Abstract
This paper proposes a method based on semidefinite programming for estimating moments of stochastic hybrid systems (SHSs). The class of SHSs considered herein consists of a finite number of discrete states and a continuous state whose dynamics as well as the reset maps and transition intensities are polynomial in the continuous state. For these SHSs, the dynamics of moments evolve according to a system of linear ordinary differential equations. However, it is generally not possible to exactly solve the system since time evolution of a specific moment may depend upon moments of order higher than it. Our methodology recasts an SHS with multiple discrete modes to a single-mode SHS with algebraic constraints. We then find lower and upper bounds on a moment of interest via a semidefinite program that includes linear constraints obtained from moment dynamics and those arising from the recasting process, along with semidefinite constraints coming from the non-negativity of moment matrices. We illustrate the methodology via an example of SHS.
| Original language | English (US) |
|---|---|
| Article number | 108634 |
| Journal | Automatica |
| Volume | 112 |
| DOIs | |
| State | Published - Feb 2020 |
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Keywords
- Convex programming
- Jump process
- Optimization
- Polynomial models
- Stochastic systems
Cite this
Moment analysis of stochastic hybrid systems using semidefinite programming. / Ghusinga, Khem Raj; Lamperski, Andrew; Singh, Abhyudai.
In: Automatica, Vol. 112, 108634, 02.2020.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Moment analysis of stochastic hybrid systems using semidefinite programming
AU - Ghusinga, Khem Raj
AU - Lamperski, Andrew
AU - Singh, Abhyudai
PY - 2020/2
Y1 - 2020/2
N2 - This paper proposes a method based on semidefinite programming for estimating moments of stochastic hybrid systems (SHSs). The class of SHSs considered herein consists of a finite number of discrete states and a continuous state whose dynamics as well as the reset maps and transition intensities are polynomial in the continuous state. For these SHSs, the dynamics of moments evolve according to a system of linear ordinary differential equations. However, it is generally not possible to exactly solve the system since time evolution of a specific moment may depend upon moments of order higher than it. Our methodology recasts an SHS with multiple discrete modes to a single-mode SHS with algebraic constraints. We then find lower and upper bounds on a moment of interest via a semidefinite program that includes linear constraints obtained from moment dynamics and those arising from the recasting process, along with semidefinite constraints coming from the non-negativity of moment matrices. We illustrate the methodology via an example of SHS.
AB - This paper proposes a method based on semidefinite programming for estimating moments of stochastic hybrid systems (SHSs). The class of SHSs considered herein consists of a finite number of discrete states and a continuous state whose dynamics as well as the reset maps and transition intensities are polynomial in the continuous state. For these SHSs, the dynamics of moments evolve according to a system of linear ordinary differential equations. However, it is generally not possible to exactly solve the system since time evolution of a specific moment may depend upon moments of order higher than it. Our methodology recasts an SHS with multiple discrete modes to a single-mode SHS with algebraic constraints. We then find lower and upper bounds on a moment of interest via a semidefinite program that includes linear constraints obtained from moment dynamics and those arising from the recasting process, along with semidefinite constraints coming from the non-negativity of moment matrices. We illustrate the methodology via an example of SHS.
KW - Convex programming
KW - Jump process
KW - Optimization
KW - Polynomial models
KW - Stochastic systems
UR - http://www.scopus.com/inward/record.url?scp=85074158719&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85074158719&partnerID=8YFLogxK
U2 - 10.1016/j.automatica.2019.108634
DO - 10.1016/j.automatica.2019.108634
M3 - Article
AN - SCOPUS:85074158719
VL - 112
JO - Automatica
JF - Automatica
SN - 0005-1098
M1 - 108634
ER -