Anisotropy-based control design for linear time--invariant systems with moments constraints of disturbances

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Abstract

In this paper, a linear discrete time-invariant system with control under the influence of a colored disturbance is considered. The external disturbance is selected from the class of non-centered stationary Gaussian sequences of random vectors with a known restriction on the level of mean anisotropy. For the specified class of control objects, a dynamic regulator is introduced, with the help of which it is necessary to ensure the boundedness of the anisotropic norm from an external disturbance to the controlled output of a closed--loop system. The control design problem is to construct an anisotropy--based dynamic regulator in terms of state--space representation. The boundedness of the closed--loop system is provided by anisotropy--based small gain theorem. Using linearizing reversible variable change, the problem can be reduced to a numerical solution of the convex optimization problem with special constraints characteristic of anisotropy--based theory. In the formulation of the problem, it is assumed that the expectation of the external disturbance is unknown, but a condition on it in the form of inequality is known. This parameter causes an additional constraint to appear in the convex optimization problem. The resulting system of inequalities is linear matrix inequalities in combination with an inequality of a special type, which is nonlinear with respect to unknown parameters, but at the same time convex in these parameters. The problem of finding the regulator matrices can be solved by standard methods.

About the authors

Alexander Viktorovich Yurchenkov

V.A. Trapeznikov Institute of Control Sciences of RAS

Email: alexander.yurchenkov@yandex.ru
Moscow

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