$l$-Problem of moments in problems of optimal control and state estimation for multidimensional fractional linear systems

In this paper, we consider multidimensional dynamical systems whose states are described by systems of linear fractional differential equations of different order. We examine problems of optimal control and optimal state estimation for systems with the Caputo and Riemann–Liouville fractional differentiation operators. We prove that under certain conditions both problems can be reduced to the $l$-problem of moments. For the resulting problem, the solvability conditions are verified and, in a number of cases, exact solutions are constructed.