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Abstract
This paper presents an approach to propagate sets of initial conditions and model parameters through dynamical systems. It is assumed that the dynamics is dependent on a number of model parameters and that the state of the system evolves from some initial conditions. Both model parameters and initial conditions vary within a set Ω. The paper presents an approach to approximate the set Ω with a polynomial expansion and to propagate, under some regularity assumptions, the polynomial representation through the dynamical system. The approach is based on a generalised polynomial algebra that replaces algebraic operators between real numbers with operators between polynomials. The paper first introduces the concept of generalised polynomial algebra and its use to propagate sets through dynamical systems. Then it analyses, both theoretically and experimentally, its time complexity and compares it against the time complexity of a nonintrusive counterpart. Finally, the paper provides an empirical convergence analysis on two illustrative examples of linear and nonlinear dynamical systems.
Original language  English 

Pages (fromto)  2249 
Number of pages  28 
Journal  Communications in Nonlinear Science and Numerical Simulation 
Volume  75 
Early online date  20 Mar 2019 
DOIs  
Publication status  Published  31 Aug 2019 
Keywords
 uncertainty propagation
 polynomial algebra
 dynamical systems
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Dive into the research topics of 'Set propagation in dynamical systems with generalised polynomial algebra and its computational complexity'. Together they form a unique fingerprint.Projects
 1 Finished

Marie Curie ITN (Stardust)
Vasile, M., Biggs, J., Burns, D., Hopkins, J., Macdonald, M., McInnes, C., Minisci, E. & Maddock, C.
European Commission  FP7  General
1/02/13 → 31/01/17
Project: Research