The information path functional approach for a dynamic modeling of a controllable stochastic process

Details The information path functional approach for a dynamic modeling of a controllable stochastic process The information path functional approach for a dynamic modeling of a controllable stochastic process

2011-12-29

arxiv.org/abs/1201.0035v1

Computer Science

Systems and Control

36 pages including 5 figures

Scientific paper

We study a stochastic control system, described by Ito's controllable equation, and evaluate the solutions by an entropy functional (EF), defined by the equation's functions of controllable drift and diffusion. Considering a control problem for this functional, we solve the EF control's variation problem (VP), which leads to both a dynamic approximation of the process' entropy functional by an information path functional (IPF) and to an information dynamic model (IDM) of the stochastic process. The IPF variation equations allow finding the optimal control functions, applied to both stochastic system and the IDM for a joint solution of the identification and optimal control problems, combined with a state's consolidation. In this optimal dual strategy, the IPF optimum predicts each current control action not only in terms of a total functional path goal, but also by setting for each following control action the renovated values of this functional's controllable drift and diffusion, identified during the optimal movement, which concurrently correct this goal. The VP information invariants allow optimal encoding of the identified dynamic model's operator and control. Examples illustrate the procedure of solving these problems, which has been implemented in practice. Key words: Entropy's and information path functionals, variation equations, information invariants, controllable dynamics, identification, cooperation, encoding.

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