scholarly journals On strong consistency of a class of recursive stochastic Newton-Raphson type algorithms with application to robust linear dynamic system identification

2008 ◽  
Vol 21 (1) ◽  
pp. 1-21
Author(s):  
Ivana Kovacevic ◽  
Branko Kovacevic ◽  
Zeljko Djurovic
Keyword(s):  
Dynamic Systems ◽  
Recursive Algorithm ◽  
Optimal Solution ◽  
Stochastic Algorithms ◽  
Recursive Algorithms ◽  
Martingale Theory ◽  
Time Dynamic ◽  
Linear Dynamic ◽  
Newton Raphson ◽  
Approximate Optimal Solution

The recursive stochastic algorithms for estimating the parameters of linear discrete-time dynamic systems in the presence of disturbance uncertainty has been considered in the paper. Problems related to the construction of min-max optimal recursive algorithms are demonstrated. In addition, the robustness of the proposed algorithms has been addressed. Since the min-max optimal solution cannot be achieved in practice, an approximate optimal solution based on a recursive stochastic Newton-Raphson type procedure is suggested. The convergence of the proposed practically applicable robustified recursive algorithm is established theoretically using the martingale theory. Both theoretical and experimental analysis related to the practical robustness of the proposed algorithm are also included. .

RECURSIVE ALGORITHM FOR ESTIMATING THE PARAMETERS OF MULTIDIMENSIONAL DISCRETE LINEAR DYNAMIC SYSTEMS OF DIFFERENT ORDERS WITH ERRORS ON THE INPUT

2018 ◽  
pp. 707-716
Author(s):  
Ilya L’vovich Sandler
Keyword(s):  
Dynamical Systems ◽  
Dynamic Systems ◽  
Quadratic Forms ◽  
Recursive Algorithm ◽  
Gradient Algorithm ◽  
Linear Dynamical Systems ◽  
Recurrent Algorithm ◽  
Linear Dynamic Systems ◽  
Stochastic Gradient Algorithm ◽  
Linear Dynamic

The paper presents a recurrent algorithm for estimating the parameters of multidimensional discrete linear dynamical systems of different orders with input errors, described by white noise. It is proved that the obtained estimates using stochastic gradient algorithm for minimization of quadratic forms are highly consistent

scholarly journals Real-Time Dynamic Traffic Control Based on Traffic-State Estimation

2019 ◽  
Vol 2673 (5) ◽  
pp. 584-595 ◽  
Author(s):  
Afzal Ahmed ◽  
Syed Ahsan Ali Naqvi ◽  
David Watling ◽  
Dong Ngoduy
Keyword(s):  
Real Time ◽  
Recursive Algorithm ◽  
Optimal Solution ◽  
Network Capacity ◽  
Transmission Model ◽  
Reliable Estimate ◽  
Cell Transmission Model ◽  
Traffic Demand ◽  
Time Dynamic ◽  
Traffic State

The accurate depiction of the existing traffic state on a road network is essential in reducing congestion and delays at signalized intersections. The existing literature in the optimization of signal timings either utilizes prediction of traffic state from traffic flow models or limited real-time measurements available from sensors. Prediction of traffic state based on historic data cannot represent the dynamics of change in traffic demand or network capacity. Similarly, data obtained from limited point sensors in a network provides estimates which contain errors. A reliable estimate of existing traffic state is, therefore, necessary to obtain signal timings which are based on the existing condition of traffic on the network. This research proposes a framework which utilizes estimates of traffic flows and travel times based on real-time estimated traffic state for obtaining optimal signal timings. The prediction of traffic state from the cell transmission model (CTM) and measurements from traffic sensors are combined in the recursive algorithm of extended Kalman filter (EKF) to obtain a reliable estimate of existing traffic state. The estimate of traffic state obtained from the CTM-EKF model is utilized in the optimization of signal timings using genetic algorithm (GA) in the proposed CTM-EKF-GA framework. The proposed framework is applied to a synthetic signalized intersection and the results are compared with a model-based optimal solution and simulated reality. The optimal delay estimated by CTM-EKF-GA framework is only 0.6% higher than the perfect solution, whereas the delay estimated by CTM-GA model is 12.9% higher than the perfect solution.

