Total Least Squares Estimation of Dynamical Systems
نویسندگان
چکیده
The Total least squares error criterion is considered for estimation problems. Exact necessary conditions for the total error criterion have been derived. Several solution methodologies are presented to solve the modified normal equations obtained from the necessary conditions. A monte-carlo simulation depicting the effect of parameter variations on the coefficients of the resulting characteristic polynomial is performed and the approximate probability distribution of the smallest eigenvalue of interest is identified. The results are applied on the parameter identification of a novel morphing wing developed at Texas A & M University.
منابع مشابه
Determination of Stability Domains for Nonlinear Dynamical Systems Using the Weighted Residuals Method
Finding a suitable estimation of stability domain around stable equilibrium points is an important issue in the study of nonlinear dynamical systems. This paper intends to apply a set of analytical-numerical methods to estimate the region of attraction for autonomous nonlinear systems. In mechanical and structural engineering, autonomous systems could be found in large deformation problems or c...
متن کاملHarmonics Estimation in Power Systems using a Fast Hybrid Algorithm
In this paper a novel hybrid algorithm for harmonics estimation in power systems is proposed. The estimation of the harmonic components is a nonlinear problem due to the nonlinearity of phase of sinusoids in distorted waveforms. Most researchers implemented nonlinear methods to extract the harmonic parameters. However, nonlinear methods for amplitude estimation increase time of convergence. Hen...
متن کاملImproved Parameter Estimation from Noisy Time Series for Nonlinear Dynamical Systems
In this paper we consider the problem of estimating the parameters of a nonlinear dynamical system given a finite time series of observations that are contaminated by observational noise. The least squares method is a standard method for parameter estimation, but for nonlinear dynamical systems it is well known that the least squares method can result in biased estimates, especially when the no...
متن کاملFrequency Domain Weighted Nonlinear Least Squares Estimation of Continuous-time, Time-Varying Systems∗
A frequency domain least squares estimator is presented for identifying linear, continuous-time, time-varying dynamical systems. The model considered is a linear, ordinary differential equation whose coefficients vary as polynomials in time. A frequency domain approach is used, thus allowing the user to determine easily the frequency band(s) of interest. It is shown that the bias errors due to ...
متن کاملStandard Errors and Confidence Intervals in Inverse Problems: Sensitivity and Associated Pitfalls
We review the asymptotic theory for standard errors in classical ordinary least squares (OLS) inverse or parameter estimation problems involving general nonlinear dynamical systems where sensitivity matrices can be used to compute the asymptotic covariance matrices. We discuss possible pitfalls in computing standard errors in regions of low parameter sensitivity and/or near a steady state solut...
متن کامل