Feng Ding

Identification of Hammerstein nonlinear ARMAX systems

Two identification algorithms, an iterative least-squares and a recursive least-squares, are developed for Hammerstein nonlinear systems with memoryless nonlinear blocks and linear dynamical blocks described by ARMAX/CARMA models. The basic idea is to replace unmeasurable noise terms in the information vectors by their estimates, and to compute the noise estimates based on the obtained parameter estimates. Convergence properties of the recursive algorithm in the stochastic framework show that the parameter estimation error consistently converges to zero under the generalized persistent excitation condition. The simulation results validate the algorithms proposed.

Gradient based iterative algorithms for solving a class of matrix equations

In this note, we apply a hierarchical identification principle to study solving the Sylvester and Lyapunov matrix equations. In our approach, we regard the unknown matrix to be solved as system parameters to be identified, and present a gradient iterative algorithm for solving the equations by minimizing certain criterion functions. We prove that the iterative solution consistently converges to the true solution for any initial value, and illustrate that the rate of convergence of the iterative solution can be enhanced by choosing the convergence factor (or step-size) appropriately. Furthermore, the iterative method is extended to solve general linear matrix equations. The algorithms proposed require less storage capacity than the existing numerical ones. Finally, the algorithms are tested on computer and the results verify the theoretical findings.

Hierarchical gradient-based identification of multivariable discrete-time systems

In this paper, we use a hierarchical identification principle to study identification problems for multivariable discrete-time systems. We propose a hierarchical gradient iterative algorithm and a hierarchical stochastic gradient algorithm and prove that the parameter estimation errors given by the algorithms converge to zero for any initial values under persistent excitation. The proposed algorithms can be applied to identification of systems involving non-stationary signals and have significant computational advantage over existing identification algorithms. Finally, we test the proposed algorithms by simulation and show their effectiveness.

Hierarchical least squares identification methods for multivariable systems

For multivariable discrete-time systems described by transfer matrices, we develop a hierarchical least squares iterative (HLSI) algorithm and a hierarchical least squares (HLS) algorithm based on a hierarchical identification principle. We show that the parameter estimation error given by the HLSI algorithm converges to zero for the deterministic cases, and that the parameter estimates by the HLS algorithm consistently converge to the true parameters for the stochastic cases. The algorithms proposed have significant computational advantage over existing identification algorithms. Finally, we test the proposed algorithms on an example and show their effectiveness.

Performance analysis of multi-innovation gradient type identification methods

It is well-known that the stochastic gradient (SG) identification algorithm has poor convergence rate. In order to improve the convergence rate, we extend the SG algorithm from the viewpoint of innovation modification and present multi-innovation gradient type identification algorithms, including a multi-innovation stochastic gradient (MISG) algorithm and a multi-innovation forgetting gradient (MIFG) algorithm. Because the multi-innovation gradient type algorithms use not only the current data but also the past data at each iteration, parameter estimation accuracy can be improved. Finally, the performance analysis and simulation results show that the proposed MISG and MIFG algorithms have faster convergence rates and better tracking performance than their corresponding SG algorithms.

Combined parameter and output estimation of dual-rate systems using an auxiliary model

For a dual-rate sampled-data system, an auxiliary model based identification algorithm for combined parameter and output estimation is proposed. The basic idea is to use an auxiliary model to estimate the unknown noise-free output (true output) of the system, and directly to identify the parameters of the underlying fast single-rate model from the dual-rate input-output data. It is shown that the parameter estimation error consistently converges to zero under generalized or weak persistent excitation conditions and unbounded noise variance, and that the output estimates uniformly converge to the true outputs. An example is included.

Auxiliary model-based least-squares identification methods for Hammerstein output-error systems

Abstract The difficulty in identification of a Hammerstein (a linear dynamical block following a memoryless nonlinear block) nonlinear output-error model is that the information vector in the identification model contains unknown variables—the noise-free (true) outputs of the system. In this paper, an auxiliary model-based least-squares identification algorithm is developed. The basic idea is to replace the unknown variables by the output of an auxiliary model. Convergence analysis of the algorithm indicates that the parameter estimation error consistently converges to zero under a generalized persistent excitation condition. The simulation results show the effectiveness of the proposed algorithms.

Hierarchical identification of lifted state-space models for general dual-rate systems

This paper is motivated by practical consideration that the input updating and output sampling rates are often limited due to sensor and actuator speed constraints. In particular, for general dual-rate systems with different updating and sampling periods, we derive the lifted state-space models (mapping relations between available dual-rate input-output data), and, by using a hierarchical identification principle, present combined parameter and state estimation algorithms for identifying the canonical lifted models based on the given dual-rate input-output data, taking into account the causality constraints of the lifted systems. Finally, we give an illustrative example to indicate that the proposed algorithm is effective.

Parameter estimation of dual-rate stochastic systems by using an output error method

In this note, a new gradient-based recursive algorithm for estimating parameters of dual-rate sampled-data systems is presented. The basic idea is, by using an output error method, to identify the single-rate models and the unknown noise-free outputs (true outputs) directly from dual-rate input-output data. Further, convergence properties of the proposed algorithm in parameter and output estimation are analyzed; and the result is illustrated and tested with an experimental water-level system.

Performance bounds of forgetting factor least-squares algorithms for time-varying systems with finite measurement data

This paper on performance analysis of parameter estimation is motivated by a practical consideration that the data length is finite. In particular, for time-varying systems, we study the properties of the well-known forgetting factor least-squares (FFLS) algorithm in detail in the stochastic framework, and derive upperbounds and lowerbounds of the parameter estimation errors (PEE), using directly the finite input-output data. The analysis indicates that the mean square PEE upperbounds and lowerbounds of the FFLS algorithm approach two finite positive constants, respectively, as the data length increases, and that these PEE upperbounds can be minimized by choosing appropriate forgetting factors. We further show that for time-invariant systems, the PEE upperbounds and lowerbounds of the ordinary least-squares algorithm both tend to zero as the data length increases. Finally, we illustrate and verify the theoretical findings with several example systems, including an experimental water-level system.