Abstract:
We present an asymptotic control theory for a system of an arbitrary number of linear oscillators under a common bounded control. We suggest a design method of a feedback control for this system. By using the DiPerna–Lions theory of singular ODEs, we prove that the suggested control law correctly defines the motion of the system. The obtained control is asymptotically optimal: the ratio of the motion time to zero under this control to the minimum one is close to 1 if the initial energy of the system is large. The results are partially based on a new perturbation theory of observable linear systems.
Key words and phrases:maximum principle, reachable sets, linear systems.