Data filtering-based least squares iterative algorithm for Hammerstein nonlinear systems by using the model decomposition

This paper focuses on the iterative identification problems for a class of Hammerstein nonlinear systems. By decomposing the system into two fictitious subsystems, a decomposition-based least squares iterative algorithm is presented for estimating the parameter vector in each subsystem. Moreover, a data filtering-based decomposition least squares iterative algorithm is proposed. The simulation results indicate that the data filtering-based least squares iterative algorithm can generate more accurate parameter estimates than the least squares iterative algorithm

State estimation for bilinear systems through minimizing the covariance matrix of the state estimation errors

This paper considers the state estimation problem of bilinear systems in the presence of disturbances. The standard Kalman filter is recognized as the best state estimator for linear systems, but it is not applicable for bilinear systems. It is well known that the extended Kalman filter (EKF) is proposed based on the Taylor expansion to linearize the nonlinear model. In this paper, we show that the EKF method is not suitable for bilinear systems because the linearization method for bilinear systems cannot describe the behavior of the considered system. Therefore, this paper proposes a state filtering method for the single-input–single-output bilinear systems by minimizing the covariance matrix of the state estimation errors. Moreover, the state estimation algorithm is extended to multiple-input–multiple-output bilinear systems. The performance analysis indicates that the state estimates can track the true states. Finally, the numerical examples illustrate the specific performance of the proposed method

Least squares-based iterative identification methods for linear-in-parameters systems using the decomposition technique

By extending the least squares-based iterative (LSI) method, this paper presents a decomposition-based LSI (D-LSI) algorithm for identifying linear-in-parameters systems and an interval-varying D-LSI algorithm for handling the identification problems of missing-data systems. The basic idea is to apply the hierarchical identification principle to decompose the original system into two fictitious sub-systems and then to derive new iterative algorithms to estimate the parameters of each sub-system. Compared with the LSI algorithm and the interval-varying LSI algorithm, the decomposition-based iterative algorithms have less computational load. The numerical simulation results demonstrate that the proposed algorithms work quite well

Highly computationally efficient state filter based on the delta operator

The Kalman filter is not suitable for the state estimation of linear systems with multistate delays, and the extended state vector Kalman filtering algorithm results in heavy computational burden because of the large dimension of the state estimation covariance matrix. Thus, in this paper, we develop a novel state estimation algorithm for enhancing the computational efficiency based on the delta operator. The computation analysis and the simulation example show the performance of the proposed algorithm

Combined state and parameter estimation for Hammerstein systems with time-delay using the Kalman filtering

This paper discusses the state and parameter estimation problem for a class of Hammerstein state space systems with time-delay. Both the process noise and the measurement noise are considered in the system. Based on the observable canonical state space form and the key term separation, a pseudo-linear regressive identification model is obtained. For the unknown states in the information vector, the Kalman filter is used to search for the optimal state estimates. A Kalman-filter based least squares iterative and a recursive least squares algorithms are proposed. Extending the information vector to include the latest information terms which are missed for the time-delay, the Kalman-filter based recursive extended least squares algorithm is derived to obtain the estimates of the unknown time-delay, parameters and states. The numerical simulation results are given to illustrate the effectiveness of the proposed algorithms

Mathematical model for predicting the performance of photovoltaic system with delayed solar irradiance

In Malaysia, solar energy is the primary renewable energy source due to its proximity to the equator. In comparison to fossil fuels, solar technology is the fastest-growing, most cost-effective, and least harmful to the environment. Photovoltaic systems convert solar irradiance into electricity. Due to some factors, the amount of solar irradiance arriving at the solar photovoltaic collector at a specific location varies. The goal of this study was to develop a mathematical model for predicting the performance of a photovoltaic system, which depends on the amount of solar irradiance. A novel model for solar irradiance in the form of a delay differential equation is introduced by including the factor of delayed solar irradiance, hour angle and the sun's motion. The simulation study is carried out for the three scenarios of weather conditions: a clear day, a slightly cloudy day, and a heavily overcast day. The numerical solution is obtained by adopting the Runge Kutta method coupled with a parameter fitting technique, the Nelder Mead algorithm, which is implemented by using MATLAB software. The data from a solar plant in Pahang, Malaysia, was used for model validation and it is found that the prediction profile for solar irradiance aligns well with the intermediate and decay phases, but deviates slightly during the growth phase. The output current and power for the solar photovoltaic panel were treated as time-dependent functions. As the solar irradiance increases, the output current and power of the solar panel will increase. The result showed that the maximum output current and output power of STP250S-20/Wd Crystalline Solar Module decreased by 42% and 76% , respectively, during slightly cloudy and heavily overcast conditions when compared to clear days. In other words, the performance of a photovoltaic module is better on clear days compared to cloudy days and heavily overcast. These findings highlight the relationship between delayed solar irradiance and the performance of the solar photovoltaic system

Adaptive filtering-based multi-innovation gradient algorithm for input nonlinear systems with autoregressive noise

In this paper, by means of the adaptive filtering technique and the multi-innovation identification theory, an adaptive filtering-based multi-innovation stochastic gradient identification algorithm is derived for Hammerstein nonlinear systems with colored noise. The new adaptive filtering configuration consists of a noise whitening filter and a parameter estimator. The simulation results show that the proposed algorithm has higher parameter estimation accuracies and faster convergence rates than the multi-innovation stochastic gradient algorithm for the same innovation length. As the innovation length increases, the filtering-based multi-innovation stochastic gradient algorithm gives smaller parameter estimation errors than the recursive least squares algorithm