Time-varying effective EEG source connectivity: the optimization of model parameters*

Introduction: The motion of many real world systems is described by essentially non-linear and non-stationary models. A number of approaches to the control of such plants are based on constructing an internal model of non-stationarity. However, the non-stationarity model parameters can vary widely, leading to more errors. It is only assumed in this paper that the change rate of the object parameters is limited, while the initial uncertainty can be quite large.Purpose: Analysis of adaptive control algorithms for non-linear and time-varying systems with an explicit reference model, synthesized by the speed gradient method.Results: An estimate was obtained for the maximum deviation of a closed-loop system solution from the reference model solution. It is shown that with sufficiently slow changes in the parameters and a small initial uncertainty, the limit error in the system can be made arbitrarily small. Systems designed by the direct approach and systems based on the identification approach are both considered. The procedures for the synthesis of an adaptive regulator and analysis of the synthesized system are illustrated by an example.Practical relevance: The obtained results allow us to build and analyze a broad class of adaptive systems with reference models under non-stationary conditions.

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Lie-Algebraic Approach for Pricing Zero-Coupon Bonds in Single-Factor Interest Rate Models

Journal of Applied Mathematics ◽

10.1155/2013/276238 ◽

2013 ◽

Vol 2013 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

C. F. Lo

Keyword(s):

Interest Rate ◽

Algebraic Approach ◽

Dynamical Symmetry ◽

Bond Pricing ◽

Model Parameters ◽

Time Varying ◽

Single Factor ◽

Bond Price ◽

Interest Rate Models ◽

Root Model

The Lie-algebraic approach has been applied to solve the bond pricing problem in single-factor interest rate models. Four of the popular single-factor models, namely, the Vasicek model, Cox-Ingersoll-Ross model, double square-root model, and Ahn-Gao model, are investigated. By exploiting the dynamical symmetry of their bond pricing equations, analytical closed-form pricing formulae can be derived in a straightfoward manner. Time-varying model parameters could also be incorporated into the derivation of the bond price formulae, and this has the added advantage of allowing yield curves to be fitted. Furthermore, the Lie-algebraic approach can be easily extended to formulate new analytically tractable single-factor interest rate models.

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Selective Linear Segmentation for Detecting Relevant Parameter Changes*

Journal of Financial Econometrics ◽

10.1093/jjfinec/nbaa032 ◽

2020 ◽

Author(s):

Arnaud Dufays ◽

Elysee Aristide Houndetoungan ◽

Alain Coën

Keyword(s):

Time Series ◽

Hedge Fund ◽

Expectation Maximization Algorithm ◽

Model Parameters ◽

Relevant Parameter ◽

Time Varying ◽

Long Time ◽

Model Selection Uncertainty ◽

Penalized Likelihood Approach ◽

Changes Over Time

Abstract Change-point (CP) processes are one flexible approach to model long time series. We propose a method to uncover which model parameters truly vary when a CP is detected. Given a set of breakpoints, we use a penalized likelihood approach to select the best set of parameters that changes over time and we prove that the penalty function leads to a consistent selection of the true model. Estimation is carried out via the deterministic annealing expectation-maximization algorithm. Our method accounts for model selection uncertainty and associates a probability to all the possible time-varying parameter specifications. Monte Carlo simulations highlight that the method works well for many time series models including heteroskedastic processes. For a sample of fourteen hedge fund (HF) strategies, using an asset-based style pricing model, we shed light on the promising ability of our method to detect the time-varying dynamics of risk exposures as well as to forecast HF returns.

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Output Adaptive Observers Design for Linear Non-Stationary Systems with Polynomial Parameters

Mekhatronika Avtomatizatsiya Upravlenie ◽

10.17587/mau.22.404-410 ◽

2021 ◽

Vol 22 (8) ◽

pp. 404-410

Author(s):

K. B. Dang ◽

A. A. Pyrkin ◽

A. A. Bobtsov ◽

A. A. Vedyakov ◽

S. I. Nizovtsev

Keyword(s):

