Comparative Study of an EKF-Based Parameter Estimation and a Nonlinear Optimization-Based Estimation on PMSM System Identification

In this study, two different parameter estimation algorithms are studied and compared. Iterated EKF and a nonlinear optimization algorithm based on on-line search methods are implemented to estimate parameters of a given permanent magnet synchronous motor whose dynamics are assumed to be known and nonlinear. In addition to parameters, initial conditions of the dynamical system are also considered to be unknown, and that comprises one of the differences of those two algorithms. The implementation of those algorithms for the problem and adaptations of the methods are detailed for some other variations of the problem that are reported in the literature. As for the computational aspect of the study, a convexity study is conducted to obtain the spherical neighborhood of the unknown terms around their correct values in the space. To obtain such a range is important to determine convexity properties of the optimization problem given in the estimation problem. In this study, an EKF-based parameter estimation algorithm and an optimization-based method are designed for a given nonlinear dynamical system. The design steps are detailed, and the efficacies and shortcomings of both algorithms are discussed regarding the numerical simulations.

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Soil nutrient cycles as a nonlinear dynamical system

Nonlinear Processes in Geophysics ◽

10.5194/npg-11-589-2004 ◽

2004 ◽

Vol 11 (5/6) ◽

pp. 589-598 ◽

Cited By ~ 35

Author(s):

S. Manzoni ◽

A. Porporato ◽

P. D'Odorico ◽

F. Laio ◽

I. Rodriguez-Iturbe

Keyword(s):

Dynamical System ◽

Initial Conditions ◽

Nonlinear Dynamical System ◽

Soil Nutrient ◽

Steady State Solution ◽

Basins Of Attraction ◽

Climatic Conditions ◽

Stable Node ◽

Nutrient Cycles ◽

Stable Focus

Abstract. An analytical model for the soil carbon and nitrogen cycles is studied from the dynamical system point of view. Its main nonlinearities and feedbacks are analyzed by considering the steady state solution under deterministic hydro-climatic conditions. It is shown that, changing hydro-climatic conditions, the system undergoes dynamical bifurcations, shifting from a stable focus to a stable node and back to a stable focus when going from dry, to well-watered, and then to saturated conditions, respectively. An alternative degenerate solution is also found in cases when the system can not sustain decomposition under steady external conditions. Different basins of attraction for "normal" and "degenerate" solutions are investigated as a function of the system initial conditions. Although preliminary and limited to the specific form of the model, the present analysis points out the importance of nonlinear dynamics in the soil nutrient cycles and their possible complex response to hydro-climatic forcing.

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Least-Squares Parameter Estimation Algorithm for a Class of Input Nonlinear Systems

Journal of Applied Mathematics ◽

10.1155/2012/684074 ◽

2012 ◽

Vol 2012 ◽

pp. 1-14 ◽

Cited By ~ 13

Author(s):

Weili Xiong ◽

Wei Fan ◽

Rui Ding

Keyword(s):

Parameter Estimation ◽

Nonlinear Systems ◽

Least Squares ◽

Moving Average ◽

Estimation Algorithm ◽

Autoregressive Moving Average ◽

Parameter Estimates ◽

Persistent Excitation ◽

Estimation Algorithms ◽

Parameter Estimation Algorithm

This paper studies least-squares parameter estimation algorithms for input nonlinear systems, including the input nonlinear controlled autoregressive (IN-CAR) model and the input nonlinear controlled autoregressive autoregressive moving average (IN-CARARMA) model. The basic idea is to obtain linear-in-parameters models by overparameterizing such nonlinear systems and to use the least-squares algorithm to estimate the unknown parameter vectors. It is proved that the parameter estimates consistently converge to their true values under the persistent excitation condition. A simulation example is provided.

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Optimal dynamic incentive scheduling for Hawk-Dove evolutionary games

10.1101/2021.08.15.456406 ◽

2021 ◽

Author(s):

Kristina Stuckey ◽

Rajvir Dua ◽

Yongqian Ma ◽

Joseph Parker ◽

Paul K Newton

Keyword(s):

