Optimal control problem of fractional order dynamical systems
V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, 65 Profsoyuznaya street, Moscow 117997, Russia +7 495 334-89-10, firstname.lastname@example.org
The optimal motion control problem of two-dimensional systems of fractional order is discussed when the control function belongs to a Banach space of functions. The analytical solution was found and its properties have been analyzed depending on the fractional differentiation indices, control time, initial and final conditions.
The work is devoted to optimal control of motion of fractional order linear systems. When draw an analogy with systems of integer order the similar tasks correspond to task about changing parameters of the motion laws for some object or system.
The two-dimensional system of private types: double integrator as the object of study was selected. As the fractional differentiation operator was Caputo operator. The initial and final conditions had a parametric dependence, define the laws of motion in the initial and final points in time. Some cases of type’s motion changes analyzed: transfer of system from quite state to steady or accelerated motion, from steady to accelerated motion.
The optimality criterion was set as the minimum of control norm at given control time. The study tasks based on the method of moments.
The analytical solving of optimal control problems and the behavior of control norm analyzed depending on the of fractional differentiation index. It shown that in some cases, these dependences are nonmonotonic and extreme nature.