Stable Inversion Based Precise Tracking for Periodic Systems

2018 ◽  
Vol 22 (1) ◽  
pp. 217-227 ◽  
Author(s):  
Qiuguo Zhu ◽  
Youling Zhang ◽  
Rong Xiong
Keyword(s):  
Periodic Systems ◽  
Stable Inversion

Precise tracking of periodic trajectories for periodic systems

2018 ◽  
Vol 41 (5) ◽  
pp. 1477-1485
Author(s):  
Youling Zhang ◽  
Qiuguo Zhu ◽  
Rong Xiong
Keyword(s):  
Trajectory Tracking ◽  
State Transition ◽  
Special Kind ◽  
Full Column Rank ◽  
Periodic Systems ◽  
Time Varying ◽  
Tracking Problem ◽  
Singular Case ◽  
Stable Inversion ◽  
Time Varying Systems

Stable inversion was an effective method to achieve precise trajectory tracking, for which the tracking problem of periodically time-varying systems was solved in the existing literature. However, iteration techniques were required to approach stable inversion, whose explicit formulas for this tracking problem cannot be obtained. To overcome this drawback, a special kind of stable inversion, named periodic inversion, for the periodic systems is proposed in this study. By means of the lifted technique, the tracking problem of the periodic systems is reformulated to be equivalent to that of lifted systems. In order to obtain precise tracking, the periodic inversion of the periodic systems or the lifted systems is proposed, and is analysed for the non-singular case and the singular case, each of which is further analysed for three cases: the full row rank case, the full column rank case and the rank-deficient case. Thus the periodic inversion of the periodic systems is computed. Accompanied with the optimal state transition method for the time-varying systems, precise trajectory tracking is achieved. The methodology is validated through simulations.

Erratum - Frustration in periodic systems : exact results for some 2D ising models

1979 ◽  
Vol 40 (10) ◽  
pp. 1024-1024
Author(s):  
G. André ◽  
R. Bidaux ◽  
J.-P. Carton ◽  
R. Conte ◽  
L. de Seze
Keyword(s):  
Ising Models ◽  
Periodic Systems ◽  
Exact Results

Further research for sensitivity analyses of discrete periodic systems

AIAA Journal ◽  
1999 ◽  
Vol 37 ◽  
pp. 653-656
Author(s):  
Ying Gu ◽  
Lifen Chen ◽  
Wenliang Wang
Keyword(s):  
Sensitivity Analyses ◽  
Periodic Systems

Optimization problems for periodic systems

2009 ◽  
Vol 45 (11) ◽  
pp. 1162-1188 ◽  
Author(s):  
F. A. Aliev ◽  
V. B. Larin
Keyword(s):  
Optimization Problems ◽  
Periodic Systems
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