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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Tutorial and Review on the State-dependent Riccati Equation

Journal of Environmental Accounting and Management 8(2) (2019) 109--166 | DOI:10.5890/JAND.2019.06.001

Saeed Rafee Nekoo

Independent Researcher, Tehran, Iran

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Abstract

This paper presents an extensive tutorial and a complete review on the state-dependent Riccati equation (SDRE). The review covers contributions from the beginning to (near the end of 2017) current trend and works, categorized according to theoretical and practical impact. The tutorial section presents the fundamental relations, derivation and necessary conditions of the SDRE as a controller, observer and estimator. The state-dependent Riccati equation serves as a continuous and discrete time controller, observer, filter and estimator in the field of control engineering. The nature of the SDRE is in nonlinear optimal control domain; and nowadays it plays a vital role in aerospace, robotics, control of unmanned aerial vehicle, aircraft, autonomous underwater vehicle, surface vessel and other nonlinear plants. Optimality, robustness, asymptotic stability, flexibility in design and a systematic procedure are some of the advantages of this method. The capability to combine the SDRE with other methods (such as sliding mode control, fuzzy, genetic, neural network and etc.) is another important feature of the approach. The mentioned characteristics, advantages and combination of the SDRE with other techniques are reviewed comprehensively in this work.

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