Nonlinear Control Problems with Fractional Derivatives

In this work, we investigate control problems for nonlinear fractional systems of differential equations. The aim is to find the control that will govern the system from a given initial state to a desired final state. First, we shall study concepts such as controllability and observability, the Gramian matrix, the Kalman rank condition, and the adjoint system, all generalized in the fractional framework. Then, we shall employ various techniques and tools from fractional calculus and functional analysis, such as linearization, a priori estimates and fixed point, in order to obtain a solution. The approach that we propose in this work is essentially novel and of importance, both in the control theory and fractional calculus.