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This paper considers the topic of state estimation for the Stochastic Hybrid System (SHS). The SHS is a class of dynamical systems which can accurately describe many interacting continuous and discrete dynamics. State estimation for the SHS, also called hybrid estimation, is an important yet challenging problem. While most previous research has addressed the hybrid estimation for some special classes...
We study the evolution of gene regulation in response to environmental fluctuations. For gene dynamics modeled by a linear system, we compute the optimal gene regulator that minimizes the expected square difference between the current protein level and the level that is assumed to be optimal for the current environment plus the cost of protein production/decay, integrated over the life span of the...
This work deals with an optimal dividend payment problem for a piecewise-deterministic compound Poisson insurance risk model. The objective is to maximize the expected discounted dividend payout up to the time of ruin. When the dividend payment rate is restricted, the value function is shown to be a solution of the corresponding Hamilton-Jacobi-Bellman equation, which in turn leads to a tractable...
The new algorithm is proposed for the estimating of linear plant's unknown parameters in the case of observations with arbitrary external noises. It is based on adding of randomized inputs (test perturbations) through the feedback channel. The assumptions about the noise are reduced to a minimum: it can virtually be arbitrary but independently of it the user must be able to add test perturbations...
In this paper we propose and study a strategic model of marketing and product adoption in social networks. Two firms compete for the spread of their products in a social network. Considering their fixed budgets, they initially determine the payoff of their products and the number of their initial seeds in a network. Afterwards, neighboring agents play a local coordination game over a fixed network...
In this paper we present simple stochastic differential equations that lead to lower-tail and/or upper tail power law behaviors. We also present a model with bi-directional Poisson counters that exhibits power law behavior near a critical point, which might be of interest to statistical physics.
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...
A new tool, in the blind deconvolution, for the estimation of both the source signals and the unknown channel dynamics has been developed. The framework for this methodology is based on a multi-channel blind deconvolution technique that has been reformulated to use Stochastic Calculus. The convolution processes is modeled as Finite Impulse Response (FIR) filters with unknown coefficients. Assuming...
This note proposes a control strategy for distributed power line frequency regulation by means of ‘smart’ appliances. The underlying assumption is that appliances are capable of constantly monitoring frequency and are designed to suitably react to its variations. We investigate an idealized model of battery charger, but the approach can be extended to other appliances for which it is acceptable to...
The separation principle is the statement that under suitable conditions the design of stochastic control can be divided into two separate problems, one of optimal control with state information and one of filtering. The literature over the past 50 years contains several derivations where subtle difficulties are overlooked and inadmissible shortcuts taken. Other contributions that have established...
We consider a linear-quadratic-Gaussian (LQG) game with a major player and a large number of minor players with mean field coupling. The state of the major player appears in the dynamics of the minor players, causing the mean field to be responsive to its control. We construct decentralized ε-Nash strategies. This is accomplished by combining (i) stochastic control with random coefficients and (ii)...
This paper discusses a stochastic model fitting process for the determining the calibration interval of precision Type N coaxial terminations. The measurements were taken weekly and over a six month period. The calibration of the vector network analyzer employs one-port error correction model using a sliding load. The observed drift rate is computed using linear regression. A second-order drift was...
This paper presents a socio-demographic model defined by sexes and structured by age. The model is a von Foerster-McKendrick model for the dynamics of population by sex and age of a general human population. The fertility and deaths rates are structured by age and they depend on the well-being variable. The well-being variable is defined by UN, HDI-Hybrid. We present the validation of the stochastic...
Program system for active parametric identification of stochastic dynamical systems described by nonlinear discrete and continuous-discrete models in state space is considered. The general case is discussed, when unknown parameters are in state equation, in observation equation, in initial conditions, in covariant matrix of dynamic interference and measurement errors.
In this paper we present an analytical model for incorporating navigational error into a search performance prediction algorithm through the construction of a corresponding utility function. The search space is partitioned into a set of cells over which a utility function formulation is developed for each. The navigational displacement error is assumed to be driven by a Mixed Ornstein Uhlenbeck stochastic...
In modern communication systems, one of the problems limiting the application of direct conversion receivers is the local oscillator port noise of sampling mixers. Ignoring the oscillator port noise contribution to the dynamical analysis of the sampling mixer will have influence on the trajectory estimation as well as its control. The intent of this note is to develop a general theory of sampling...
In this paper, a methodology for propagation of uncertainty in stochastic nonlinear dynamical systems is investigated. The process noise is approximated using Karhunen-Loève (KL) expansion. Perron-Frobenius (PF) operator is used to predict the evolution of uncertainty. A multivariate Kolmogorov-Smirnov test is used to verify the proposed framework. The method is applied to predict uncertainty evolution...
The noise-free CMOS inverter is described by a first- order non-linear differential equation that can be regarded as a standard case in electronic circuits from the system-theoretic viewpoint. In lieu of the noise-free CMOS inverter, this paper explains the stochastic CMOS inverter at the low power supply voltage. The method of this paper utilizes the Kolmogorov-Fokker-Planck equation for the noise...
This paper presents a bi-level consumer-utility optimization model to schedule an energy consumption pattern of controllable loads in the face of a time varying price function depending on system conditions and market operations. The controllable loads are classified into three types based on their natures and operating characteristics for an upper-level consumer's problem. To formulate the stochastic...
By extended mapping method and Hermite transformation, we study the generalized stochastic KdV equation, and obtain some families of stochastic exact solutions, which include Jacobi elliptic function-like, combined Jacobi elliptic function-like, soliton-like, kink-bell soliton-like and triangular function-like solutions.
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