Instabilizability Conditions for Continuous-Time Stochastic Systems Under Control Input Constraints

Ahmet Cetinkaya; Masako Kishida

doi:10.1109/LCSYS.2021.3105452

Instabilizability Conditions for Continuous-Time Stochastic Systems Under Control Input Constraints

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper, we investigate constrained control of continuous-time linear stochastic systems. We show that for certain system parameter settings, constrained control policies can never achieve stabilization. Specifically, we explore a class of control policies that are constrained to have a bounded average second moment for Ito-type stochastic differential equations with additive and multiplicative noise. We prove that in certain settings of the system parameters and the bounding constant of the control constraint, divergence of the second moment of the system state is inevitable regardless of the initial state value and regardless of how the control policy is designed.

Original language	English
Journal	IEEE Control Systems Letters
DOIs	https://doi.org/10.1109/LCSYS.2021.3105452
Publication status	Accepted/In press - 2021
Externally published	Yes

Keywords

Actuators
Additives
constrained control
Differential equations
linear systems.
Packet loss
Probabilistic logic
Stochastic processes
Stochastic systems
Stochastic systems

ASJC Scopus subject areas

Control and Systems Engineering
Control and Optimization

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10.1109/LCSYS.2021.3105452

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title = "Instabilizability Conditions for Continuous-Time Stochastic Systems Under Control Input Constraints",

abstract = "In this paper, we investigate constrained control of continuous-time linear stochastic systems. We show that for certain system parameter settings, constrained control policies can never achieve stabilization. Specifically, we explore a class of control policies that are constrained to have a bounded average second moment for Ito-type stochastic differential equations with additive and multiplicative noise. We prove that in certain settings of the system parameters and the bounding constant of the control constraint, divergence of the second moment of the system state is inevitable regardless of the initial state value and regardless of how the control policy is designed.",

keywords = "Actuators, Additives, constrained control, Differential equations, linear systems., Packet loss, Probabilistic logic, Stochastic processes, Stochastic systems, Stochastic systems",

author = "Ahmet Cetinkaya and Masako Kishida",

note = "Publisher Copyright: IEEE",

year = "2021",

doi = "10.1109/LCSYS.2021.3105452",

language = "English",

journal = "IEEE Control Systems Letters",

issn = "2475-1456",

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T1 - Instabilizability Conditions for Continuous-Time Stochastic Systems Under Control Input Constraints

AU - Cetinkaya, Ahmet

AU - Kishida, Masako

N1 - Publisher Copyright: IEEE

PY - 2021

Y1 - 2021

N2 - In this paper, we investigate constrained control of continuous-time linear stochastic systems. We show that for certain system parameter settings, constrained control policies can never achieve stabilization. Specifically, we explore a class of control policies that are constrained to have a bounded average second moment for Ito-type stochastic differential equations with additive and multiplicative noise. We prove that in certain settings of the system parameters and the bounding constant of the control constraint, divergence of the second moment of the system state is inevitable regardless of the initial state value and regardless of how the control policy is designed.

AB - In this paper, we investigate constrained control of continuous-time linear stochastic systems. We show that for certain system parameter settings, constrained control policies can never achieve stabilization. Specifically, we explore a class of control policies that are constrained to have a bounded average second moment for Ito-type stochastic differential equations with additive and multiplicative noise. We prove that in certain settings of the system parameters and the bounding constant of the control constraint, divergence of the second moment of the system state is inevitable regardless of the initial state value and regardless of how the control policy is designed.

KW - Actuators

KW - Additives

KW - constrained control

KW - Differential equations

KW - linear systems.

KW - Packet loss

KW - Probabilistic logic

KW - Stochastic processes

KW - Stochastic systems

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DO - 10.1109/LCSYS.2021.3105452

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SN - 2475-1456

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

ER -

Instabilizability Conditions for Continuous-Time Stochastic Systems Under Control Input Constraints

Abstract

Keywords

ASJC Scopus subject areas

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