Controllability and Energy-Optimal Control of Time-Variant Fractional Systems

Time-variant fractional models are used to describe many applications, e.g. lithium-ion batteries. For such models, neither a controllability criterion for state space equations nor the energy-optimal control function are available so far. To overcome this limitation, in this paper a reachability and controllability definition for time-variant fractional state space systems is formulated and the analytical solution of the energy-optimal control problem is derived. In this context, a fractional Gramian-Matrix appears. The fact that the fractional system state must be interpreted differently than the state of a regular system is central to this paper. The reason for the difference in the interpretation is that the fractional system state additionally depends on an initialization procedure.