Minimum time and minimum energy for linear systems; a variational approach (Q2232795)

A variational approach for the control problem for an abstract linear system is developed. The following two problems are considered: the norm optimal control problem on a fixed time interval and the problem of bringing the system to zero in the minimum time. It is noted that these problems are equivalent for certain control systems. A little analysis of the relevant literature is provided. Then, with the use of the technique related to the classical pseudoinverse for linear bounded operators acting between Hilbert spaces, the authors prove the equivalence of the problems for a specific class of abstract linear systems. This is done by reducing the considered problems to a corresponding extreme problem with special bounds. Illustrative examples are also given.