A Quantized State Integrator With Second Order Errors Over Monotonic Segments

Rasika Mahawattege; James Nutaro

doi:10.23919/ANNSIM55834.2022.9859427

A Quantized State Integrator With Second Order Errors Over Monotonic Segments

Rasika Mahawattege, James Nutaro

Computational Systems Engineering and Cy

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

We introduce a novel quantized state integration method that is analogous to the explicit, second order Runge-Kutta technique. A feature of this method is that, for a single differential equation over an interval where the solution is monotonic, it exhibits an error proportional to the square of the integration quantum. We offer a theoretical proof of this behavior and demonstrate it with a numerical example. At the same time, an extension of the method to a system with input causes the errors to become proportional to the integration quantum. The latter observation fits established theory; the former appears to be a new result that might offer new insights into the construction of quantized state integration methods.

Original language	English
Title of host publication	Proceedings of the 2022 Annual Modeling and Simulation Conference, ANNSIM 2022
Editors	Cristina Ruiz Martin, Niloufar Emami, Maria Julia Blas, Roya Rezaee
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	428-436
Number of pages	9
ISBN (Electronic)	9781713852889
DOIs	https://doi.org/10.23919/ANNSIM55834.2022.9859427
State	Published - 2022
Event	2022 Annual Modeling and Simulation Conference, ANNSIM 2022 - San Diego, United States Duration: Jul 18 2022 → Jul 20 2022

Publication series

Name	Proceedings of the 2022 Annual Modeling and Simulation Conference, ANNSIM 2022

Conference

Conference	2022 Annual Modeling and Simulation Conference, ANNSIM 2022
Country/Territory	United States
City	San Diego
Period	07/18/22 → 07/20/22

Funding

This research was supported in part by an appointment with the National Science Foundation (NSF) Mathematical Sciences Graduate Internship (MSGI) Program sponsored by the NSF Division of Mathematical Sciences. This program is administered by the Oak Ridge Institute for Science and Education (ORISE) through an interagency agreement between the U.S. Department of Energy (DOE) and NSF. ORISE is managed for DOE by ORAU. All opinions expressed in this paper are the author’s and do not necessarily reflect the policies and views of NSF, ORAU/ORISE, or DOE.

Funders	Funder number
National Science Foundation
U.S. Department of Energy
Division of Mathematical Sciences
Oak Ridge Institute for Science and Education

Keywords

discrete event simulation
numerical integration
quantized state systems

Access to Document

10.23919/ANNSIM55834.2022.9859427

Cite this

Mahawattege, R., & Nutaro, J. (2022). A Quantized State Integrator With Second Order Errors Over Monotonic Segments. In C. R. Martin, N. Emami, M. J. Blas, & R. Rezaee (Eds.), Proceedings of the 2022 Annual Modeling and Simulation Conference, ANNSIM 2022 (pp. 428-436). (Proceedings of the 2022 Annual Modeling and Simulation Conference, ANNSIM 2022). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.23919/ANNSIM55834.2022.9859427

Mahawattege, Rasika ; Nutaro, James. / A Quantized State Integrator With Second Order Errors Over Monotonic Segments. Proceedings of the 2022 Annual Modeling and Simulation Conference, ANNSIM 2022. editor / Cristina Ruiz Martin ; Niloufar Emami ; Maria Julia Blas ; Roya Rezaee. Institute of Electrical and Electronics Engineers Inc., 2022. pp. 428-436 (Proceedings of the 2022 Annual Modeling and Simulation Conference, ANNSIM 2022).

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abstract = "We introduce a novel quantized state integration method that is analogous to the explicit, second order Runge-Kutta technique. A feature of this method is that, for a single differential equation over an interval where the solution is monotonic, it exhibits an error proportional to the square of the integration quantum. We offer a theoretical proof of this behavior and demonstrate it with a numerical example. At the same time, an extension of the method to a system with input causes the errors to become proportional to the integration quantum. The latter observation fits established theory; the former appears to be a new result that might offer new insights into the construction of quantized state integration methods.",

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Mahawattege, R & Nutaro, J 2022, A Quantized State Integrator With Second Order Errors Over Monotonic Segments. in CR Martin, N Emami, MJ Blas & R Rezaee (eds), Proceedings of the 2022 Annual Modeling and Simulation Conference, ANNSIM 2022. Proceedings of the 2022 Annual Modeling and Simulation Conference, ANNSIM 2022, Institute of Electrical and Electronics Engineers Inc., pp. 428-436, 2022 Annual Modeling and Simulation Conference, ANNSIM 2022, San Diego, United States, 07/18/22. https://doi.org/10.23919/ANNSIM55834.2022.9859427

A Quantized State Integrator With Second Order Errors Over Monotonic Segments. / Mahawattege, Rasika; Nutaro, James.
Proceedings of the 2022 Annual Modeling and Simulation Conference, ANNSIM 2022. ed. / Cristina Ruiz Martin; Niloufar Emami; Maria Julia Blas; Roya Rezaee. Institute of Electrical and Electronics Engineers Inc., 2022. p. 428-436 (Proceedings of the 2022 Annual Modeling and Simulation Conference, ANNSIM 2022).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - We introduce a novel quantized state integration method that is analogous to the explicit, second order Runge-Kutta technique. A feature of this method is that, for a single differential equation over an interval where the solution is monotonic, it exhibits an error proportional to the square of the integration quantum. We offer a theoretical proof of this behavior and demonstrate it with a numerical example. At the same time, an extension of the method to a system with input causes the errors to become proportional to the integration quantum. The latter observation fits established theory; the former appears to be a new result that might offer new insights into the construction of quantized state integration methods.

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Mahawattege R, Nutaro J. A Quantized State Integrator With Second Order Errors Over Monotonic Segments. In Martin CR, Emami N, Blas MJ, Rezaee R, editors, Proceedings of the 2022 Annual Modeling and Simulation Conference, ANNSIM 2022. Institute of Electrical and Electronics Engineers Inc. 2022. p. 428-436. (Proceedings of the 2022 Annual Modeling and Simulation Conference, ANNSIM 2022). doi: 10.23919/ANNSIM55834.2022.9859427

A Quantized State Integrator With Second Order Errors Over Monotonic Segments

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