Investigation of two kinds of optimal control problem for fractional order pendulum using the method of moments

The optimal control problem of two kinds investigated for pendulum of fractional order in case when admissible control search evaluated in space of functions which are quadratic integrable on the segment. The first kind of problem is to search control which passes the system in given state with minimal control norm at given control time. The second one is to search control which passes the system in given state with minimal control time at given control norm restriction. It is shown that both of these problems can be reduced to the problem of moments. For the last problem the conditions derived which define possibility of statement and solvability. Explicit solution for optimal control problem obtained analytically. Computational experiments evaluated and dependencies of control norm and minimal transition time from order of fractional derivative investigated. Also qualitative dynamics of investigated system studied: boundaries of integral funnel and phase trajectories in optimal control mode calculated.