Article

Towars a Theory of Stochastic Hybrid Systems

Authors:

Jianghai Hu,

John Lygeros,

Shankar SastryAuthors Info & Claims

HSCC '00: Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control

Pages 160 - 173

Published: 23 March 2000 Publication History

Abstract

n this paper, we present a scheme of stochastic hybrid system which introduces randomness to the deterministic framework of the traditional hybrid systems by allowing the flow inside each invariant set of the discrete state variables to be governed by stochastic differential equation (SDE) rather than the deterministic ones. The notion of embedded Markov chains is proposed for such systems and some illustrative example from high way model is presented. As an important application, these ideas are then applied to the state space discretization of one dimensional SDE to obtain the natural discretized stochastic hybrid system together with its embedded MC. The invariant distribution and exit probability from interval of the MC are studied and it is shown that they converge to their counterparts for the solution process of the original SDE as the discretization step goes to zero. As a result, the discretized stochastic hybrid system provides a useful tool for studying various sample path properties of the SDE.

References

[1]

E. Altman and V. Gaitsgory. Asymptotic optimization of a nonlinear hybrid system governed by a Markov decision process. SIAM Journal of Control and Optimization , 35(6):2070-2085, 1997.

Crossref

Google Scholar

[2]

Gopal K. Basak, Arnab Bisi, and Mrinal K. Ghosh. Ergodic control of random singular diffusions. In IEEE Conference on Decision and Control, pages 2545-2550, Kobe, Japan, 1996.

Google Scholar

[3]

Richard Durrett. Probability: theory and examples, 2nd edition. Duxbury Press, 1996.

Crossref

Google Scholar

[4]

Richard Durrett. Stochastic calculus: A practical introduction. CRC Press, 1996.

Google Scholar

[5]

J.A. Filar and V. Gaitsgory. Control of singularly perturbed hybrid stochastic systems. In IEEE Conference on Decision and Control, pages 511-516, Kobe, Japan, 1996.

Google Scholar

[6]

John Lygeros. Hybrid systems: modeling, analysis and control. preprint, 1999.

Google Scholar

[7]

Bernt Oksendal. Stochastic Differential Equations, an introduction with application. Fifth edition. Springer-Verlag, 1998.

Crossref

Google Scholar

[8]

L. Perko. Differential equation and dynamical systems, 2nd edition. Springer-Verlag, 1996.

Crossref

Google Scholar

[9]

E. Skafidas, R.J. Evans, and I.M. Mareels. Optimal controller switching for stochastic systems. In IEEE Conference on Decision and Control, pages 3950-3955, San Diego, CA, 1997.

Crossref

Google Scholar

[10]

Ching-Chih Tsai. Composite stabilization of singularly perturbed stochastic hybrid systems. International Journal of Control, 71(6):1005-1020, 1998.

Google Scholar

[11]

Ching-Chih Tsai and Abraham H. Haddad. Averaging, aggregation and optimal control of singulayly perturbed stochastic hybrid systems. International Journal of Control, 68(1):31-50, 1997.

Google Scholar

Cited By

View all

Aineto DScala EOnaindia ESerina IKoenig SStern RVallati M(2023)Falsification of cyber-physical systems using PDDL+ planningProceedings of the Thirty-Third International Conference on Automated Planning and Scheduling10.1609/icaps.v33i1.27172(2-6)Online publication date: 8-Jul-2023
https://dl.acm.org/doi/10.1609/icaps.v33i1.27172
Corso AMoss RKoren MLee RKochenderfer M(2022)A Survey of Algorithms for Black-Box Safety Validation of Cyber-Physical SystemsJournal of Artificial Intelligence Research10.1613/jair.1.1271672(377-428)Online publication date: 4-Jan-2022
https://dl.acm.org/doi/10.1613/jair.1.12716
Wang YRoohi NWest MViswanathan MDullerud G(2021)Verifying Stochastic Hybrid Systems with Temporal Logic Specifications via Model ReductionACM Transactions on Embedded Computing Systems10.1145/348338020:6(1-27)Online publication date: 15-Nov-2021
https://dl.acm.org/doi/10.1145/3483380
Show More Cited By

Index Terms

Towars a Theory of Stochastic Hybrid Systems
1. Mathematics of computing
  1. Probability and statistics
    1. Stochastic processes

Index terms have been assigned to the content through auto-classification.

