Method for the Synthesis of Adaptive Algorithms for Estimating the Parameters of Dynamic Systems Based on the Decomposition Principle and the Joint Maximum Methodology

2020 ◽  
pp. 22-28
Author(s):  
Andrey A. Kostoglotov ◽  
Anton S. Penkov ◽  
Sergey V. Lazarenko
Keyword(s):  
Dynamic Systems ◽  
Estimation Error ◽  
The State ◽  
Structural Adaptation ◽  
Maximum Function ◽  
Error Functional ◽  
Rate Of Dissipation ◽  
Motion Invariants ◽  
Explicit Relation ◽  
Decomposition Principle

A method of synthesis of a filter for estimating the state of dynamic systems of Kalman type with an adaptive model built on the basis of the principle of decomposition of the system using kinematic relations from the condition of constancy of motion invariants has been developed. The structure of the model is determined from the condition of the maximum function of the generalized power up to a nonlinear synthesizing function that determines the rate of dissipation and, accordingly, the degree of structural adaptation. The resulting model has an explicit relation with the gradient of the estimation error functional, which makes it possible to adapt to the intensity of regular and random influences and can be used to construct a filter for estimating the state of the Kalman structure. On the basis of the developed method, a discrete algorithm is obtained and its comparative analysis with the classical Kalman filter is carried out.

scholarly journals Quasi-optimal synthesis of an adaptive filter in the problem of estimating the state of dynamic systems

2020 ◽  
Vol 210 ◽  
pp. 01002
Author(s):  
Andrey Kostoglotov ◽  
Anton Penkov ◽  
Sergey Lazarenko
Keyword(s):  
Dynamic Systems ◽  
Degrees Of Freedom ◽  
Optimal Estimation ◽  
The State ◽  
System Model ◽  
Motion Model ◽  
Unknown Parameters ◽  
Generalized Lagrangian ◽  
Controlled Motion ◽  
Decomposition Principle

The problem of synthesis of filters to estimate the state of dynamical systems is considered based on the condition for the maximum of the generalized power function and stationarity of the generalized Lagrangian and Hamiltonian of the estimated system model. The paper demonstrates that the use of invariants in combination with the decomposition principle makes it possible to simplify the equations of controlled motion and reduce them to a system of independent equations in terms of the number of degrees of freedom. This approach reduces the number of unknown parameters of the motion model, which greatly simplifies the adaptation process when developing filters for quasi-optimal estimation of the state parameters of dynamic systems. Comparative analysis of the results of the mathematical simulation shows that the application of the proposed method increases the efficiency of filters of the Kalman structure.

scholarly journals Event-Triggering State and Fault Estimation for a Class of Nonlinear Systems Subject to Sensor Saturations

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1242
Author(s):  
Cong Huang ◽  
Bo Shen ◽  
Lei Zou ◽  
Yuxuan Shen
Keyword(s):  
Nonlinear Systems ◽  
Difference Equations ◽  
Estimation Error ◽  
Upper Bounds ◽  
The State ◽  
Fault Estimation ◽  
Triggering Mechanism ◽  
Transmission Frequency ◽  
Current Transmission ◽  
Event Triggering

This paper is concerned with the state and fault estimation issue for nonlinear systems with sensor saturations and fault signals. For the sake of avoiding the communication burden, an event-triggering protocol is utilized to govern the transmission frequency of the measurements from the sensor to its corresponding recursive estimator. Under the event-triggering mechanism (ETM), the current transmission is released only when the relative error of measurements is bigger than a prescribed threshold. The objective of this paper is to design an event-triggering recursive state and fault estimator such that the estimation error covariances for the state and fault are both guaranteed with upper bounds and subsequently derive the gain matrices minimizing such upper bounds, relying on the solutions to a set of difference equations. Finally, two experimental examples are given to validate the effectiveness of the designed algorithm.

scholarly journals New observer-based control design for mismatched uncertain systems with time-delay

2016 ◽  
Vol 26 (4) ◽  
pp. 597-610 ◽  
Author(s):  
Van Van Huynh
Keyword(s):  
Time Delay ◽  
Estimation Error ◽  
The State ◽  
Delay Systems ◽  
Linear Matrix ◽  
Time Delay Systems ◽  
Parameter Uncertainties ◽  
State Matrix ◽  
Control Techniques ◽  
Uncertain Time

Abstract In this paper, the state estimation problem for a class of mismatched uncertain time-delay systems is addressed. The estimation uses observer-based control techniques. The mismatched uncertain time-delay systems investigated in this study include mismatched parameter uncertainties in the state matrix and in the delayed state matrix. First, based on a new lemma with appropriately choosing Lyapunov functional, new results for stabilization of mismatched uncertain time-delay systems are provided on the basis of a linear matrix inequality (LMI) framework and the asymptotic convergence properties for the estimation error is ensured. Second, the control and observer gains are given from single LMI feasible solution which can overcome the drawback of the bilinear matrix inequalities approach often reported in the literature. Finally, a numerical example is used to demonstrate the efficacy of the proposed method.

