Imperial College London
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ProfessorSergeiChernyshenko

Faculty of Engineering, Department of Aeronautics

Chair in Aerodynamics
 
 
 
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Contact

 

+44 (0)20 7594 5548s.chernyshenko Website

 
 
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Location

 

211aCity and Guilds BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Fantuzzi:2016:10.1137/15M1053347,
author = {Fantuzzi, G and Goluskin, D and Huang, D and Chernyshenko, SI},
doi = {10.1137/15M1053347},
journal = {SIAM Journal on Applied Dynamical Systems},
pages = {1962--1988},
title = {Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization},
url = {http://dx.doi.org/10.1137/15M1053347},
volume = {15},
year = {2016}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - We describe methods for proving upper and lower bounds on infinite-time averages in deterministic dynamical systems and on stationary expectations in stochastic systems. The dynamics and the quantities to be bounded are assumed to be polynomial functions of the state variables. The methods are computer-assisted, using sum-of-squares polynomials to formulate sufficient conditions that can be checked by semidefinite programming. In the deterministic case, we seek tight bounds that apply to particular local attractors. An obstacle to proving such bounds is that they do not hold globally; they are generally violated by trajectories starting outside the local basin of attraction. We describe two closely related ways past this obstacle: one that requires knowing a subset of the basin of attraction, and another that considers the zero-noise limit of the corresponding stochastic system. The bounding methods are illustrated using the van der Pol oscillator. We bound deterministic averages on the attracting limit cycle above and below to within 1% , which requires a lower bound that does not hold for the unstable fixed point at the origin. We obtain similarly tight upper and lower bounds on stochastic expectations for a range of noise amplitudes. Limitations of our methods for certain types of deterministic systems are discussed, along with prospects for improvement.
AU  - Fantuzzi,G
AU  - Goluskin,D
AU  - Huang,D
AU  - Chernyshenko,SI
DO  - 10.1137/15M1053347
EP  - 1988
PY  - 2016///
SN  - 1536-0040
SP  - 1962
TI  - Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization
T2  - SIAM Journal on Applied Dynamical Systems
UR  - http://dx.doi.org/10.1137/15M1053347
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000391588600007&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://epubs.siam.org/doi/10.1137/15M1053347
UR  - http://hdl.handle.net/10044/1/49658
VL  - 15
ER  -
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