Robust Control Design for Suppressing Random Exogenous Disturbances in Parametrically Uncertain Linear Systems
The design problems of robust static controllers for discrete-time systems with norm-
bounded parametric uncertainties and random input disturbances are considered. The con-
trollers under consideration stabilize the plant for all possible values of uncertainty from a
given set of parameters and also guarantee a desired suppression level for random exogenous
disturbances. A numerical example is given.
In this paper we consider the task of inner objects mapping for the building with a bunch of moving around it autonomous agents which use narrow beam of radio waves using WiFi frequency (2.4 GHz). Linear model of pixel-wise radio waves attenuation is considered. SIRT algorithm with TV and Tikhonov regularizations is used for the task of tomography reconstruction. Properties of the presented model are studied during simulation using synthetic data consisting of 8 buildings with inner object with different shapes. Dependency between mapping quality and transmission power is found. Simulation results confirm suggested approachs usability
In this paper, a new variant of accelerated gradient descent is proposed. The proposed method does not require any information about the objective function, uses exact line search for the practical accelerations of convergence, converges according to the well-known lower bounds for both convex and non-convex objective functions, possesses primal–dual properties and can be applied in the non-euclidian set-up. As far as we know this is the first such method possessing all of the above properties at the same time. We also present a universal version of the method which is applicable to non-smooth problems. We demonstrate how in practice one can efficiently use the combination of line-search and primal-duality by considering a convex optimization problem with a simple structure (for example, linearly constrained)
Modern imaging methods rely strongly on Bayesian inference techniques to solve challenging imaging problems. Currently, the predominant Bayesian computation approach is convex optimization, which scales very efficiently to high-dimensional image models and delivers accurate point estimation results. However, in order to perform more complex analyses, for example, image uncertainty quantification or model selection, it is necessary to use more computationally intensive Bayesian computation techniques such as Markov chain Monte Carlo methods. This paper presents a new and highly efficient Markov chain Monte Carlo methodology to perform Bayesian computation for high-dimensional models that are log-concave and nonsmooth, a class of models that is central in imaging sciences. The methodology is based on a regularized unadjusted Langevin algorithm that exploits tools from convex analysis, namely, Moreau--Yoshida envelopes and proximal operators, to construct Markov chains with favorable convergence properties. In addition to scaling efficiently to high-dimensions, the method is straightforward to apply to models that are currently solved by using proximal optimization algorithms. We provide a detailed theoretical analysis of the proposed methodology, including asymptotic and nonasymptotic convergence results with easily verifiable conditions, and explicit bounds on the convergence rates. The proposed methodology is demonstrated with four experiments related to image deconvolution and tomographic reconstruction with total-variation and $\ell_1$ priors, where we conduct a range of challenging Bayesian analyses related to uncertainty quantification, hypothesis testing, and model selection in the absence of ground truth.
We consider smooth stochastic convex optimization problems in the context of algorithms which are based on directional derivatives of the objective function. This context can be considered as an intermediate one between derivative-free optimization and gradient-based optimization. We assume that at any given point and for any given direction, a stochastic approximation for the directional derivative of the objective function at this point and in this direction is available with some additive noise. The noise is assumed to be of an unknown nature, but bounded in the absolute value. We underline that we consider directional derivatives in any direction, as opposed to coordinate descent methods which use only derivatives in coordinate directions. For this setting, we propose a non-accelerated and an accelerated directional derivative method and provide their complexity bounds. Our non-accelerated algorithm has a complexity bound which is similar to the gradient-based algorithm, that is, without any dimension-dependent factor. Our accelerated algorithm has a complexity bound which coincides with the complexity bound of the accelerated gradient-based algorithm up to a factor of square root of the problem dimension. We extend these results to strongly convex problems.
In this paper we introduce a unified analysis of a large family of variants of proximal stochastic gradient descent (SGD) which so far have required different intuitions, convergence analyses, have different applications, and which have been developed separately in various communities. We show that our framework includes methods with and without the following tricks, and their combinations: variance reduction, importance sampling, mini-batch sampling, quantization, and coordinate sub-sampling. As a by-product, we obtain the first unified theory of SGD and randomized coordinate descent (RCD) methods, the first unified theory of variance reduced and non-variance-reduced SGD methods, and the first unified theory of quantized and non-quantized methods. A key to our approach is a parametric assumption on the iterates and stochastic gradients. In a single theorem we establish a linear convergence result under this assumption and strong-quasi convexity of the loss function. Whenever we recover an existing method as a special case, our theorem gives the best known complexity result. Our approach can be used to motivate the development of new useful methods, and offers pre-proved convergence guarantees. To illustrate the strength of our approach, we develop five new variants of SGD, and through numerical experiments demonstrate some of their properties.
