaffordable whenever fluid flows must be simulated in almost real-time. Reduced order models (ROMs) relying, e.g., on proper orthogonal decomposition (POD) provide reliable approximations to parameter-dependent fluid dynamics problems in rapid times. However, they might require expensive hyper-reduction strategies for handling parameterized nonlinear terms, and enriched reduced spaces (or Petrov–Galerkin projections) if a mixed velocity–pressure formulation is considered, possibly hampering the evaluation of reliable solutions in real-time. Dealing with fluid–structure interactions entails even greater difficulties. The proposed deep learning (DL)-based ROMs overcome all these limitations by learning, in a nonintrusive way, both the nonlinear trial manifold and the reduced dynamics. To do so, they rely on deep neural networks, after performing a former dimensionality reduction through POD, enhancing their training times substantially. The resulting POD-DL-ROMs are shown to provide accurate results in almost real-time for the flow around a cylinder benchmark, the fluid–structure interaction between an elastic beam attached to a fixed, rigid block and a laminar incompressible flow, and the blood flow in a cerebral aneurysm.

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