Elena N. Gryazina

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We address randomized methods for control and optimization based on generating points uniformly distributed in a set. For control systems this sets are either stability domain in the space of feedback controllers, or quadratic stability domain, or robust stability domain, or level set for a performance specification. By generating random points in the(More)
This paper introduces a new Matlab package, Ract, aimed at solving a class of probabilistic analysis and synthesis problems arising in control. The package offers a convenient way for defining various types of structured uncertainties as well as formulating and analyzing the ensuing robustness analysis tasks from a probabilistic point of view. It also(More)
This paper addresses the problem of stabilization of LTI systems via static output feedback (sof) and optimal H2 and H∞ sof control. Various algorithms based on the same mixed LMI/randomized approach are defined for the computation of sets of stabilizing sof and optimal H2 and H∞ sof control. The main idea is to combine a particular relaxed LMI(More)
— In previous works the authors proposed to use Hit-and-Run (H&R) versions of Markov Chain Monte Carlo (MCMC) algorithms for various problems of control and optimization. However the results are unsatisfactory for " bad " sets, such as level sets of ill-posed functions. The idea of the present paper is to exploit the technique developed for interior-point(More)
Hit-and-Run is known to be one of the best random sampling algorithms, its mixing time is polynomial in dimension. Nevertheless, in practice the number of steps required to achieve uniformly distributed samples is rather high. We propose new random walk algorithm based on billiard trajectories. Numerical experiments demonstrate much faster convergence to(More)
Randomized methods for control and optimization become highly popular [1, 2]. They often exploit modern versions of Monte Carlo technique, based on Markov Chain Monte Carlo (MCMC) approach [3, 4]. The examples of such MCMC methods as Hit-and-Run and Shake-and-Bake applied to various control and optimization problems are provided in [5, 6]. However the(More)
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