Hierarchical Newton and least squares iterative estimation algorithm for dynamic systems by transfer functions based on the impulse responses

Abstract

This paper develops a parameter estimation algorithm for linear continuous-time systems based on the hierarchical principle and the parameter decomposition strategy. Although the linear continuous-time system is a linear system, its output response is a highly nonlinear function with respect to the system parameters. In order to propose a direct estimation algorithm, a criterion function is constructed between the response output and the observation output by means of the discrete sampled data. Then a scheme by combining the Newton iteration and the least squares iteration is builded to minimise the criterion function and derive the parameter estimation algorithm. In light of the different features between the system parameters and the output function, two subalgorithms are derived by using the parameter decomposition. In order to remove the associate terms between the two sub-algorithms, a Newton and least squares iterative algorithm is deduced to identify system parameters. Compared with the Newton iterative estimation algorithm without the parameter decomposition, the complexity of the hierarchical Newton and least squares iterative estimation algorithm is reduced because the dimension of the Hessian matrix is lessened after the parameter decomposition. The experimental results show that the proposed algorithm has good performance.

Highly computationally efficient state filter based on the delta operator

“…To improve the computational efficiency, this section presents a direct state estimation algorithm in a two-step process for the linear system in (1)- (2).…”

“…1 Compared with the transfer function representation, [2][3][4] it can be applied to more complex systems such as multiinput multioutput systems 5 and nonlinear systems. 1 Compared with the transfer function representation, [2][3][4] it can be applied to more complex systems such as multiinput multioutput systems 5 and nonlinear systems.…”

“…As the basis of modern control theory, the state-space representation is an effective mathematical model to totally describe the dynamic behaviors of physical systems. 1 Compared with the transfer function representation, [2][3][4] it can be applied to more complex systems such as multiinput multioutput systems 5 and nonlinear systems. 6 Filtering methods have been widely used in parameter estimation, 7,8 and the combined state and parameter estimation of state-space systems have attracted much attention throughout the world.…”

“…s) ∶= (s) −X(s|s) ∈ R nr + n n r + n Sum 3(nr + n) 3 + 9(nr + n)2 3(nr + n) 3 + 3(nr + n) 2 +8(nr + n) + 2 +4(nr + n) + 1 Total flop N 1 ∶ = 6(nr + n) 3 + 12(nr + n) 2 + 12(nr + n) + 3…”

Adaptive parameter estimation for a general dynamical system with unknown states

“…10,11 Parameter estimation and state filtering are basic for system control and system analysis. 12,13 Many parameter estimation methods, such as hierarchical identification methods, 14,15 Newton identification methods, [16][17][18] and coupled identification methods, 19,20 have been widely studied. In the literature, Waschburger and Galvão investigated a method to estimate the input delays of a discrete-time state-space model by utilizing the standard least squares methods to minimize a quadratic cost function of the prediction error of the system states within a given time range.…”