Linear quadratic control problem with fixed final state for discrete-time distributed systems (Q2703060)

Linear, discrete-time, infinite-dimensional, stationary control systems are considered. Next, a quadratic control problem with fixed initial and final states is formulated and discussed. Using controllability results the relationships between exact controllability and the minimum energy control problem are pointed out. Next, applying the Hilbert uniqueness method the solution to the minimum energy control problem is presented. In the proofs of the main results optimization methods in Hilbert spaces are extensively used. Finally, a simple illustrative application is given. Moreover, several remarks and comments on the controllability and minimum energy control problems for infinite-dimensional discrete-time control systems are presented. It should be pointed out, that similar considerations concerning controllability and minimum energy control problems for continuous-time control systems can be found in the monograph [\textit{J. Klamka}, ``Controllability of dynamical systems'', Kluwer (1991; Zbl 0732.93008)].