Spectral analysis of ARMA processes by Prony's method
State-space realization of nonlinear control systems: unification and extension via pseudo-linear algebra
In this paper the tools of pseudo-linear algebra are applied to the realization problem, allowing to unify the study of the continuous- and discrete-time nonlinear control systems under a single algebraic framework. The realization of nonlinear input-output equation, defined in terms of the pseudo-linear operator, in the classical state-space form is addressed by the polynomial approach in which the system is described by two polynomials from the non-commutative ring of skew polynomials. This allows...
Stochastic Inverse Problem with Noisy Simulator. Application to aeronautical model
Inverse problem is a current practice in engineering where the goal is to identify parameters from observed data through numerical models. These numerical models, also called Simulators, are built to represent the phenomenon making possible the inference. However, such representation can include some part of variability or commonly called uncertainty (see [4]), arising from some variables of the model. The phenomenon we study is the fuel mass needed to link two given countries with a commercial...
Superposition of diffusions with linear generator and its multifractal limit process
In this paper a new multifractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differencial Generator (LISDLG) is presented which realistically characterizes the network traffic multifractality. Several properties of the LISDLG model are presented including long range dependence, cumulants, logarithm of the characteristic function, dilative stability, spectrum and bispectrum. The model captures higher-order statistics by the cumulants. The relevance...
Superposition of Diffusions with Linear Generator and its Multifractal Limit Process
In this paper a new multifractal stochastic process called Limit of the Integrated Superposition of Diffusion processes with Linear differencial Generator (LISDLG) is presented which realistically characterizes the network traffic multifractality. Several properties of the LISDLG model are presented including long range dependence, cumulants, logarithm of the characteristic function, dilative stability, spectrum and bispectrum. The model captures higher-order statistics by the cumulants. The relevance...
Sweep coverage of discrete time multi-robot networks with general topologies
This paper addresses a sweep coverage problem of multi-robot networks with general topologies. To deal with environmental uncertainties, we present discrete time sweep coverage algorithms to guarantee the complete coverage of the given region by sweeping in parallel with workload partition. Moreover, the error between actual coverage time and the optimal time is estimated with the aid of continuous time results. Finally, numerical simulation is conducted to verify the theoretical results.
The finite automata approaches in stringology
We present an overview of four approaches of the finite automata use in stringology: deterministic finite automaton, deterministic simulation of nondeterministic finite automaton, finite automaton as a model of computation, and compositions of finite automata solutions. We also show how the finite automata can process strings build over more complex alphabet than just single symbols (degenerate symbols, strings, variables).
The Frisch scheme in algebraic and dynamic identification problems
This paper considers the problem of determining linear relations from data affected by additive noise in the context of the Frisch scheme. The loci of solutions of the Frisch scheme and their properties are first described in the algebraic case. In this context two main problems are analyzed: the evaluation of the maximal number of linear relations compatible with data affected by errors and the determination of the linear relation actually linking the noiseless data. Subsequently the extension...
The gamma-uniform distribution and its applications
Up to present for modelling and analyzing of random phenomenons, some statistical distributions are proposed. This paper considers a new general class of distributions, generated from the logit of the gamma random variable. A special case of this family is the Gamma-Uniform distribution. We derive expressions for the four moments, variance, skewness, kurtosis, Shannon and Rényi entropy of this distribution. We also discuss the asymptotic distribution of the extreme order statistics, simulation issues,...
The output least squares identifiability of the diffusion coefficient from an H–observation in a 2–D elliptic equation
Output least squares stability for the diffusion coefficient in an elliptic equation in dimension two is analyzed. This guarantees Lipschitz stability of the solution of the least squares formulation with respect to perturbations in the data independently of their attainability. The analysis shows the influence of the flow direction on the parameter to be estimated. A scale analysis for multi-scale resolution of the unknown parameter is provided.
The Output Least Squares Identifiability of the Diffusion Coefficient from an H1–Observation in a 2–D Elliptic Equation
Output least squares stability for the diffusion coefficient in an elliptic equation in dimension two is analyzed. This guarantees Lipschitz stability of the solution of the least squares formulation with respect to perturbations in the data independently of their attainability. The analysis shows the influence of the flow direction on the parameter to be estimated. A scale analysis for multi-scale resolution of the unknown parameter is provided.
The recursive identification problem in control and signal processing applications
The strong pointwise convergence of nearest neighbor function fitting algorithm with applications to system identification
The strongest t-norm for fuzzy metric spaces
In this paper, we prove that for a given positive continuous t-norm there is a fuzzy metric space in the sense of George and Veeramani, for which the given t-norm is the strongest one. For the opposite problem, we obtain that there is a fuzzy metric space for which there is no strongest t-norm. As an application of the main results, it is shown that there are infinite non-isometric fuzzy metrics on an infinite set.
Tree and local computations in a cross–entropy minimization problem with marginal constraints
In probability theory, Bayesian statistics, artificial intelligence and database theory the minimum cross-entropy principle is often used to estimate a distribution with a given set of marginal distributions under the proportionality assumption with respect to a given “prior” distribution . Such an estimation problem admits a solution if and only if there exists an extension of that is dominated by . In this paper we consider the case that is not given explicitly, but is specified as the...
Адаптивная идентификация распределенных систем при размытом наблюдении
Вариационная задача оптимизации измерений в алгоритмах идентификации и управления