scholarly journals Stability of non-linear filter for deterministic dynamics

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Anugu Sumith Reddy ◽  
Amit Apte
Keyword(s):  
State Space ◽  
Stochastic Dynamics ◽  
Initial Conditions ◽  
Linear Filter ◽  
Independent Observation ◽  
Deterministic Dynamics ◽  
Observation Process ◽  
Compact State ◽  
The Stability ◽  
Non Linear Filter

<p style='text-indent:20px;'>This papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time filters. Earlier works on the stability of the nonlinear filters are in the context of stochastic dynamics and assume conditions like compact state space or time independent observation model, whereas we prove filter stability for deterministic dynamics with more general assumptions on the state space and observation process. We give several examples of systems that satisfy these assumptions. We also show that the asymptotic structure of the filtering distribution is related to the dynamical properties of the signal.</p>

On Dynamic Tooth Load and Stability of a Spur-Gear System Using the State-Space Approach

1985 ◽  
Vol 107 (1) ◽  
pp. 54-60 ◽  
Author(s):  
A. S. Kumar ◽  
T. S. Sankar ◽  
M. O. M. Osman
Keyword(s):  
State Space ◽  
Dynamic Load ◽  
Initial Conditions ◽  
Gear Tooth ◽  
Spur Gear ◽  
The State ◽  
Gear System ◽  
Computational Time ◽  
Steady State Condition ◽  
The Stability

In this study, a new approach using the state-space method is presented for the dynamic load analysis of spur gear systems. This approach gives the dynamic load on gear tooth in mesh as well as information on the stability of the gear system. Also a procedure is given for the selection of proper initial conditions that enable the steady-state condition to be reached faster, conditions that result in considerable savings in computational time. The variations in the dynamic load with respect to changes in contact position, operating speed, backlash, damping, and stiffness are also investigated. In addition, the stability of the gear system is studied, using the Floquet theory and the well-known stability conditions of difference systems.

scholarly journals State-Space Model of Quasi-Z-Source Inverter-PV Systems for Transient Dynamics Studies and Network Stability Assessment

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4150
Author(s):  
Lluís Monjo ◽  
Luis Sainz ◽  
Juan José Mesas ◽  
Joaquín Pedra
Keyword(s):  
Power Systems ◽  
State Space ◽  
State Space Model ◽  
Pv System ◽  
Pv Systems ◽  
Renewable Power ◽  
Ac Networks ◽  
Transient Interactions ◽  
The Stability ◽  
Averaged Model

Photovoltaic (PV) power systems are increasingly being used as renewable power generation sources. Quasi-Z-source inverters (qZSI) are a recent, high-potential technology that can be used to integrate PV power systems into AC networks. Simultaneously, concerns regarding the stability of PV power systems are increasing. Converters reduce the damping of grid-connected converter systems, leading to instability. Several studies have analyzed the stability and dynamics of qZSI, although the characterization of qZSI-PV system dynamics in order to study transient interactions and stability has not yet been properly completed. This paper contributes a small-signal, state-space-averaged model of qZSI-PV systems in order to study these issues. The model is also applied to investigate the stability of PV power systems by analyzing the influence of system parameters. Moreover, solutions to mitigate the instabilities are proposed and the stability is verified using PSCAD time domain simulations.

A PHYSICAL INTERPRETATION OF MELNIKOV’S METHOD

1992 ◽  
Vol 02 (01) ◽  
pp. 1-9 ◽  
Author(s):  
YOHANNES KETEMA
Keyword(s):  
Physical Interpretation ◽  
Poincaré Map ◽  
Initial Conditions ◽  
Homoclinic Orbits ◽  
Poincare Map ◽  
Stable And Unstable Manifolds ◽  
Melnikov's Method ◽  
Melnikov’S Method ◽  
Sensitive Dependence ◽  
The Stability

This paper is concerned with analyzing Melnikov’s method in terms of the flow generated by a vector field in contrast to the approach based on the Poincare map and giving a physical interpretation of the method. It is shown that the direct implication of a transverse crossing between the stable and unstable manifolds to a saddle point of the Poincare map is the existence of two distinct preserved homoclinic orbits of the continuous time system. The stability of these orbits and their role in the phenomenon of sensitive dependence on initial conditions is discussed and a physical example is given.

