Abstract
This paper deals with the technique application of adaptation on manifolds for stochastic nonlinear models. The analysis and control approach are used to implement the principle of directed self-organization and decomposition of non-linear dynamic systems is used. A new problem statement for the synthesis of a robust stochastic regulator based on the principles of control on manifolds is discussed. The paper presents a new algorithm to design a stochastic discrete control system and provides illustrative example of solving nonlinear stochastic control problem based on the designed regulator. The properties of the control algorithm for a second-order object are formulated. It is shown that the designed control gives a minimum of variance of the response variable and a minimal dispersion of the Lagrange-Euler function, which is used for the structure of the stochastic control system.
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Acknowledgment
The reported study was funded by RFBR according to the research project №. 17-08-00920.
The author expresses her acknowledgment to Professor Kolesnikov A.A., Honored worker of science and engineering of the Russian Federation, for useful discussions.
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Kolesnikova, S. (2019). Stochastic Discrete Nonlinear Control System for Minimum Dispersion of the Output Variable. In: Silhavy, R. (eds) Cybernetics and Automation Control Theory Methods in Intelligent Algorithms. CSOC 2019. Advances in Intelligent Systems and Computing, vol 986. Springer, Cham. https://doi.org/10.1007/978-3-030-19813-8_33
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DOI: https://doi.org/10.1007/978-3-030-19813-8_33
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