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Nonextensive statistical mechanics represents a consistent theoretical framework for investigation of complex systems. We propose the nonlinear stochastic differenctial equations yielding q-Gaussian distribution of signal intensity, featured in the nonextensive statistical mechanics. In addition, the proposed equations generate signals with 1/f behavior of the power spectral density. The joint reproduction...
We find exact mappings for a class of limit cycle systems with noise onto quasi-symplectic dynamics, including a van der Pol type oscillator. A dual role potential function is obtained as a component of the quasi-symplectic dynamics. Each component of the quasi-symplectic dynamics has an individual physical meaning and can be measured independently. Based on a stochastic interpretation different from...
We derive a system of stochastic differential equations simulating the dynamics of the three agent groups with herding interaction. Proposed approach can be valuable in the modeling of the complex socio-economic systems with similar composition of the agents. We demonstrate how the sophisticated statistical features of the absolute return in the financial markets can be reproduced by extending the...
In the report the dependence of mean angular frequency in spin-torque nano-oscillators (STNO) on the intensity of external magnetic field fluctuations and other parameters is analyzed. Using the analytical expression for polar angle distribution and numerical simulations it is shown that the deviation of mean frequency can be considerable and always increase with the approach to the boundaries of...
In this paper, we present an approach for designing a non linear observer to estimate the states of a non linear stochastic discrete time T-S system. The non linear observer design involves representation of the non linear system as a family of local linear state space models. The state estimator for each linear local state space model uses standard Kalman filter theory and then, linear modeled filter...
Many control methods implicitly depend on the assumption that time is accurately known. For example, the finite-horizon linear quadratic regulator is a linear policy with time-varying gains. Such policies may be infeasible for controllers without accurate clocks, such as the motor systems in humans and other animals, since gains would be applied at incorrect times. Little appears to be known, however,...
The paper presents MATLAB based software framework designed for nonlinear state estimation of discrete-time dynamic systems. The framework is designed to facilitate implementation, testing and use of various nonlinear state estimation methods. It allows simple description of the problem, specification of estimation experiment and processing the resulting data in order to simply compare various estimators...
Event-triggered and self-triggered control, in which the time of update to the controls is based on either current or outdated sampled data, have recently been employed to reduce the computational load or resource consumption for distributed real-time control systems. In this work, we propose a self-triggered scheme for nonlinear controlled stochastic differential equations with additive noise terms...
In this paper, we deal with the bounded real lemma for stochastic singular systems with multiplicative noises. Based on the adaptation of Itô calculus, the admissibility for this class of systems is defined and the bounded real lemma is derived using the mean square exponential stability. This lemma is then used to synthetize a ℌ∞ output feedback controller for the considered class of systems that...
Linear, state delayed, discrete-time systems with stochastic uncertainties in their state-space model are considered. The problems of both H∞ state-feedback control and filtering are solved, for the stationary case, via an input-output approach by which the system is replaced by a nonretarded system with deterministic norm-bounded uncertainties. In both problems, a cost function is defined which is...
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...
Nowadays with the development of inertial sensors based on Micro-Electromechanical Systems (MEMS), embedded accelerometers and gyroscopes can be found in several devices and platforms ranging from watches, smart phones, video game consoles up to terrestrial navigation and unmanned aerial vehicles (UAVs), etc. Despite the wide range of applications where such sensors are being used, it is well known...
The interaction between gene expression and metabolism is a form of feedback control that allows cells to up- or downregulate specific reactions according to the environmental conditions. Although gene expression is an inherently stochastic process, the effect of genetic feedback on the propagation of noise to the metabolic layer remains largely unexplored. These systems operate in two timescales,...
The paper deals with a method for the simulation of hybrid systems containing multiconductor transmission lines (MTL) with randomly varying primary parameters. A core of the method lies on a theory of stochastic differential equations (SDE) considering the system responses as stochastic processes. In fact, due to a hybrid nature of the system containing also parts with lumped parameters, a system...
In this paper, we develop theoretical results based on a proposed method for modeling switching noise for a class of hybrid systems with piecewise linear partitioned state space, and state-depending switching. We devise a stochastic model of such systems, whose global dynamics is governed by a continuous-time stochastic process. The main result of this paper is that we may identify the realizations...
This paper addresses the problem of characterizing a switching strategy for stabilization of switched linear stochastic systems with state-dependent noise. The strategy is based on the determination of a minimum dwell time. Sufficient conditions that assure exponential mean square stability and a guaranteed cost-to-go performance index are established by analyzing the time evolution of the second-order...
The paper deals with a method for simulation of transmission line (TL) models with randomly varied parameters, based on the theory of stochastic differential equations (SDE). The random changes of both excitation sources and TL model parameters can be considered. Voltage and/or current responses are represented in the form of the sample means and proper confidence intervals to provide reliable estimates...
Homogeneous cell populations can exhibit considerable cell-to-cell variation in the level of a given protein. Both intrinsic and extrinsic sources of noise have been implicated in driving this variability in protein level. More specifically, intrinsic noise is the protein variability that is different across genes and arises from the inherent stochastic nature of biochemical processes involved in...
This paper is concerned with stochastic reaction-diffusion kinetics governed by the reaction-diffusion master equation. Specifically, the primary goal of this paper is to provide a mechanistic basis of Turing pattern formation that is induced by intrinsic noise. To this end, we first derive an approximate reaction-diffusion system by using linear noise approximation. We show that the approximated...
The conditional mean estimator for a two-state linear system with additive Cauchy measurement and process noises is developed. Although the Cauchy densities that model the process and measurement noise have an undefined first moment and an infinite second moment, the probability density function conditioned on linear noisy measurements does have a finite mean and variance. The conditional probability...
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