Dynamical System ◽

Initial Conditions ◽

Replicator Dynamics ◽

Minimum Principle ◽

Nonlinear Dynamical System ◽

Evolutionary Games ◽

Time Dependent ◽

Upper And Lower Bounds ◽

Trade Offs ◽

Optimal Dynamic

The Hawk-Dove mathematical game offers a paradigm of the trade-offs associated with aggressive and passive behaviors. When two (or more) populations of players (animals, insect populations, countries in military conflict, economic competitors, microbial communities, populations of co-evolving tumor cells, or reinforcement learners adopting different strategies) compete, their success or failure can be measured by their frequency in the population (successful behavior is reinforced, unsuccessful behavior is not), and the system is governed by the replicator dynamical system. We develop a time-dependent optimal-adaptive control theory for this nonlinear dynamical system in which the payoffs of the Hawk-Dove payoff matrix are dynamically altered (dynamic incentives) to produce (bang-bang) control schedules that (i) maximize the aggressive population at the end of time T, and (ii) minimize the aggressive population at the end of time T. These two distinct time-dependent strategies produce upper and lower bounds on the outcomes from all strategies since they represent two extremizers of the cost function using the Pontryagin maximum (minimum) principle. We extend the results forward to times nT (n = 1, ..., 5) in an adaptive way that uses the optimal value at the end of time nT to produce the new schedule for time (n+1)T. Two special schedules and initial conditions are identified that produce absolute maximizers and minimizers over an arbitrary number of cycles for $0 \le T \le 3$. For T > 3, our optimum schedules can drive either population to extinction or fixation. The method described can be used to produce optimal dynamic incentive schedules for many different applications in which the 2 x 2 replicator dynamics is used as a governing model.

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Estimation of oscillation velocities of oscillator network

Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine ◽

10.37069/1683-4720-2018-32-17 ◽

2018 ◽

Vol 32 ◽

pp. 182-189

Author(s):

Volodymyr Shcherbak ◽

Iryna Dmytryshyn

Keyword(s):

Dynamical System ◽

Nonlinear Oscillations ◽

Initial Conditions ◽

Nonlinear Dynamical System ◽

Stable Limit Cycle ◽

Nonlinear Observer ◽

Stable Limit ◽

Nonlinear Dynamical ◽

Biomechanical Models ◽

Neural Ensembles

The study of the collective behavior of multiscale dynamic processes is currently one of the most urgent problems of nonlinear dynamics. Such systems arise on modelling of many cyclical biological or physical processes. It is of fundamental importance for understanding the basic laws of synchronous dynamics of distributed active subsystems with oscillations, such as neural ensembles, biomechanical models of cardiac or locomotor activity, models of turbulent media, etc. Since the nonlinear oscillations that are observed in such systems have a stable limit cycle , which does not depend on the initial conditions, then a system of interconnected nonlinear oscillators is usually used as a model of multiscale processes. The equations of Lienar type are often used as the main dynamic model of each of these oscillators. In a number of practical control problems of such interconnected oscillators it is necessary to determine the oscillation velocities by known data. This problem is considered as observation problem for nonlinear dynamical system. A new method – a synthesis of invariant relations is used to design a nonlinear observer. The method allows us to represent unknowns as a function of known quantities. The scheme of the construction of invariant relations consists in the expansion of the original dynamical system by equations of some controlled subsystem (integrator). Control in the additional system is used for the synthesis of some relations that are invariant for the extended system and have the attraction property for all of its trajectories. Such relations are considered in observation problems as additional equations for unknown state vector of initial oscillators ensemble. To design the observer, first we introduce a observer for unique oscillator of Lienar type and prove its exponential convergence. This observer is then extended on several coupled Lienar type oscillators. The performance of the proposed method is investigated by numerical simulations.

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GLSDC Based Parameter Estimation Algorithm for a PMSM Model

Energies ◽

10.3390/en14030611 ◽

2021 ◽

Vol 14 (3) ◽

pp. 611

Author(s):

Artun Sel ◽

Bilgehan Sel ◽

Cosku Kasnakoglu

Keyword(s):

Parameter Estimation ◽

Permanent Magnet Synchronous Motor ◽

Estimation Algorithm ◽

Industrial Applications ◽

Convergence Time ◽

Initial State ◽

Input And Output ◽

Noisy Input ◽

Before And After ◽

Parameter Estimation Algorithm

In this study, a GLSDC (Gaussian Least Squares Differential Correction) based parameter estimation algorithm is used to identify a PMSM (Permanent Magnet Synchronous Motor) model. In this method, a nonlinear model is assumed to be the correct representation of the underlying state dynamics and the output signals are assumed to be measured in a noisy environment. Using noisy input and output signals, parameters that constitute the coefficients of the nonlinear state and input signal terms are to be estimated using the state transition matrix which is computed by the numerical means that are detailed. Since a GLSDC algorithm requires correct initial state value, this term is also estimated in addition to the unknown coefficients whose bounds are assumed to be known, which is mostly the case in the industrial applications. The batch input and output signals are used to iteratively estimate the parameter set before and after the convergence, and to recover the filtered state trajectories. A couple of different scenarios are tested by means of numerical simulations and the results are addressed. Different methods are discussed to compute better initial estimate values, to shorten the convergence time.

