Optimal control of stochastic hybrid system with jumps: A numerical approximation

Date

2014-03-15

Author

Temoçin, Büşra Zeynep
Weber, Gerhard Wilhelm

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

170
views

0
downloads

The generalized class of stochastic hybrid systems consists of models with regime changes including the occurrence of impulsive behavior. In this paper, the stochastic hybrid processes with jumps are approximated by locally consistent Markov decision processes that preserve local mean and covariance. We further apply a randomized switching policy for approximating the dynamics on the switching boundaries. To investigate the validity of the approximation, we study a stochastic optimal control problem. On the basis of the discrete approximation, we solve the optimal control problem and show that the solution obtained from the discretized problem converges to the solution of the original optimal control problem.

Subject Keywords

Stochastic hybrid systems, Jump diffusions, Markov processes, Switching approximation, Optimal control

URI

https://hdl.handle.net/11511/56845

Journal

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

DOI

https://doi.org/10.1016/j.cam.2013.10.021

Collections

Graduate School of Applied Mathematics, Article

Suggestions

OpenMETU
Core

Stochastic simulations of biological networks under impulses Yazıcı, Müge; Purutçuoğlu Gazi, Vilda; Department of Statistics (2016) The impulses are one of the sources of fluctuations which lead to the sharp changes in the biochemical systems such as the changes in epidemic and population models. In this study, as the novelty, we implement these effects in exact stochastic simulation algorithms, namely, the Gillespie method and the first reaction method, by changing the chemical master equations (CME) with impulses. Hereby in the extension of these approaches with impulses, we consider different scenarios such as the sudden decrease of ...
Optimal Limit Order Book Trading Strategies with Stochastic Volatility in the Underlying Asset Aydoğan, Burcu; Uğur, Ömür; Aksoy, Ümit (2022-1-01) In quantitative finance, there have been numerous new aspects and developments related with the stochastic control and optimization problems which handle the controlled variables of performing the behavior of a dynamical system to achieve certain objectives. In this paper, we address the optimal trading strategies via price impact models using Heston stochastic volatility framework including jump processes either in price or in volatility of the price dynamics with the aim of maximizing expected return of t...
Application of stochastic simulations of biological networks under different impulsive scenarios Purutçuoğlu Gazi, Vilda (null; 2016-06-01) The impulses are one of the sources of fluctuations which lead to the sharp changes in the biochemical systems such as the changes in epidemic and population models. These effects have been comprehensively studied under deterministic models, whereas, have not been analyzed in stochastic models. Hereby, in this study, we implement these effects in two exact stochastic simulation algorithms, namely, the direct method and the first reaction method under different dimensional systems and impulses scenarios. In ...
Hierarchical control with partial observations: Sufficient conditions Boutin, Olivier; Komenda, Jan; Masopust, Tomas; Schmidt, Klaus Verner; Van Schuppen, Jan H. (2011-12-01) In this paper, hierarchical control of both monolithic and modular discrete-event systems under partial observations is studied. Two new conditions, called observation consistency and local observation consistency, are proposed. These conditions are sufficient for the preservation of observability between the original and the abstracted plant. Moreover, it is shown that both conditions are compositional, that is, they are preserved by the synchronous product. This property makes it possible to use hierarchi...
Linear Analysis of Zero-Lift Pitching Moment Coefficient and Gravity Effects on Missile Autopilots Ovec, Naz T.; Erer, Koray S.; Kutay, Ali Türker (2015-03-14) The most of the studies on disturbance rejection are covered with robust control methods, where this paper suggests a narrowed but a more simplified linear model based technique to assess the robustness of the controllers. In this paper presented, the problems originated from the disturbances are aimed to be obtained as far in advance as possible. The method used in this work reduces the iterative fine tuning time course between the non-linear simulation and the linear model; hence it enhances the authority...

Citation Formats

B. Z. Temoçin and G. W. Weber, “Optimal control of stochastic hybrid system with jumps: A numerical approximation,” JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, pp. 443–451, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/56845.