Optimal control problems over large time intervals (Q1091599)

Consider a linear quadratic optimal control problem with prescribed initial and final states, in which the time interval T is large - it does not appear that a criterion is given to determine when this condition actually occurs. The authors show that most of the transient activity occurs near \(t=0\) and \(t=T\), that the state vector remains small away from these points, and that the optimal trajectory and control for the original problem can be approximately obtained by piecing together the optimal trajectories and controls for two infinite-time problems.