Optimal control of a class of piecewise deterministic processes

A new control strategy for a class of piecewise deterministic processes (PDP) is presented. In this class, PDP stochastic processes consist of ordinary differential equations that are subject to random switches corresponding to a discrete Markov process. The proposed strategy aims at controlling the probability density function (PDF) of the PDP. The optimal control formulation is based on the hyperbolic Fokker–Planck system that governs the time evolution of the PDF of the PDP and on tracking objectives of terminal configuration with a target PDF. The corresponding optimization problems are formulated as a sequence of open-loop hyperbolic optimality systems following a model predictive control framework. These systems are discretized by first-order schemes that guarantee positivity and conservativeness of the numerical PDF solution. The effectiveness of the proposed computational control framework is validated considering PDP with dichotomic noise.

Non-Markovian Dynamic And Nmr Spectra In Solids

The influence of non-Markov molecular motions on NMR absorption spectra has been investigated. It has been shown that the simple non-Markov model of water molecular motion with fluctuations driven by dichotomic noise very well explains the observed temperature dependence of NMR spectra in the mineral natrolite. - PACS number: 05.40.+j, 33.25.+k, 76.20.+q