Abstract:
A number of problems for dynamic analyze, state estimation, and control design for linear and nonlinear system with uncertain disturbancies can be reduced to optimization problems with differential linear matrix inequalities. The numerical methods are offered for solving such problems by discretization on the considered interval and reducing to the set of interconnected optimization problems at discrete points in time with constraints in the form of linear matrix inequalities. The proposed methods, in comparison with those existing in the literature, guarantee the fulfillment of the differential constaints and allow one to determine the control gain not only at the sampling points but at all points inside the considered time interval.
Keywords:
state estimation, differential linear matrix inequalities, optimization problem, numerical solution, control design.
Citation:
A. I. Malikov, D. I. Dubakina, “Numerical methods for solving optimization problems with differential linear matrix inequalities”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 4, 74–86
\Bibitem{MalDub20}
\by A.~I.~Malikov, D.~I.~Dubakina
\paper Numerical methods for solving optimization problems with differential linear matrix inequalities
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2020
\issue 4
\pages 74--86
\mathnet{http://mi.mathnet.ru/ivm9563}
\crossref{https://doi.org/10.26907/0021-3446-2020-4-74-86}
Linking options:
https://www.mathnet.ru/eng/ivm9563
https://www.mathnet.ru/eng/ivm/y2020/i4/p74
This publication is cited in the following 2 articles:
A. I. Malikov, “State estimation and stabilization of nonlinear systems with sampled-data control and uncertain disturbances”, Autom. Remote Control, 82:4 (2021), 634–653
A. I. Malikov, “State estimation and control for linear aperiodic impulsive systems with uncertain disturbances”, Russian Math. (Iz. VUZ), 65:6 (2021), 36–46
Citation in format AMSBIB
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