Recommendations

Stability analysis for stochastic hybrid systems

This survey addresses stability analysis for stochastic hybrid systems (SHS), which are dynamical systems that combine continuous change and instantaneous change and that also include random effects. We re-emphasize the common features found in most of ...
Abstraction-based Synthesis of Stochastic Hybrid Systems
HSCC '24: Proceedings of the 27th ACM International Conference on Hybrid Systems: Computation and Control

In this work, we develop a framework for formally constructing finite abstractions, also known as finite Markov decision processes (MDPs), for continuous-space stochastic hybrid systems. These complex systems encompass both continuous dynamics, ...
Limiting Discounted-Cost Control of Partially Observable Stochastic Systems

This paper presents two main results on partially observable (PO) stochastic systems. In the first one, we consider a general PO system $$ x_{t+1}= F (x_t, a_t, xi_t), , y_t= G(x_t, eta_t) (t=0,1,ldots) hspace{1in} (*) $$ on Borel spaces, with possibly ...

Comments

Information & Contributors

Information

Published In

HSCC '00: Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control

March 2000

461 pages

ISBN:3540672591

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 23 March 2000

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

30
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 16 Oct 2024

Other Metrics

View Author Metrics

Citations

Cited By

View all

Aineto DScala EOnaindia ESerina IKoenig SStern RVallati M(2023)Falsification of cyber-physical systems using PDDL+ planningProceedings of the Thirty-Third International Conference on Automated Planning and Scheduling10.1609/icaps.v33i1.27172(2-6)Online publication date: 8-Jul-2023
https://dl.acm.org/doi/10.1609/icaps.v33i1.27172
Corso AMoss RKoren MLee RKochenderfer M(2022)A Survey of Algorithms for Black-Box Safety Validation of Cyber-Physical SystemsJournal of Artificial Intelligence Research10.1613/jair.1.1271672(377-428)Online publication date: 4-Jan-2022
https://dl.acm.org/doi/10.1613/jair.1.12716
Wang YRoohi NWest MViswanathan MDullerud G(2021)Verifying Stochastic Hybrid Systems with Temporal Logic Specifications via Model ReductionACM Transactions on Embedded Computing Systems10.1145/348338020:6(1-27)Online publication date: 15-Nov-2021
https://dl.acm.org/doi/10.1145/3483380
Wu YHu JZhang X(2019)Moment estimators for the parameters of Ornstein-Uhlenbeck processes driven by compound Poisson processesDiscrete Event Dynamic Systems10.1007/s10626-019-00276-y29:1(57-77)Online publication date: 1-Mar-2019
https://dl.acm.org/doi/10.1007/s10626-019-00276-y
Gburek DBaier C(2018)Bisimulations, logics, and trace distributions for stochastic systems with rewardsProceedings of the 21st International Conference on Hybrid Systems: Computation and Control (part of CPS Week)10.1145/3178126.3178139(31-40)Online publication date: 11-Apr-2018
https://dl.acm.org/doi/10.1145/3178126.3178139
Huang CChen XLin WYang ZLi X(2017)Probabilistic Safety Verification of Stochastic Hybrid Systems Using Barrier CertificatesACM Transactions on Embedded Computing Systems10.1145/312650816:5s(1-19)Online publication date: 27-Sep-2017
https://dl.acm.org/doi/10.1145/3126508
Papadopoulos APrandini M(2016)Model reduction of switched affine systemsAutomatica (Journal of IFAC)10.1016/j.automatica.2016.03.01970:C(57-65)Online publication date: 1-Aug-2016
https://dl.acm.org/doi/10.1016/j.automatica.2016.03.019
Peng YWang SZhan NZhang L(2015)Extending Hybrid CSP with Probability and StochasticityProceedings of the First International Symposium on Dependable Software Engineering: Theories, Tools, and Applications - Volume 940910.1007/978-3-319-25942-0_6(87-102)Online publication date: 4-Nov-2015
https://dl.acm.org/doi/10.1007/978-3-319-25942-0_6
Lin HAntsaklis P(2014)Hybrid Dynamical SystemsFoundations and Trends in Systems and Control10.1561/26000000011:1(1-172)Online publication date: 31-Mar-2014
https://dl.acm.org/doi/10.1561/2600000001
Temoçin BWeber G(2014)Optimal control of stochastic hybrid system with jumpsJournal of Computational and Applied Mathematics10.1016/j.cam.2013.10.021259(443-451)Online publication date: 1-Mar-2014
https://dl.acm.org/doi/10.1016/j.cam.2013.10.021
Show More Cited By

View Options

View options

Get Access

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Abstract

References

Cited By

Index Terms

Recommendations

Stability analysis for stochastic hybrid systems

Abstraction-based Synthesis of Stochastic Hybrid Systems

Limiting Discounted-Cost Control of Partially Observable Stochastic Systems

Comments

Information

Published In

Publisher

Publication History

Qualifiers

Contributors

Other Metrics

Bibliometrics

Article Metrics

Other Metrics

Citations

Cited By

View options

Get Access

Login options

Full Access

Figures

Other

Share

Share this Publication link

Share on social media

Affiliations