Abstract
Consideration is given to the problem of stabilization of a specified (supporting) mode as a degenerate problem of minimization of the root-mean-square deviation from it where there are no deviations of control actions. This formulation makes it possible to completely use available limited control resources for stabilization. We propose a method of approximate optimal synthesis in the neighborhood of a turnpike manifold that is obtained as a solution in the form of optimal synthesis of linearly quadratic problem with unbounded linear control. The investigation is performed for a linearized discrete model of the controlled system; however, the obtained stabilizing control can be applied in the initial nonlinear system directly or after the correction by regular iterations.
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Original Russian Text © M.Yu. Ukhin, 2008, published in Avtomatika i Telemekhanika, 2008, No. 4, pp. 149–156.
This work was supported by the Russian Foundation for Basic Research, project no. 05-01-00260.
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Ukhin, M.Y. Degenerate problem of stabilization of a specified trajectory. Autom Remote Control 69, 682–689 (2008). https://doi.org/10.1134/S0005117908040140
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DOI: https://doi.org/10.1134/S0005117908040140