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Identifying meaningful signal buried in noise is a problem of interest arising in diverse scenarios of data-driven modeling. We present here a theoretical framework for exploiting intrinsic geometry in data that resists noise corruption, and might be identifiable under severe obfuscation. Our approach is based on uncovering a valid complete inner product on the space of ergodic stationary finite valued...
This paper is to study the stabilizability and stabilization issues of linear dynamical systems based on the delayed and noisy feedback control. For the general linear systems, the necessary conditions and sufficient conditions for mean square and almost sure stabilizability are deduced and the corresponding feedback controls are designed according to the generalized algebraic Riccati equation. It...
Results of mathematical modelling of the phenomena of a stochastic resonance and stochastic filtration are submitted at influence on two-state output system — the Shmitt trigger of a mix of a signal and noise. Physical studies of stochastic resonance usually deal with real or numerical experiments. Theoretical approaches face a number of difficulties. To describe the diffusion system, one needs to...
Mean-squared-error (MSE) lower bounds are widely used for performance analysis in stochastic filtering problems. In many problems of this type, the nature of part of the unknown state parameters is circular or periodic. In this case, we are interested in the modulo-T estimation errors and not in the plain error values. Thus, the MSE risk and conventional MSE bounds are inappropriate for periodic stochastic...
The paper deals with state estimation of nonlinear stochastic dynamic systems. In particular, the stress is laid on development of second-order discrete-time filters for nonlinear continuous-discrete models. Two different filters are derived based on different order of nonlinear function approximation and discretization of the continuous dynamics equation. For the approximation the Taylor expansion...
Second order CS stochastic processes are non-stationary stochastic processes, where the TDCM depends on the global time and the time difference, and the dependence on the global time is periodic. This autocorrelation function can be represented by a 2D cyclic correlation spectrum containing delta functions at frequencies multiple to the cycle frequency of the stochastic process. Accordingly a CS stochastic...
In this paper, we present an open-loop Stochastic Model Predictive Control (SMPC) method for discrete-time nonlinear systems whose state is defined on the unit circle. This modeling approach allows considering systems that include periodicity in a more natural way than standard approaches based on linear spaces. The main idea of this work is twofold: (i) we model the quantities of the system, i.e...
In this paper, we consider infinite-horizon networked LQG control over multipurpose networks that do not provide acknowledgments (UDP-like networks). The information communicated over the network experiences transmission delays and losses that are modeled as stochastic processes. In oder to mitigate the delays and losses in the controller-actuator channel, the controller transmits sequences of predicted...
This paper is concerned with stabilization control problem for discrete time systems with random input delay. The random delay is not required to be less than a sampling interval as in previous works but it can vary in any range of finite length. By defining an appropriate stochastic variable, a random delayed system is converted into a multiplicative-noise stochastic system with multiple constant...
This paper addresses optimal mean-square performance for multiple-input multiple-output (MIMO) linear time invariant (LTI) systems subject to exogenous noise and communication losses between the plant and controller. First we derive linear matrix inequalities (LMIs) for analysis of mean-square stability and performance, then we show how a pair of semidefinite programs (SDPs) can be used to convexly...
A stochastic model predictive control (SMPC) approach is presented for discrete-time linear systems with arbitrary time-invariant probabilistic uncertainties and additive Gaussian process noise. Closed-loop stability of the SMPC approach is established by appropriate selection of the cost function. Polynomial chaos is used for uncertainty propagation through system dynamics. The performance of the...
This paper develops multi-scale data assimilation/filtering algorithms that are driven by the data, that take advantage of scale interaction to appropriately reduce the dimension of the problem. We incorporate an optimal particle filtering algorithm that generates the best importance sampling density. This particle method consists of control terms in the “prognostic” equations that nudge the particles...
The most important part of the neural network research is the learning. The process of learning in our brain is essentially several adjustment processes of connection strength between neurons. It is very difficult to figure out how this mechanism works in the complex network and how the connection strength influences brain functions. In this research, we study the minimal elements block of a learning...
We consider linear continuous-time systems with multiplicative noise and polytopic type parameter uncertainty and we address the problems of H∞ state-feedback control and filtering of these systems. These problems are solved by applying a vertex dependent Lyapunov function that considerably reduces the over-design associated with the classical “quadratic” design that is based on a single Lyapunov...
This work investigates the joint design of fronthaul compression and precoding for the downlink of Cloud Radio Access Networks (C-RANs). The main goal is that of bringing insight into an aspect of the optimal functional split between Radio Units (RUs) and Central Unit (CU), namely: where should precoding be performed? Unlike previous works, we tackle this issue for a practical scenario with block-ergodic...
We study the secure degrees of freedom (d.o.f.) of helper-assisted Gaussian wiretap channel with shared key between the transmitter and the helper. Given that the rate of the key scales with power as γ over 2 log SNR, we show that secure d.o.f. is min{1+γ over 2, 1}. The achievability proof combines real interference alignment with the artificial noise transmission technique. Using the shared key...
Restricted Boltzmann Machines and Deep Belief Networks have been successfully used in a wide variety of applications including image classification and speech recognition. Inference and learning in these algorithms uses a Markov Chain Monte Carlo procedure called Gibbs sampling. A sigmoidal function forms the kernel of this sampler which can be realized from the firing statistics of noisy integrate-and-fire...
A time-domain methodology for noise analysis of neural interface front-end with arbitrary deterministic neuron model excitations is presented. Rather than estimating noise behavior by a population of realizations, the neural interface front-end is described as a set of stochastic differential equations and closure approximations are introduced to obtain the noise variances, covariances and cross-correlations...
This paper presents a novel stochastic model for the impulsive noise measured in the narrowband indoor Power Line Communication (PLC) environment. Based on extensive measurements carried out inside several buildings, the impulsive noise has been characterized and modelled for the low frequency range transmission over power lines. An appropriate method has been used to finely extract pulses and their...
This paper addresses the problem of optimal control of a unicycle-type robot perturbed with stochastic noise in an environment with sparsely populated obstacles. The objective is that the robot pose converges to a neighborhood of a desired position and orientation. A feedback control law is constructed such that it is compatible with the differential constraints of the unicycle. The construction is...
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