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Efficient calculation of expected (mean) propagation factor for wave propagation above a random long-range terrain is achieved. An adaptive sparse grid collocation algorithm (ASGC) is applied for interpolating each component function from an adaptive high dimensional model representations (HDMR) decomposition. The decomposition reveals significant elimination of redundant sampling. The obtained results...
In this paper, we propose a new concept named separation time of the bounded confidence opinion models, the Hegselmann-Krause (HK) model and Deffuant-Weisbuch (DW) model. Different from others who care about the limit states of the opinion dynamics, we try to study the phenomenon among the opinion evolution process. The separation time describes the initial time of the formation of the stable opinion...
In this paper, we study the competition among the primary users (PUs) in a Dynamic Spectrum Leasing (DSL) system where multiple PUs lease spectrum to the secondary users (SUs) for monetary rewards. Considering the uncertainties of the PUs' channel gains and of the SUs' demands for spectrum, the competition among the PUs is formulated as a stochastic Nash game. Due to the uncertainties, the PUs aim...
This paper addresses opportunistic spectrum access (OSA) in non-cooperative cognitive radio networks (CRNs). The selfish behaviors of the secondary users (SUs) will cause a CRN to collapse. The SUs are thus enabled to build beliefs about how other SUs would respond to their decision makings. The interaction among the SUs is modeled as a stochastic learning process. In this way, each SU can independently...
This paper investigates the stability of linear systems with stochastic delay in discrete time. Stability of the mean and second moment of the non-deterministic system is determined by a set of deterministic discrete-time equations with distributed delay. A theorem is provided that guarantees convergence of the state with convergence of the second moment, assuming that delays are identically independently...
We propose two distributed algorithms, one for solving the weight-balance problem and another for solving the bistochastic matrix formation problem, in a distributed system whose components (nodes) can exchange information via interconnection links (edges) that form an arbitrary, possibly directed, strongly connected communication topology (digraph). Both distributed algorithms achieve their goal...
In this paper, a linear closed-loop Stackelberg strategy for a class of singularly perturbed stochastic systems (SPSS) governed by Itô differential equations is considered. Necessary conditions for the solution are established via a set of cross-coupled algebraic Lyapunov and Riccati equations (CALREs). After studying the asymptotic behavior of the solution for these stochastic equations, two new...
This paper applies contraction theory to establish necessary conditions for contraction, hence, exponential convergence of the unscented Kalman-Bucy Filter. It follows that regions of contraction can subsequently be defined, given such necessary conditions. Both state and measurement models are Itô-type stochastic differential equations. By employing a virtual/actual system framework, a special relation...
Unconditional consensus is the property of a consensus algorithm for multiple agents, to produce consensus irrespective of the particular time or state at which the agent states are initialized. Under a weak condition, so-called balanced asymmetry, on the sequence (An) of stochastic matrices in the agents states update algorithm, it is shown that (i) the set of accumulation points of states as n grows...
This paper considers the problem of stabilization of stochastic Linear Parameter Varying (LPV) discrete time systems in the presence of convex state and input constraints. By using a randomization approach, a convex finite horizon optimal control problem is derived, even when the dependence of the system's matrices on the time-varying parameters is nonlinear. This convex problem can be solved efficiently,...
The moving horizon estimation (MHE) problem is investigated in this paper for a class of networked systems with packet dropouts. The packet dropout is described by a binary switching random sequence. The main purpose of this paper is to design a estimator such that, for all possible packet dropouts, the state estimation error sequence is convergent. By choosing a stochastic cost function, the optimal...
By combining randomized smoothing techniques with accelerated gradient methods, we obtain convergence rates for stochastic optimization procedures, both in expectation and with high probability, that have optimal dependence on the variance of the gradient estimates. To the best of our knowledge, these are the first variance-based rates for non-smooth optimization. A combination of our techniques with...
Network optimization problems are often solved by dual gradient descent algorithms which can be implemented in a distributed manner but are known to have slow convergence rates. The accelerated dual descent (ADD) method improves this convergence rate by distributed computation of approximate Newton steps. This paper shows that a stochastic version of ADD can be used to solve network optimization problems...
We propose to use a global metamodeling technique known as stochastic kriging to improve the efficiency of Discrete Optimization-via-Simulation (DOvS) algorithms. Stochastic kriging metamodel allows the DOvS algorithm to utilize all information collected during the optimization process and identify solutions that are most likely to lead to significant improvement in solution quality. We call the approach...
We consider a class of pure-state preparation problems for stochastic quantum dynamics, by means of Hamiltonian control, continuous measurement and quantum feedback, in the presence of a Markovian environment. We prove that, whenever suitable dissipative effects are induced either by the unmonitored environment or by continuous-time measurements, open-loop time-invariant control is in principle sufficient...
We analyze the convergence of gradient-based optimization algorithms that base their updates on delayed stochastic gradient information. The main application of our results is to gradient-based distributed optimization algorithms where a master node performs parameter updates while worker nodes compute stochastic gradients based on local information in parallel, which may give rise to delays due to...
In this paper, we propose a distributed algorithm for optimal routing in wireless multi-hop networks. We build our approach on a recently proposed model for stochastic routing, whereby each node selects a neighbor to forward a packet according to a given probability distribution. Our solution relies on dual decomposition techniques with regularization, that can significantly improve on the slow convergence...
In this paper, a constrained consensus problem is studied in unbalanced networks in the presence of communication delays. Here each agent needs to lie in a closed convex set while reaching a consensus. The communication graphs considered are directed, dynamically changing, and not necessarily balanced and only the union of the graphs is assumed to be strongly connected among each time interval of...
Discrete representation of random ultra wideband (UWB) signals based on wavelet basis and its characteristics determination method are suggested. Conditions for uniform convergence in probability on [0,T] of wavelet expansions for random process X={X(t),t ∈ R]} are discussed. Suggest stochastic model may be used in design process of information systems.
Discrete representation of random ultra wideband (UWB) signals based on wavelet basis and its characteristics determination method are suggested. Conditions for uniform convergence in probability on [0,T] of wavelet expansions for random process X={X(t),t ∈ R]} are discussed. Suggest stochastic model may be used in design process of information systems.
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