Discrete-time filtering for nonlinear polynomial systems

Abstract

This paper presents a suboptimal ${\mathcal{H}}_{\infty }$ filtering problem solution for a class of discrete-time nonlinear polynomial systems over linear observations. The solution is obtained splitting the whole problem into finding a-priori and a-posteriori equations for state estimates and gain matrices. The closed-form filtering equations for the state estimate and gain matrix are obtained in case of a third-degree polynomial system. Numerical simulations are carried out to show effectiveness of the proposed filter. The obtained filter is compared to the extended Kalman-like ${\mathcal{H}}_{\infty }$ filter.

Keywords:

• discrete time systems
• state estimation

Additional information

Funding

The authors thank the Mexican Science and Technology Council (CONACYT) for financial support of a postdoctoral stay of the second author [grant number 129081].

Notes on contributors

M.V. Basin

Michael V. Basin received his PhD degree in Physical and Mathematical Sciences with major in Automatic Control and System Analysis from the Moscow Aviation Institute in 1992. His working experiences include senior scientist position in the Institute of Control Science (Russian Academy of Sciences) in 1992–1996, visiting professor position in the University of Nevada at Reno in 1996–1997, and full professor position in the Autonomous University of Nuevo Leon, Mexico, from 1998. Starting from 1992, Dr. Basin published more than 100 research papers in international referred journals and more than 130 papers in proceedings of the leading Institute of Electrical and Electronics Engineers (IEEE) and International Federation of Automatic Control (IFAC) conferences and symposiums. He is the author of the monograph “New Trends in Optimal Filtering and Control for Polynomial and Time-Delay Systems,” published by Springer. His works are cited more than 1000 times. Dr. Basin has supervised 11 doctoral and 6 master's theses (all of them are successfully defended) and is currently supervising 5 doctoral theses. He serves as the editor-in-chief of Journal of The Franklin Institute, an associate editor of Automatica, IET-Control Theory and Applications, International Journal of Systems Science, and other journals, as a session chairman at a series of the leading IEEE and IFAC conferences, and as a reviewer for a number of leading international journals and conferences in the area of automatic control. He serves as a member of the IEEE Control System Society Technical Committees on Intelligent Control and Variable Structure Systems/Sliding Mode Control and the IEEE Industrial Electronics Society Technical Committee on Data-Driven Control and Monitoring, Program Committee member of IEEE Conference on Decision and Control 2008, IEEE Conferences on Control Applications 2009, 2012, IEEE International Symposium on Intelligent Control 2013, IEEE Workshops on Variable Structure Systems 2010, 2012, 2014, World Automation Congress 2012, Mexican Automatic Control Conferences 2006, 2008, 2011. Dr. Basin was awarded a title of Highly Cited Researcher by Thomson Reuters (International Science Institute), the publisher of Science Citation Index, in 2009; he is a Senior Member of the IEEE Control Systems Society and a regular member of the Mexican Academy of Sciences. His research interests include optimal filtering and control problems, stochastic systems, time-delay systems, identification, sliding mode control and variable structure systems.

M. Hernandez-Gonzalez

Miguel Hernandez-Gonzalez received his Master's degree in 2008 and his PhD degree in 2011 in the field of Electrical Engineering (Automatic Control) from Centro de Investigacion y de Estudios Avanzados del IPN (CINVESTAV), Zapopan, Jalisco, Mexico. His research interests include stochastic processes, nonlinear systems and neural networks.