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Using generalized Fibonacci sequences for solving the one-dimensional LQR problem and its discrete-time Riccati equation
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Department of Technology, Narvik University College.
Department of Technology, Narvik University College.
2010 (English)In: Modeling, Identification and Control, ISSN 0332-7353, E-ISSN 1890-1328, Vol. 31, no 1, p. 1-18Article in journal (Refereed) Published
Abstract [en]

In this article we develop a method of solving general one-dimensional Linear Quadratic Regulator (LQR) problems in optimal control theory, using a generalized form of Fibonacci numbers. We find the solution R (k) of the corresponding discrete-time Riccati equation in terms of ratios of generalized Fibonacci numbers. An explicit Binet type formula for R (k) is also found, removing the need for recursively finding the solution at a given timestep. Moreover, we show that it is also possible to express the feedback gain, the penalty functional and the controller state in terms of these ratios. A generalized golden ratio appears in the corresponding in finite horizon problem. Finally, we show the use of the method in a few examples.

Place, publisher, year, edition, pages
2010. Vol. 31, no 1, p. 1-18
National Category
Mathematical Analysis
Research subject
Mathematics
Identifiers
URN: urn:nbn:se:ltu:diva-6067DOI: 10.4173/mic.2010.1.1Local ID: 444b0fc0-b1ae-11df-a707-000ea68e967bOAI: oai:DiVA.org:ltu-6067DiVA: diva2:978944
Note
Validerad; 2010; 20100827 (andbra)Available from: 2016-09-29 Created: 2016-09-29 Last updated: 2017-11-24Bibliographically approved

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