Adaptive step size numerical integration for stochastic differential equations with discontinuous drift and diffusion

Stochastic hybrid systems (SHSs) are a modelling framework for a cyber-physical system (CPS), used to simulate, validate, and verify safety critical controllers under uncertainty. Popular simulation tools can miss detecting discontinuities when simulating SHS, thereby producing incorrect outputs dur...

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Veröffentlicht in:Numerical algorithms Jg. 87; H. 2; S. 849 - 872
1. Verfasser: Malik, Avinash
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.06.2021
Springer Nature B.V
Schlagworte:
Algebra
Algorithms
Computer Science
Continuity (mathematics)
Cyber-physical systems
Differential equations
Discontinuity
Drift
Hybrid systems
Numeric Computing
Numerical Analysis
Numerical integration
Ordinary differential equations
Original Paper
Random variables
Safety critical
Semantics
Simulation
Theory of Computation
Stochastic hybrid systems
Stochastic differential equations
Numerical integration algorithms
Convergence analysis
ISSN:1017-1398, 1572-9265
Online-Zugang:Volltext
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Zusammenfassung:Stochastic hybrid systems (SHSs) are a modelling framework for a cyber-physical system (CPS), used to simulate, validate, and verify safety critical controllers under uncertainty. Popular simulation tools can miss detecting discontinuities when simulating SHS, thereby producing incorrect outputs during simulation. We propose a novel adaptive step size simulation/integration technique for a subset of SHS—stochastic differential equations (SDEs) with discontinuous drift and diffusion coefficients. Each integration step, of the Euler-Maruyama numerical solution of the SDEs, is made dependent upon the values of the continuous variables inducing the discontinuity. This in turn guarantees convergence of the system trajectory towards the discontinuity without missing it. A thorough analysis and extensive benchmarking of the proposed integration technique shows the efficacy of the approach when simulating complex SHSs.
Bibliographie:ObjectType-Article-1
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ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-020-00990-x