THE PARAMETER IDENTIFICATION PROBLEM FOR SYSTEM OF DIFFERENTIAL EQUATIONS

In this paper, the parameter identification problem for system of ordinary differential equations is considered. The parameter identification problem for system of ordinary differential equations is investigated by the Dzhumabaev’s parametrization method. At first, conditions for a unique solvability of the parameter identification problem for system of ordinary differential equations are obtained in the term of fundamental matrix of system’s differential part. Further, we establish conditions for a unique solvability of the parameter identification problem for system of ordinary differential equations in the terms of initial data. Algorithm for finding of approximate solution to a unique solvability of the parameter identification problem for system of ordinary differential equations is proposed and the conditions for its convergence are setted. Results this paper can be use for investigating of various problems with parameter and control problems for system of ordinary differential equations. The approach in this paper can be apply to the parameter identification problems for partial differential equations.

Simultaneous Indirect Inference, Impulse Responses and ARMA Models

A two-stage simulation-based framework is proposed to derive Identification Robust confidence sets by applying Indirect Inference, in the context of Autoregressive Moving Average (ARMA) processes for finite samples. Resulting objective functions are treated as test statistics, which are inverted rather than optimized, via the Monte Carlo test method. Simulation studies illustrate accurate size and good power. Projected impulse-response confidence bands are simultaneous by construction and exhibit robustness to parameter identification problems. The persistence of shocks on oil prices and returns is analyzed via impulse-response confidence bands. Our findings support the usefulness of impulse-responses as an empirically relevant transformation of the confidence set.

Recursive Algorithms for Multivariable Output-Error-Like ARMA Systems

This paper studies the parameter identification problems for multivariable output-error-like systems with colored noises. Based on the hierarchical identification principle, the original system is decomposed into several subsystems. However, each subsystem contains the same parameter vector, which leads to redundant computation. By taking the average of the parameter estimation vectors of each subsystem, a partially-coupled subsystem recursive generalized extended least squares (PC-S-RGELS) algorithm is presented to cut down the redundant parameter estimates. Furthermore, a partially-coupled recursive generalized extended least squares (PC-RGELS) algorithm is presented to further reduce the computational cost and the redundant estimates by using the coupling identification concept. Finally, an example indicates the effectiveness of the derived algorithms.

Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data

It is well-known that mathematical models are the basis for system analysis and controller design. This paper considers the parameter identification problems of stochastic systems by the controlled autoregressive model. A gradient-based iterative algorithm is derived from observation data by using the gradient search. By using the multi-innovation identification theory, we propose a multi-innovation gradient-based iterative algorithm to improve the performance of the algorithm. Finally, a numerical simulation example is given to demonstrate the effectiveness of the proposed algorithms.