Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Optimization and Control

arXiv:1106.3759 (math)
[Submitted on 19 Jun 2011 (v1), last revised 1 Aug 2011 (this version, v2)]

Title:Frequency Theorem for discrete time stochastic system with multiplicative noise

Authors:Peter Situmbeko Nalitolela, Nikolai Dokuchaev
View PDF
Abstract:In this paper we consider the problem of minimizing a quadratic functional for a discrete-time linear stochastic system with multiplicative noise, on a standard probability space, in infinite time horizon. We show that the necessary and sufficient conditions for the existence of the optimal control can be formulated as matrix inequalities in frequency domain. Furthermore, we show that if the optimal control exists, then certain Lyapunov equations must have a solution. The optimal control is obtained by solving a deterministic linear-quadratic optimal control problem whose functional depends on the solution to the Lyapunov equations. Moreover, we show that under certain conditions, solvability of the Lyapunov equations is guaranteed. We also show that, if the frequency inequalities are strict, then the solution is unique up to equivalence.
Subjects: Optimization and Control (math.OC); Systems and Control (eess.SY)
MSC classes: 93E20, 49N10
Cite as: arXiv:1106.3759 [math.OC]
  (or arXiv:1106.3759v2 [math.OC] for this version)
  https://doi.org/10.48550/arXiv.1106.3759

Submission history

From: Peter Nalitolela [view email]
[v1] Sun, 19 Jun 2011 16:40:26 UTC (10 KB)
[v2] Mon, 1 Aug 2011 04:11:23 UTC (10 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.OC
< prev   |   next >
new | recent | 2011-06
Change to browse by:
cs
cs.SY
math

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)