Recursive Identification of Continuous Two-Dimensional Systems in the Presence of Additive Colored Noise

ABSTRACT

In this paper, a recursive algorithm is developed to estimate the parameters of a partial differential equation as a continuous two-dimensional (2-D) system in the presence of additive colored noise. The system is modelled as hybrid Box–Jenkins model. No comprehensive algorithm for identification of continuous 2-D systems simultaneous with noise process parameter estimation has been proposed so far. Also, there is no recursive method to identify the continuous 2-D systems. The proposed algorithm estimates the noise-free system parameters and colored noise process parameters based on the instrumental variable method simultaneously. Finally, the performance of the proposed method is evaluated by a numerical example.

Keywords::

• Two-dimensional continuous systems
• Recursive algorithm
• Instrumental variable
• Stochastic estimation

Additional information

Notes on contributors

Mohsen Shafieirad

Mohsen Shafieirad was born in 1983. He received the BSc degree in Control Engineering from the Isfahan University of Technology, Isfahan, Iran, in 2005 and his MSc and PhD degrees in Control Engineering from Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran, in 2008 and 2014, respectively. M. Shafieirad received Rank 1 of the PhD entrance exam of Amirkabir University of Technology, and an outstanding student in BSc of Isfahan University of Technology. He is the author of over 12 research papers. His interests are in the area of multi-dimensional (M-D) systems, PDE identification, digital signal processing, sensor & ad-hoc networks, and multi-agent systems.

E-mail: [email protected]

Masoud Shafiee

Masoud Shafiee was born in 1957. He received his BSc degree in Mathematics in 1975, his MSc degree in Mathematics and MSc degree in Systems Engineering from Wright State University, Dayton, Ohio, in 1980 and 1982, respectively, and his MSc and PhD degrees in Electrical Engineering from Louisiana State University, Baton Rouge, LA, in 1984 and 1987, respectively. Prof. M. Shafiee is currently a Full Professor in the Department of Electrical Engineering at Amirkabir University of Technology, Tehran, Iran. He is also with SIC Research Institute, Amirkabir University of Technology, Tehran, Iran. Prof. Shafiee is the author of over 230 research papers and 13 books (as author) and 11 books (as translator). His research interests include multidimensional (M-D) system, singular systems, information and communications, robotics, and network stability.

E-mail: [email protected]

Mehrdad Abedi

Mehrdad Abedi received his BS, MS, and PhD from Tehran University, London University, and Newcastle University in 1970, 1973, and 1977, respectively. He worked for GEC (UK) until 1978. He then joined the Electrical Engineering Department of Amirkabir University (Tehran, Iran) where he is now a Professor and a member of the Center of Excellency on Power System. Prof. Abedi has published more than 25 books and 160 papers in various journals and conferences. He is a distinguished Professor in Iran and is a prize winner for two of his outstanding books. He is also a member of Iranian Academy of Science and member of CIGRE. His main interests are electrical machines and power systems modelling, operation, and control.

E-mail: [email protected]