Deterministic and Stochastic Fixed-Time Stability of Discrete-time Autonomous Systems

Farzaneh Tatari; Hamidreza Modares

doi:10.1109/JAS.2023.123405

Volume 10 Issue 4

Apr. 2023

IEEE/CAA Journal of Automatica Sinica

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Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2023 > 10(4): 945-956

F. Tatari and H. Modares, “Deterministic and stochastic fixed-time stability of discrete-time autonomous systems,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 4, pp. 945–956, Apr. 2023. doi: 10.1109/JAS.2023.123405

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F. Tatari and H. Modares, “Deterministic and stochastic fixed-time stability of discrete-time autonomous systems,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 4, pp. 945–956, Apr. 2023. doi: 10.1109/JAS.2023.123405

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Deterministic and Stochastic Fixed-Time Stability of Discrete-time Autonomous Systems

doi: 10.1109/JAS.2023.123405

Farzaneh Tatari^1
,,
Hamidreza Modares^{1
,
,}

Mechanical Engineering Department, Michigan State University, Michigan 48824-1226 USA

Funds: This work relates to Department of Navy award N00014-22-1-2159 issued by the Office of Naval Research

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Author Bio:
Farzaneh Tatari received the B.Sc. degree from Shahrood University of Technology, Iran, in 2007 and the M.Sc. and Ph.D. degrees in electrical engineering from Ferdowsi University of Mashhad, Iran, in 2010 and 2015, respectively. She was an Assistant Professor in Electrical and Computer Engineering Department, Semnan University, Iran, from 2017 to 2019, and a Postdoctoral Research Fellow at the KIOS Research and Innovation Center of Excellence in the University of Cyprus, Cyprus, from 2019 to 2020. She is currently with Mechanical Engineering Department, Michigan State University, USA. Her current research interests include reinforcement learning, concurrent learning, optimal adaptive control and distributed control. Dr. Tatari is a Guest Associate Editor of the Frontiers in Control Engineering: Adaptive, Robust and Fault Tolerant Control, and she also serves as a Reviewer of several international journals, including IEEE Transactions on Neural Networks and Learning Systems, IEEE Control Systems Letters, and Automatica

Hamidreza Modares (Senior Member, IEEE) received the B.S. degree from the University of Tehran, Iran, in 2004, the M.S. degree from the Shahrood University of Technology, Iran, in 2006, and the Ph.D. degree from the University of Texas at Arlington, USA, in 2015. He was a Senior Lecturer with the Shahrood University of Technology, from 2006 to 2009 and a Faculty Research Associate with the University of Texas at Arlington, USA, from 2015 to 2016. He is currently an Assistant Professor in Mechanical Engineering Department, Michigan State University, USA. His current research interests include cyber-physical systems, reinforcement learning, distributed control, robotics, and machine learning. Dr. Modares was a recipient of the Best Paper Award from the 2015 IEEE International Symposium on Resilient Control Systems. He is also an Associate Editor of the IEEE Transactions on Neural Networks and Learning Systems
Corresponding author: Hamidreza Modares, e-mail: modaresh@msu.edu
Received Date: 2022-11-22
Accepted Date: 2022-12-18

Available Online: 2023-02-07

Abstract

Abstract

This paper studies deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems. Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT systems is certified. Extensions to systems under deterministic perturbations as well as stochastic noise are then considered. For the former, sensitivity to perturbations for fixed-time stable DT systems is analyzed, and it is shown that fixed-time attractiveness results from the presented Lyapunov conditions. For the latter, sufficient Lyapunov conditions for fixed-time stability in probability of nonlinear stochastic DT systems are presented. The fixed upper bound of the settling-time function is derived for both fixed-time stable and fixed-time attractive systems, and a stochastic settling-time function fixed upper bound is derived for stochastic DT systems. Illustrative examples are given along with simulation results to verify the introduced results.
- Discrete-time (DT) systems,
- fixed-time stability,
- nonlinear systems,
- stochastic systems

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References(52)

References

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Highlights

The deterministic and stochastic fixed-time stability of autonomous nonlinear discrete-time (DT) systems are presented in this paper
Lyapunov conditions are first presented under which the fixed-time stability of deterministic DT systems is certified
Extensions to systems under deterministic perturbations as well as stochastic noise are then considered. For the former, the sensitivity to perturbations for fixed-time stable DT systems is analyzed, and it is shown that fixed-time attractiveness is resulted from the presented Lyapunov conditions. For the latter, sufficient Lyapunov conditions for fixed-time stability in probability of nonlinear stochastic DT systems are presented
The fixed upper bound of the settling-time function is derived for both fixed-time stable and fixedtime attractive systems, and the stochastic settling-time function fixed upper bound is derived for stochastic DT systems
Illustrative examples are given along with simulation results to verify the introduced results

Deterministic and Stochastic Fixed-Time Stability of Discrete-time Autonomous Systems

doi: 10.1109/JAS.2023.123405

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通讯作者: 陈斌, bchen63@163.com

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