TITLE:
Time Optimal Control in Time Series Movement
AUTHORS:
Ognjen Vukovic
KEYWORDS:
Time-Series, Equilibrium State, Time Optimal Control, Analysis, Control Vector, Financial Disruption
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.3 No.9,
September
11,
2015
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.