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On Periodic Motions in the First-Order Nonlinear Systems

Volume 4B: Dynamics, Vibration, and Control ◽

10.1115/imece2016-66219 ◽

2016 ◽

Author(s):

Albert C. J. Luo ◽

Yeyin Xu ◽

Zhaobo Chen

Keyword(s):

Dynamical System ◽

Fourier Series ◽

Dynamical Systems ◽

Analytical Solutions ◽

Nonlinear Dynamical Systems ◽

Initial Conditions ◽

Nonlinear Dynamical System ◽

Periodic Motions ◽

Nonlinear Dynamical ◽

First Order

In this paper, analytical solutions of periodic motions in the first-order nonlinear dynamical system are discussed from the finite Fourier series expression. The first-order nonlinear dynamical system is transformed to the dynamical system of coefficients in the Fourier series. From investigation of such dynamical system of coefficients, the analytical solutions of periodic motions are obtained, and the corresponding stability and bifurcation of periodic motions will be determined. In fact, this method provides a frequency-response analysis of periodic motions in nonlinear dynamical systems, which is alike the Laplace transformation of periodic motions for nonlinear dynamical systems. The harmonic frequency-amplitude curves are obtained for different-order harmonic terms in the Fourier series. Through such frequency-amplitude curves, the nonlinear characteristics of periodic motions in the first-order nonlinear system can be determined. From analytical solutions, the initial conditions are obtained for numerical simulations. From such initial conditions, numerical simulations are completed in comparison of the analytical solutions of periodic motions.

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Estimación de Parámetros Para Cargas Contaminantes Conectadas a las Redes de Distribucción

KnE Engineering ◽

10.18502/keg.v3i1.1423 ◽

2018 ◽

Vol 3 (1) ◽

pp. 171

Author(s):

Pedro Raúl De León Guerra

Keyword(s):

Parameter Estimation ◽

Least Squares ◽

Distribution System ◽

Initial Conditions ◽

Weighted Least Squares ◽

Current Model ◽

Estimation Algorithm ◽

Load Model ◽

Electric Distribution System ◽

Parameter Estimation Algorithm

In this paper we propose a new algorithm for the estimation of the parameters of the harmonic loads connected to the electric distribution system. The new parameter estimation algorithm is based on the weighted least-squares technique. The estimation algorithm solves an optimization problem and minimizes a set of variables which must comply with a series of specifications or characteristics of the harmonic loads. The estimation algorithm is able to obtain a load model with good accuracy comparatively to current -model of the system, due to a good engineering estimation of the initial conditions. Finally the new estimation algorithm could be used for power quality studies and to measure the contribution of the harmonic contamination of the clients connected to the electrical distribution system.Keywords: Harmonics, parameter estimation, weighted least squares, models.

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CHAOS-BASED SIGNAL PROCESSING

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127400000517 ◽

2000 ◽

Vol 10 (04) ◽

pp. 737-748 ◽

Cited By ~ 5

Author(s):

HERVÉ DEDIEU ◽

MACIEJ OGORZAŁEK

Keyword(s):

Dynamical System ◽

Signal Processing ◽

Initial Conditions ◽

Average Distance ◽

Nonlinear Dynamical System ◽

Measured Signal ◽

Waveform Generator ◽

Signal Restoration ◽

Nonlinear Dynamical ◽

Signal Coding

Given a time series measured (or generated) by a known or an unknown dynamical system we address a series of problems which can be considered as advanced signal processing tasks, namely: (1) section-wise approximation of the measured signal by pieces of trajectories from a chosen nonlinear dynamical system (model); (2) signal restoration when the measured signal has been corrupted e.g. by quantization; (3) signal coding and compression. These tasks can be addressed using a new approach to the shadowing problem based on nonlinear observability problem. Its goal is to reproduce initial conditions for a dynamical system under consideration (approximating waveform generator) giving rise to an orbit which is optimal in the sense of average distance from the measured (or prescribed) transient output waveform. We present the results obtained using the Chua's circuit as approximating waveform generator.

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