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Time Optimal Control in Time Series Movement

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DOI: 10.4236/jamp.2015.39139    1,638 Downloads   1,971 Views  
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ABSTRACT

The paper analyses time series that exhibit equilibrium states. It analyses the formation of equilibrium and how the system can return to the aforementioned equilibrium. The tool that is used in the aforementioned analysis is time optimal control in the phase plane. It is proved that equilibrium state is sustainable if initial state is not too far from the equilibrium as well as control vector is large enough. On the other hand, if initial state is one standard deviation away from equilibrium state, it is proved that equilibrium cannot be reached. It is the same case with control vector. If it is unbounded, time optimal control cannot be applied. The approach that is introduced represents unconventional method of analysing equilibrium in time series.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Vukovic, O. (2015) Time Optimal Control in Time Series Movement. Journal of Applied Mathematics and Physics, 3, 1122-1125. doi: 10.4236/jamp.2015.39139.

References

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http://dx.doi.org/10.1007/978-3-642-65024-6
[2] King, A.C., Billingham, J. and Otto, S.R. (2003) Differential Equations: Linear, Nonlinear, Ordinary, Partial. Cambridge University Press, Cambridge.
http://dx.doi.org/10.1017/cbo9780511755293
[3] Hamilton, J.D. (1994) Time Series Analysis (Vol. 2). Princeton University Press, Princeton.
[4] Leitmann, G. (1966) An Introduction to Optimal Control. McGraw-Hill, New York.
[5] Macki, J. and Strauss, A. (2012) Introduction to Optimal Control Theory. Springer Science & Business Media, Berlin.

  
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