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On stochastic sensitivity control in discrete systems

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Abstract

For a discrete nonlinear controlled stochastic system, we consider the scatter range of random states around the equilibrium. We consider the problem of designing a regulator that would allow to form a stable stationary probability distribution with a given covariance around this equilibrium. For small random perturbations, we propose to approximate the scatter range of trajectories in the neighborhood of a stable equilibrium with a stochastic sensitivity matrix. We pose the regulator design problem for a regulator that forms a desired stochastic sensitivity matrix in a controlled system. For the considered design problem, we introduce the notion of a reachability set and give its constructive description. The efficiency of the proposed approach is demonstrated on the example of controlling the stationary distribution on random states in stochastically perturbed Verhulst and Hénon models.

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Authors and Affiliations

  1. Ural State University, Ekaterinburg, Russia

    I. A. Bashkirtseva & L. B. Ryashko

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  1. I. A. Bashkirtseva
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  2. L. B. Ryashko
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This work was supported in part by the Russian Foundation for Basic Research, projects nos. 09-01-00026, 09-08-00048, 10-01-96022ural, Federal Agency of Education, project no. 2.1.1/2571, and the Federal Target Program, project no. 02.740.11.0202.

Original Russian Text © I.A. Bashkirtseva, L.B. Ryashko, 2010, published in Avtomatika i Telemekhanika, 2010, No. 9, pp. 103–119.

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Bashkirtseva, I.A., Ryashko, L.B. On stochastic sensitivity control in discrete systems. Autom Remote Control 71, 1833–1848 (2010). https://doi.org/10.1134/S0005117910090079

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