A new algorithm for finding CRM-model coefficients

2019 ◽  
Vol 5 (3) ◽  
pp. 164-185 ◽  
Author(s):  
Alexander D. Bekman ◽  
Sergey V. Stepanov ◽  
Alexander A. Ruchkin ◽  
Dmitry V. Zelenin
Keyword(s):  
Approximate Solution ◽  
Optimization Problem ◽  
Optimal Solution ◽  
Complex Form ◽  
Approximate Solutions ◽  
The Other ◽  
Programming Algorithm ◽  
Stochastic Algorithms ◽  
Large Set ◽  
Flow Rates

The quantitative evaluation of producer and injector well interference based on well operation data (profiles of flow rates/injectivities and bottomhole/reservoir pressures) with the help of CRM (Capacitance-Resistive Models) is an optimization problem with large set of variables and constraints. The analytical solution cannot be found because of the complex form of the objective function for this problem. Attempts to find the solution with stochastic algorithms take unacceptable time and the result may be far from the optimal solution. Besides, the use of universal (commercial) optimizers hides the details of step by step solution from the user, for example&nbsp;— the ambiguity of the solution as the result of data inaccuracy.<br> The present article concerns two variants of CRM problem. The authors present a new algorithm of solving the problems with the help of “General Quadratic Programming Algorithm”. The main advantage of the new algorithm is the greater performance in comparison with the other known algorithms. Its other advantage is the possibility of an ambiguity analysis. This article studies the conditions which guarantee that the first variant of problem has a unique solution, which can be found with the presented algorithm. Another algorithm for finding the approximate solution for the second variant of the problem is also considered. The method of visualization of approximate solutions set is presented. The results of experiments comparing the new algorithm with some previously known are given.

scholarly journals On the Uncertainty Identification for Linear Dynamic Systems Using Stochastic Embedding Approach with Gaussian Mixture Models

Sensors ◽  
2021 ◽  
Vol 21 (11) ◽  
pp. 3837
Author(s):  
Rafael Orellana ◽  
Rodrigo Carvajal ◽  
Pedro Escárate ◽  
Juan C. Agüero
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Dynamic Systems ◽  
Gaussian Mixture ◽  
Error Model ◽  
Fault Detection And Diagnosis ◽  
Deterministic Models ◽  
Linear Dynamic Systems ◽  
Linear Dynamic

In control and monitoring of manufacturing processes, it is key to understand model uncertainty in order to achieve the required levels of consistency, quality, and economy, among others. In aerospace applications, models need to be very precise and able to describe the entire dynamics of an aircraft. In addition, the complexity of modern real systems has turned deterministic models impractical, since they cannot adequately represent the behavior of disturbances in sensors and actuators, and tool and machine wear, to name a few. Thus, it is necessary to deal with model uncertainties in the dynamics of the plant by incorporating a stochastic behavior. These uncertainties could also affect the effectiveness of fault diagnosis methodologies used to increment the safety and reliability in real-world systems. Determining suitable dynamic system models of real processes is essential to obtain effective process control strategies and accurate fault detection and diagnosis methodologies that deliver good performance. In this paper, a maximum likelihood estimation algorithm for the uncertainty modeling in linear dynamic systems is developed utilizing a stochastic embedding approach. In this approach, system uncertainties are accounted for as a stochastic error term in a transfer function. In this paper, we model the error-model probability density function as a finite Gaussian mixture model. For the estimation of the nominal model and the probability density function of the parameters of the error-model, we develop an iterative algorithm based on the Expectation-Maximization algorithm using the data from independent experiments. The benefits of our proposal are illustrated via numerical simulations.

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