We consider convex optimization problems with the objective function having Lipshitz-continuous p-th order derivative, where p ≥ 1. We propose a new tensor method, which closes the gap between the lower O ε − 2 3p+1 and upper O ε − 1 p+1 iteration complexity bounds for this class of optimization problems. We also consider uniformly convex functions, and show how the proposed method can be accelerated under this additional assumption. Moreover, we introduce a p-th order condition number which naturally arises in the complexity analysis of tensor methods under this assumption. Finally, we make a numerical study of the proposed optimal method and show that in practice it is faster than the best known accelerated tensor method. We also compare the performance of tensor methods for p = 2 and p = 3 and show that the 3rd-order method is superior to the 2nd-order method in practice. Keywords: Convex optimization, unconstrained minimization, tensor methods, worst-case complexity, global complexity bounds, condition number.
We study the complexity of approximating the Wasserstein barycenter of m discrete measures, or histograms of size n, by contrasting two alternative approaches that use entropic regularization. The first approach is based on the Iterative Bregman Projections (IBP) algorithm for which our novel analysis gives a complexity bound proportional to $m n^2 / \epsilon^2$ to approximate the original non-regularized barycenter. On the other hand, using an approach based on accelerated gradient descent, we obtain a complexity proportional to $m n^2 / \epsilon$. As a byproduct, we show that the regularization parameter in both approaches has to be proportional to $\epsilon$, which causes instability of both algorithms when the desired accuracy is high. To overcome this issue, we propose a novel proximal-IBP algorithm, which can be seen as a proximal gradient method, which uses IBP on each iteration to make a proximal step. We also consider the question of scalability of these algorithms using approaches from distributed optimization and show that the first algorithm can be implemented in a centralized distributed setting (master/slave), while the second one is amenable to a more general decentralized distributed setting with an arbitrary network topology.
Modern transport systems are characterized by the development and implementation of intelligent transport technologies. Today, dynamic forecast models are not used in practice in the operation of a passenger terminal. Decision making is based on some regulatory values for passenger traffic, but this is not sufficient for efficient terminal management. Modern passenger terminals are characterized by dynamic process variability and consideration of diverse options, taking into account the criteria of safety, reliability analysis, and the continuous research of passenger processing. For any modern marine passenger terminal, it is necessary to use the tool to simulate passenger flows in dynamics. Only in this way it is possible to obtain the analytical information and use it for decision making when solving the problem of the amount of personnel required for passenger service, transport safety, some forecasting tasks and so on. Of particular relevance is the choice of the mathematical transport model and the practical conditions for the implementation of the model in the real terminal operation. In this article, the analysis technique of intelligent simulation-based terminal services provides a new mathematical model of passenger movement inside the terminal and presents a new software instrument. Moreover, the conditions of implementation of some transportation models during the operation of marine passenger terminal are examined. The study represents an example of analytical information used for the forecast of the terminal operations, the analysis of the workload and the efficiency of the organization of the marine terminal.
This book constitutes the joint refereed proceedings of the 17th International Conference on Next Generation Wired/Wireless Advanced Networks and Systems, NEW2AN 2017, the 10th Conference on Internet of Things and Smart Spaces, ruSMART 2017. The 71 revised full papers presented were carefully reviewed and selected from 202 submissions. The papers of NEW2AN focus on advanced wireless networking and applications; lower-layer communication enablers; novel and innovative approaches to performance and efficiency analysis of ad-hoc and machine-type systems; employed game-theoretical formulations, Markov chain models, and advanced queuing theory; grapheme and other emerging material, photonics and optics; generation and processing of signals; and business aspects. The ruSMART papers deal with fully-customized applications and services. The NsCC Workshop papers capture the current state-of-the-art in the field of molecular and nanoscale communications such as information, communication and network theoretical analysis of molecular and nanonetwork, mobility in molecular and nanonetworks; novel and practical communication protocols; routing schemes and architectures; design/engineering/evaluation of molecular and nonoscale communication systems; potential applications and interconnections to the Internet (e.g. the Internet of Nano Things).
14th International Scientific-Technical Conference on Actual Problems of Electronics Instrument Engineering, APEIE 2018 - Proceedings
Описывается созданный макет манипулятора с биоэлектрическим управлением. Манипулятор сделан в форме человеческой ладони, движение пальцев которой управляется через электромиосигналы оператора. В среде LabVIEW разработан виртуальный прибор, позволяющий с помощью дискретного вейвлет-преобразования осуществить анализ электромиосигналов оператора, определить моменты мышечной активности и сформировать по результатам анализа сигналы управления манипулятором.