Mathematical Methods in Robust Control of Linear Stochastic Systems

Drăgan, Vasile; Morozan, Toader; Stoica, Adrian–Mihail

doi:10.1007/978-1-4614-8663-3

Cited by 110 publications

(199 citation statements)

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“…The definition of stochastic stabilizability, which was an essential assumption in the section introduced by Li et al [18], Dragan and Morozan [11], Dragan et al [12]. which is asymptotically mean-square stable, i.e., lim…”

Section: Resultsmentioning

confidence: 99%

“…Partially, this is due to the fact that often dynamic systems are inherently vulnerable to component failures or repairs, changing of subsystem interconnections, or abrupt variations of the nominal operating conditions. There exists a very rich list of references of articles and books dealing with control problems for this class of systems (see, e.g., [3,11,12,22] and the references therein). Now, this kind of system has proven being useful in describing hybrid dynamics arising in electric power systems [21], communications systems [1], control of nuclear power plants [27], manufacturing systems [4,14], and economic systems (see [8,13,20,37,38], etc).…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Nash Games for Markov Jump Linear Systems with State- and Control-Dependent Noise

Zhu

Zhang

Ning

2014

J. Oper. Res. Soc. China

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This paper investigates Nash games for a class of linear stochastic systems governed by Itô's differential equation with Markovian jump parameters both in finite-time horizon and infinite-time horizon. First, stochastic Nash games are formulated by applying the results of indefinite stochastic linear quadratic (LQ) control problems. Second, in order to obtain Nash equilibrium strategies, crosscoupled stochastic Riccati differential (algebraic) equations (CSRDEs and CSRAEs) are derived. Moreover, in order to demonstrate the validity of the obtained results, stochastic H 2 /H ? control with state-and control-dependent noise is discussed as an immediate application. Finally, a numerical example is provided.

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Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic Nash Games for Markov Jump Linear Systems with State- and Control-Dependent Noise

Zhu

Zhang

Ning

2014

J. Oper. Res. Soc. China

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“…From [13], for all t 0 ≥ 0 and ξ measurable with respect to F t and E|ξ| 2 < ∞ there exists a unique continuous solution (1), that is the solution of the matrix equation…”

Section: A Problem Reductionmentioning

confidence: 99%

“…Some of the publications related to the robust filter problem for time delay systems are [6]- [9]. Additionally, comprehensive reviews of theory and algorithms for stochastic or time delay systems are given in [5] and [10]- [13].…”

Section: Introductionmentioning

confidence: 99%

Optimal filtering for Itô-Stochastic continuous-time systems with multiple delayed measurements

Kong

Saif

Zhang

2011

Proceedings of the 2011 American Control Conference

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This paper focuses on the problem of Kalman filtering for Itô stochastic continuous-time systems with multiple delayed measurements, for which very little work exist to date. For an Itô-stochastic system, its stochastic differential and integral have a significant place and are different from other stochastic systems owing to the Wiener or the Brownian process. In this paper, an Itô stochastic continuous-time system with multiple delayed measurements is first reduced to a system with delay free measurements by applying the stochastic analysis and calculus of stochastic variables. Next, the Itô differentials for the optimal filter and its error variance are derived. Finally, through an illustrative example, the performance of the designed optimal filter is verified.

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“…Initially optimal control was applied to sciences such as economics and financial, but today it is used in most of them. Performance index and differential equation are control problems parts, to solve these problems we can use Hamilton-Jacobi-Bellman equation by using them [3], [6], [7]. Using optimal control in economics and financial is more attractive, for example finding a model for analyzing dynamic pairs trading strategies.…”

Section: Introductionmentioning

confidence: 99%

Credit Rating via Dynamic Slack-Based Measure And It´s Optimal Investment Strategy

Delavarkhalafi¹,

A.Poursherafatan²

2015

Data Envelopment Analysis and Decision Science

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In this paper we check the credit rating of firms applied for a loan. In this regard we introduce a model, named Dynamic Slack-Based Measure (DSBM) for measuring credit rating of applicant companies. Selection of financial ratios that represent the financial state of a company -in the best possible way-is one of the most challenging parts of any credit rating analysis. At first, ranking needs to identify the appropriate variables. Therefore we introduce five financial variables to provide a ranking. As noted above, we assess the performance of these firms. Then we introduce the dynamic model of SBM and theorems, also we discuss the overall structure of DSBM. Then we will present the implementation and the simulation model. After that, we propose a stochastic controlled dynamic system model to express the optimal strategy. Banks expect companies selected with DSBM model, act in accordance with this strategy. This stochastic dynamic system is originated from the balance sheets of firms applying for a loan. Finally we evaluate the performance of the system and strategy problem.

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Mathematical Methods in Robust Control of Linear Stochastic Systems

Cited by 110 publications

References 0 publications

Stochastic Nash Games for Markov Jump Linear Systems with State- and Control-Dependent Noise

Stochastic Nash Games for Markov Jump Linear Systems with State- and Control-Dependent Noise

Optimal filtering for Itô-Stochastic continuous-time systems with multiple delayed measurements

Credit Rating via Dynamic Slack-Based Measure And It´s Optimal Investment Strategy

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Mathematical Methods in Robust Control of Linear Stochastic Systems

Cited by 110 publications

References 0 publications

Stochastic Nash Games for Markov Jump Linear Systems with State- and Control-Dependent Noise

Stochastic Nash Games for Markov Jump Linear Systems with State- and Control-Dependent Noise

Optimal filtering for It&#x00F4;-Stochastic continuous-time systems with multiple delayed measurements

Credit Rating via Dynamic Slack-Based Measure And It´s Optimal Investment Strategy

Contact Info

Product

Resources

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Optimal filtering for Itô-Stochastic continuous-time systems with multiple delayed measurements