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Multiplicative stochastic systems: Optimization and analysis

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Abstract

We consider the H 2/H ∞-optimal control problem for a dynamical system defined by a linear stochastic Itô equation whose drift and diffusion coefficients linearly depend on the state vector, the control signal, and the external disturbance. The optimization is carried out under the a priori requirement of maximum possible dam** of the harmful influence of external disturbances on the system operation. We present theorems on the solvability of matrix Riccati differential equations to which the original optimization problem is reduced.

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Authors and Affiliations

  1. Institute of Control Sciences of the Russian Academy of Sciences, Moscow, 117997, Russia

    M. E. Shaikin

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  1. M. E. Shaikin
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Correspondence to M. E. Shaikin.

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Original Russian Text © M.E. Shaikin, 2017, published in Differentsial’nye Uravneniya, 2017, Vol. 53, No. 3, pp. 391–406.

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Shaikin, M.E. Multiplicative stochastic systems: Optimization and analysis. Diff Equat 53, 382–397 (2017). https://doi.org/10.1134/S0012266117030090

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  • DOI: https://doi.org/10.1134/S0012266117030090

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