DocumentCode :
116387
Title :
Representation and LQR of exact fractional order systems
Author :
Shu Liang ; Sheng-Guo Wang ; Yong Wang
Author_Institution :
UNC Charlotte, Charlotte, NC, USA
fYear :
2014
fDate :
15-17 Dec. 2014
Firstpage :
6908
Lastpage :
6913
Abstract :
This paper proposes an efficient mathematical operator called spatial product whereby fractional order systems (FOSs) can be represented as a standard state space form of partial differential equations. This infinite dimensional model represents the true state of the FOS and is adopted in this study, whereas the widely used pseudo state space equation with Caputo´s definition is only an approximate model. We derive the exact state space solution of the FOS in terms of the spatial product and also reveal a separation property with respect to the initialization of FOSs. Furthermore, the linear quadratic regulator (LQR) and the H2 control of FOSs are studied in such rigorous frame. The results show that these optimal control problems can be formatted as Riccati-type equations in the sense of the spatial product.
Keywords :
H control; linear quadratic control; partial differential equations; state-space methods; Caputo definition; FOS; H2 control; LQR; Riccati-type equations; exact state space solution; fractional order systems; infinite dimensional model; linear quadratic regulation; optimal control; partial differential equations; separation property; Aerospace electronics; Distribution functions; Equations; Mathematical model; Optimal control; Performance analysis; Standards;
fLanguage :
English
Publisher :
ieee
Conference_Titel :
Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on
Conference_Location :
Los Angeles, CA
Print_ISBN :
978-1-4799-7746-8
Type :
conf
DOI :
10.1109/CDC.2014.7040474
Filename :
7040474
Link To Document :
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