Dynamic approximation of a random information functional

Lerner, Vladimir S.

doi:10.1016/j.jmaa.2006.04.041

Cited by 6 publications

(15 citation statements)

References 4 publications

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“…The variation problem is considered for the two level's micro-and macrodescriptions of complex object, which is characterized by a controllable random microprocessx t and a dynamic macroprocess x t , both undergo the control u t and disturbances ζ t = ζ(t, ω) that depend on a current randomness ω [1].…”

Section: The Problem Statementsmentioning

confidence: 99%

“…with the standard limitations on function of controllable shift and diffusion, being a continuous, continuously differentiable everywhere on Δ, excluding maybe the set {τ k } m k=1 , defined by the applied control u t [1], which belongs to a space of the piece-wise continuous on Δ functions KC(Δ, U ), u ∈ U . Unknown macroprocess follows from an extremal probabilistic approximation of the microlevel process with the aid of the applied control…”

Section: The Problem Statementsmentioning

confidence: 99%

“…(Instead of disturbances ζ t , a given microprocessx 1 t can be used in (2.3)(b)-(c).) According to [1] for the considered Markov diffusion processes, we get the following expressions for the probabilities:…”

Section: The Problem Statementsmentioning

confidence: 99%

“…Following R. Feynman's ideology [2], we apply the path functional, found in [1], to uncover the unknown information regularities of a random process. The considered variation principle's mathematical and information formalisms describe the information regularities of creation of the dynamics from stochastics.…”

Section: Introductionmentioning

confidence: 99%

“…This leads to the path functional's connection to information theory and to developing the model, obtained by a minimization of such an information functional, which becomes the object's own (eigen)information functional. The described solution of the variation problem is an exceptional one because of both the targeting of the newly established path functional [1] and the connection of the microlevel stochastics to information macrodynamics (IMD). No particularly analogous solutions currently exist in known publications.…”

Section: Introductionmentioning

confidence: 99%

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Solution to the variation problem for information path functional of a controlled random process

Lerner

2007

Journal of Mathematical Analysis and Applications

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The paper introduces a new approach to dynamic modeling, using the variation principle, applied to a functional on trajectories of a controlled random process, and its connection to the process' information functional. In [V.S. Lerner, Dynamic approximation of a random information functional, J. Math. Anal. Appl. 327 (1) (2007) 494-514, available online 5-24-06], we presented the information path functional with the Lagrangian, determined by the parameters of a controlled stochastic equation. In this paper, the solution to the path functional's variation problem provides both a dynamic model of a random process and the model's optimal control, which allows us to build a two-level information model with a random process at the microlevel and a dynamic process at the macrolevel. A wide class of random objects, modeled by the Markov diffusion process and a common structure of the process' information functional, leads to a universal information structure of the dynamic model, which is specified and identified on a particular object with the applied optimal control functions. The developed mathematical formalism, based on classical methods, is aimed toward the solution of problems identification, combined with an optimal control synthesis, which is practically implemented and also demonstrated in the paper's example.

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Section: The Problem Statementsmentioning

confidence: 99%

Section: The Problem Statementsmentioning

confidence: 99%

Section: The Problem Statementsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Solution to the variation problem for information path functional of a controlled random process

Lerner

2007

Journal of Mathematical Analysis and Applications

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The boundary value problem and the Jensen inequality for an entropy functional of a Markov diffusion process

Lerner

2009

Journal of Mathematical Analysis and Applications

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The paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process, expressed through an additive functional of the diffusion process, with a Lagrangian, determined by the parameters of a controlled stochastic equation. These results include a minimum condition for the entropy functional and the functional's Jensen inequality, which both are useful for the solution of important mathematical and applied problems.

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Cooperative information space distributed macromodels

Lerner

2008

International Journal of Control

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Dynamic approximation of a random information functional

Cited by 6 publications

References 4 publications

Solution to the variation problem for information path functional of a controlled random process

Solution to the variation problem for information path functional of a controlled random process

The boundary value problem and the Jensen inequality for an entropy functional of a Markov diffusion process

Cooperative information space distributed macromodels

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