Linear Time ◽

State Observer ◽

Observer Design ◽

Model Parameters ◽

Time Varying ◽

State Variables ◽

Unknown Constant ◽

Established Method ◽

Time Varying Parameters ◽

True Values

The article deals with the problem of state observer design for a linear time-varying plant. To solve this problem, a number of realistic assumptions are considered, assuming that the model parameters are polynomial functions of time with unknown coefficients. The problem of observer design is solved in the class of identification approaches, which provide transformation of the original mathematical model of the plant to a static linear regression equation, in which, instead of unknown constant parameters, there are state variables of generators that model non-stationary parameters. To recover the unknown functions of the regression model, we use the recently well-established method of dynamic regressor extension and mixing (DREM), which allows to obtain monotone estimates, as well as to accelerate the convergence of estimates to the true values. Despite the fact that the article deals with the problem of state observer design, it is worth noting the possibility of using the proposed approach to solve an independent and actual estimation problem of unknown time-varying parameters.

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Simulating and analyzing artificial nonstationary earthquake ground motions

Bulletin of the Seismological Society of America ◽

10.1785/bssa0720020615 ◽

1982 ◽

Vol 72 (2) ◽

pp. 615-636

Author(s):

Robert F. Nau ◽

Robert M. Oliver ◽

Karl S. Pister

Keyword(s):

Difference Equations ◽

Kalman Filters ◽

Ground Motions ◽

Structural Response ◽

Model Parameters ◽

Time Varying ◽

Nonparametric Method ◽

Linear Difference Equations ◽

Earthquake Ground Motions ◽

Earthquake Accelerograms

Abstract This paper describes models used to simulate earthquake accelerograms and analyses of these artificial accelerogram records for use in structural response studies. The artificial accelerogram records are generated by a class of linear linear difference equations which have been previously identified as suitable for describing ground motions. The major contributions of the paper are the use of Kalman filters for estimating time-varying model parameters, and the development of an effective nonparametric method for estimating the variance envelopes of the accelerogram records.

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Using Sliding Mode Control to Adjust Drum Level of a Boiler Unit With Time Varying Parameters

ASME 2010 10th Biennial Conference on Engineering Systems Design and Analysis, Volume 5 ◽

10.1115/esda2010-24105 ◽

2010 ◽

Cited By ~ 1

Author(s):

Hamed Moradi ◽

Firooz Bakhtiari-Nejad ◽

Majid Saffar-Avval ◽

Aria Alasty

Keyword(s):

Water Level ◽

Transfer Functions ◽

Sliding Mode ◽

Operating Conditions ◽

Model Parameters ◽

Feed Water ◽

Time Varying ◽

Boiler Unit ◽

Varying Parameters ◽

Time Varying Parameters

Stable control of water level of drum is of great importance for economic operation of power plant steam generator systems. In this paper, a linear model of the boiler unit with time varying parameters is used for simulation. Two transfer functions between drum water level (output variable) and feed-water and steam mass rates (input variables) are considered. Variation of model parameters may be arisen from disturbances affecting water level of drum, model uncertainties and parameter mismatch due to the variant operating conditions. To achieve a perfect tracking of the desired drum water level, two sliding mode controllers are designed separately. Results show that the designed controllers result in bounded values of control signals, satisfying the actuators constraints.

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The Time-Varying Effect of Monetary Policy on Asset Prices

Review of Economics and Statistics ◽

10.1162/rest_a_00840 ◽

2020 ◽

Vol 102 (4) ◽

pp. 690-704 ◽

Cited By ~ 8

Author(s):

Pascal Paul

Keyword(s):

Monetary Policy ◽

Asset Prices ◽

House Prices ◽

The United States ◽

Model Parameters ◽

Time Varying ◽

Real Economy ◽

Monetary Policy Shocks ◽

Vector Autoregressive ◽

Policy Shocks

This paper studies how monetary policy jointly affects asset prices and the real economy in the United States. I develop an estimator that uses high-frequency surprises as a proxy for the structural monetary policy shocks. This is achieved by integrating the surprises into a vector autoregressive model as an exogenous variable. I use current short-term rate surprises because these are least affected by an information effect. When allowing for time-varying model parameters, I find that compared to the response of output, the reaction of stock and house prices to monetary policy shocks was particularly low before the 2007–2009 financial crisis.

