The Averaged Control System of Fast Oscillating Control Systems

Details The Averaged Control System of Fast Oscillating Control Systems The Averaged Control System of Fast Oscillating Control Systems

2011-12-05

arxiv.org/abs/1112.0983v2

Mathematics

Optimization and Control

Scientific paper

For control systems that either have an explicit periodic dependence on time or have periodic solutions and small controls, we define an average control system that takes into account all possible variations of the control, and prove that its solutions approximate all solutions of the oscillating systems as oscillations go faster. The dimension of its velocity set is characterised geomtrically. When it is maximum the average system defines a Finsler metric, unfortunately not twice differntiable in general. Under particular assumptions, valid for the control two body system, this Finsler metric generates a Hamiltonian flow on the cotangent bundle. For minimum time control, this average system proves that averaging the Hamiltonian given by the maximum principle is a valid approximation.

Affiliated with

Also associated with

No associations

Rating

The Averaged Control System of Fast Oscillating Control Systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Averaged Control System of Fast Oscillating Control Systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Averaged Control System of Fast Oscillating Control Systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-396017