INFORMATION AND TELECOMMUNICATION NETWORK SECURITY MANAGEMENT METHODOLOGY

2021 ◽  
Author(s):  
М.А. КАРПОВ ◽  
М.В. МИТРОФАНОВ ◽  
О.С. ЛАУТА ◽  
Д.А. ПАЛЬЦИН
Keyword(s):  
State Space ◽  
Dynamic Systems ◽  
Telecommunication Network ◽  
The State ◽  
Complex Dynamic ◽  
Computing Power ◽  
Complex Dynamic Systems ◽  
Situational Management ◽  
The Cost ◽  
Network Security Management

Исследуются вопросы ситуативного управления сложными динамическими системами. Анализируются релевантные работы в области ситуативного управления системами защиты. Приводятся результаты разработки алгоритма эффектив -ного управления, позволяющего уменьшать пространство состояний управляемого объекта. Показано, что представленная методика позволяет спрогнозировать количество итераций управления в зависимости от сегмента пространства состояний и выбранного количества переходов. Данный подход позволяет воздействовать на сложные динамические системы в реальном времени, причем затраты на вычислительные мощности системы управления и ее подсистем сокращаются. The issues of situational management of complex dynamic systems are investigated. Relevant works in the field of situational management of protection systems are analyzed. The article presents the results of the development of an efficient control algorithm that allows reducing the state space of the controlled object. The presented technique makes it possible to predict the number of control iterations depending on the segment of the state space and the selected number of transitions. This approach allows you to act on complex dynamic systems in real time, while the cost of the computing power of the control system and its subsystems is reduced. Keywords: INFORMATION AND TELECOMMUNICATION NETWORK, SCRIPT FORECAST, MANAGEMENT SYSTEM, SITUATIONAL MANAGEMENT, ITCN SECURITY SYSTEM

scholarly journals State Uncertainty Normality Detection

2019 ◽  
Vol 67 (3) ◽  
pp. 1044-1062
Author(s):  
Sven K. Flegel ◽  
James C. Bennett
Keyword(s):  
State Estimation ◽  
Orbit Determination ◽  
Estimation Error ◽  
The State ◽  
Body Motion ◽  
Optical Observations ◽  
Test Cases ◽  
Unscented Transform ◽  
State Uncertainty ◽  
Random Particle

AbstractTwo fundamentally different approaches of determining normality of the probability density function of the state estimation error are compared by application to a range of test cases. The first method is the Henze-Zirkler test, which operates on a random particle sample. The variability of its result is quantified. Using this method, departure from normality has been found to occur in three stages which are detailed. The second test compares the offset in whitened space of the predicted state to the predicted covariance mean obtained from the unscented transform. This test is much more efficient than the random particle based approach and can be applied using any perturbations model. The comparison is performed on the state estimation error in Cartesian space and using two-body motion without process noise. The more efficient, unscented transform based approach shows excellent agreement with the Henze-Zirkler test for constructed test cases. Application to orbit determination results from passive optical observations assessed with a Batch-Least-Squares orbit determination however reveals some discrepancies which have yet to be understood and underline the importance of rigorous testing.

Impulsive finite-time observer design for uncertain positive linear systems with L2-gain analysis

2020 ◽  
Vol 42 (10) ◽  
pp. 1871-1881 ◽  
Author(s):  
Morteza Motahhari ◽  
Mohammad Hossein Shafiei
Keyword(s):  
Linear Systems ◽  
Finite Time ◽  
Estimation Error ◽  
Sufficient Conditions ◽  
The State ◽  
Observer Design ◽  
Linear Matrix ◽  
Time Interval ◽  
State Variables ◽  
L2 Gain

This paper is concerned with the design of a finite-time positive observer (FTPO) for continuous-time positive linear systems, which is robust regarding the L2-gain performance. In positive observers, the estimation of the state variables is always nonnegative. In contrast to previous positive observers with asymptotic convergence, an FTPO estimates positive state variables in a finite time. The proposed FTPO observer, using two Identity Luenberger observers and based on the impulsive framework, estimates exactly the state variables of positive systems in a predetermined time interval. Furthermore, sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the L2-gain performance of the estimation error. Finally, the performance and robustness of the proposed FTPO are validated using numerical simulations.

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