Random filters which preserve the stability of random inputs

1988 ◽  
Vol 20 (2) ◽  
pp. 275-294 ◽  
Author(s):  
Stamatis Cambanis
Keyword(s):  
Transfer Function ◽  
Moving Average ◽  
Random Processes ◽  
Time Shift ◽  
Linear Filter ◽  
Random Inputs ◽  
The Stability ◽  
Non Gaussian ◽  
Random Gain

A stationary stable random processes goes through an independently distributed random linear filter. It is shown that when the input is Gaussian or harmonizable stable, then the output is also stable provided the filter&s transfer function has non-random gain. In contrast, when the input is a non-Gaussian stable moving average, then the output is stable provided the filter&s randomness is due only to a random global sign and time shift.

Parallel-Process (Simultaneous) Machining and its Stability

1999 ◽  
Author(s):  
O. Burak Ozdoganlar ◽  
William J. Endres
Keyword(s):  
Initial Conditions ◽  
General System ◽  
Parallel Process ◽  
Analytical Stability ◽  
Multiple Processes ◽  
Or Practice ◽  
Machining System ◽  
Eigenvector Analysis ◽  
The Stability ◽  
Machining Operations

Abstract This paper presents a mathematical perspective, to complement the intuitive or practice-oriented perspective, to classifying machining operations as parallel-process (simultaneous) or single-process in nature. Illustrative scenarios are provided to demonstrate how these two perspectives may lead in different situations to the same or different conclusions regarding process parallelism. A model representation of a general parallel-process machining system is presented, based on which the general parallel-process stability eigenvalue problem is formulated. For a special simplified case of the general system, analytical methods are employed to derive a fully analytical stability solution. Thorough study of this solution through eigenvector analysis sheds light on some fundamental phenomena of parallel-process machining stability, such as dependence of the stability solution on phasing of the initial conditions (disturbances). This establishes the importance, when employing numerical time-domain simulation for such analyses, of specifying initial conditions for the multiple processes to be arbitrarily phased so that correct results are achieved across all spindle speeds.

scholarly journals Improved estimations of stochastic chemical kinetics by finite-state expansion

2021 ◽  
Vol 477 (2251) ◽  
pp. 20200964
Author(s):  
Tabea Waizmann ◽  
Luca Bortolussi ◽  
Andrea Vandin ◽  
Mirco Tribastone
Keyword(s):  
Master Equation ◽  
State Space ◽  
Stochastic Dynamics ◽  
Reaction Network ◽  
Discrete State ◽  
State Expansion ◽  
Analytical Approximations ◽  
Finite State ◽  
Stochastic Reaction ◽  
Discrete State Space

Stochastic reaction networks are a fundamental model to describe interactions between species where random fluctuations are relevant. The master equation provides the evolution of the probability distribution across the discrete state space consisting of vectors of population counts for each species. However, since its exact solution is often elusive, several analytical approximations have been proposed. The deterministic rate equation (DRE) gives a macroscopic approximation as a compact system of differential equations that estimate the average populations for each species, but it may be inaccurate in the case of nonlinear interaction dynamics. Here we propose finite-state expansion (FSE), an analytical method mediating between the microscopic and the macroscopic interpretations of a stochastic reaction network by coupling the master equation dynamics of a chosen subset of the discrete state space with the mean population dynamics of the DRE. An algorithm translates a network into an expanded one where each discrete state is represented as a further distinct species. This translation exactly preserves the stochastic dynamics, but the DRE of the expanded network can be interpreted as a correction to the original one. The effectiveness of FSE is demonstrated in models that challenge state-of-the-art techniques due to intrinsic noise, multi-scale populations and multi-stability.

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