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Turing and Benjamin–Feir instability mechanisms in non-autonomous systems

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2020.0003 ◽

2020 ◽

Vol 476 (2238) ◽

pp. 20200003 ◽

Cited By ~ 3

Author(s):

Robert A. Van Gorder

Keyword(s):

Autonomous Systems ◽

Reaction Diffusion ◽

Reaction Rates ◽

Time Dependent ◽

Model Parameters ◽

Time Varying ◽

Reaction Diffusion Systems ◽

Diffusion Systems ◽

Dependent Model ◽

Spatio Temporal

The Turing and Benjamin–Feir instabilities are two of the primary instability mechanisms useful for studying the transition from homogeneous states to heterogeneous spatial or spatio-temporal states in reaction–diffusion systems. We consider the case when the underlying reaction–diffusion system is non-autonomous or has a base state which varies in time, as in this case standard approaches, which rely on temporal eigenvalues, break down. We are able to establish respective criteria for the onset of each instability using comparison principles, obtaining inequalities which involve the in general time-dependent model parameters and their time derivatives. In the autonomous limit where the base state is constant in time, our results exactly recover the respective Turing and Benjamin–Feir conditions known in the literature. Our results make the Turing and Benjamin–Feir analysis amenable for a wide collection of applications, and allow one to better understand instabilities emergent due to a variety of non-autonomous mechanisms, including time-varying diffusion coefficients, time-varying reaction rates, time-dependent transitions between reaction kinetics and base states which change in time (such as heteroclinic connections between unique steady states, or limit cycles), to name a few examples.

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Time-Varying Delay Estimation Applied to the Surface Electromyography Signals Using the Parametric Approach

Fluctuation and Noise Letters ◽

10.1142/s0219477518500153 ◽

2018 ◽

Vol 17 (02) ◽

pp. 1850015 ◽

Cited By ~ 1

Author(s):

Gia Thien Luu ◽

Abdelbassit Boualem ◽

Tran Trung Duy ◽

Philippe Ravier ◽

Olivier Butteli

Keyword(s):

Parametric Method ◽

Optimization Technique ◽

Likelihood Estimation ◽

Model Parameters ◽

Fiber Direction ◽

Time Varying ◽

Time Varying Delay ◽

Power Spectral ◽

Changes Over Time ◽

Varying Delay

Muscle Fiber Conduction Velocity (MFCV) can be calculated from the time delay between the surface electromyographic (sEMG) signals recorded by electrodes aligned with the fiber direction. In order to take into account the non-stationarity during the dynamic contraction (the most daily life situation) of the data, the developed methods have to consider that the MFCV changes over time, which induces time-varying delays and the data is non-stationary (change of Power Spectral Density (PSD)). In this paper, the problem of TVD estimation is considered using a parametric method. First, the polynomial model of TVD has been proposed. Then, the TVD model parameters are estimated by using a maximum likelihood estimation (MLE) strategy solved by a deterministic optimization technique (Newton) and stochastic optimization technique, called simulated annealing (SA). The performance of the two techniques is also compared. We also derive two appropriate Cramer–Rao Lower Bounds (CRLB) for the estimated TVD model parameters and for the TVD waveforms. Monte-Carlo simulation results show that the estimation of both the model parameters and the TVD function is unbiased and that the variance obtained is close to the derived CRBs. A comparison with non-parametric approaches of the TVD estimation is also presented and shows the superiority of the method proposed.

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PID PARAMETERS OPTIMIZATION USING PSO TECHNIQUE FOR NONLINEAR ELECTRO HYDRAULIC ACTUATOR

Jurnal Teknologi ◽

10.11113/jt.v77.6793 ◽

2015 ◽

Vol 77 (28) ◽

Cited By ~ 1

Author(s):

Siti Marhainis Othman ◽

Mohd Fua’ad Rahmat ◽

Sahazati Md. Rozali ◽

Sazilah Salleh

Keyword(s):

Particle Swarm Optimization ◽

Simulation Study ◽

Pid Control ◽

Parameters Optimization ◽

Model Parameters ◽

Time Varying ◽

Proportional Integral Derivative ◽

Hydraulic Actuator ◽

Swarm Optimization ◽

Control Scheme

Electro-hydraulic actuator (EHA) system inherently suffers from uncertainties, nonlinearities and time- varying in its model parameters which cause the modeling and controller designs are more complicated. Proportional Integral Derivative (PID) control scheme has been proposed and the main problem with its application is to tune the parameters to its optimum values. This study will look into an optimization of PID parameters using particle swarm optimization (PSO). Simulation study has been done in Matlab and Simulink.

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