NDLI: A branch-and-bound algorithm to compute the worst-case norm of uncertain linear systems under inputs with magnitude and rate constraints

Content Provider	SpringerLink
Author	Khaisongkram, Wathanyoo Banjerdpongchai, David
Copyright Year	2012
Abstract	This paper extends the worst-case norm (WCN) of linear systems subject to inputs with magnitude and rate bounds to the WCN of uncertain linear systems under the same inputs. While the WCN for linear systems can be accurately approximated by simply solving a sparse linear programming, the computation of the WCN for uncertain linear systems leads to an NP-hard problem. In this paper, a branch-and-bound algorithm is applied to calculate the WCN in the presence of uncertainty. Subsequently, we derive the bounds for two approximation errors, namely, the truncation error and the discretization error, which are resulted from the proposed WCN computation method. Based on these error bounds, we give a brief guideline for choosing appropriate values of the terminal time and the sampling time. Numerical examples demonstate that computation time of the proposed algorithm is reasonable within certain problem dimensions. An exhaustive search is employed to validate the branch-and-bound algorithm. Finally, we suggest a means to improve the WCN computation for problems with higher dimension.
Starting Page	449
Ending Page	458
Page Count	10
File Format	PDF
ISSN	15986446
Journal	International Journal of Control, Automation and Systems
Volume Number	10
Issue Number	3
e-ISSN	20054092
Language	English
Publisher	Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers
Publisher Date	2012-06-13
Publisher Place	Heidelberg
Access Restriction	Subscribed
Subject Keyword	Branch-and-bound algorithm linear programming uncertain linear system worst-case norm. Control, Robotics, Mechatronics
Content Type	Text
Resource Type	Article
Subject	Control and Systems Engineering Computer Science Applications

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