LQ optimal control problem in a behavioral setting: New perspectives on the problem statement and solution

This paper aims at providing some new insights into the linear quadratic optimization problem in the behavioral approach. A new problem statement is given and some comparisons with the standard LQ problem in the state space approach are provided. The problem solution is analyzed in detailed terms so that all optimal trajectories can be easily computed from the initial data. Noteworthy, the set of optimal solutions proves to be a behavior, too. The asymptotic stability of the optimal behavior as well as the finiteness of the cost function are finally discussed.