Optimal Control of Vehicular Formations with Nearest Neighbor Interactions

Details Optimal Control of Vehicular Formations with Nearest Neighbor Interactions Optimal Control of Vehicular Formations with Nearest Neighbor Interactions

2011-12-18

arxiv.org/abs/1112.4113v1

Mathematics

Optimization and Control

To appear in IEEE Trans. Automat. Control; 15 pages, 10 figures

Scientific paper

We consider the design of optimal localized feedback gains for one-dimensional formations in which vehicles only use information from their immediate neighbors. The control objective is to enhance coherence of the formation by making it behave like a rigid lattice. For the single-integrator model with symmetric gains, we establish convexity, implying that the globally optimal controller can be computed efficiently. We also identify a class of convex problems for double-integrators by restricting the controller to symmetric position and uniform diagonal velocity gains. To obtain the optimal non-symmetric gains for both the single- and the double-integrator models, we solve a parameterized family of optimal control problems ranging from an easily solvable problem to the problem of interest as the underlying parameter increases. When this parameter is kept small, we employ perturbation analysis to decouple the matrix equations that result from the optimality conditions, thereby rendering the unique optimal feedback gain. This solution is used to initialize a homotopy-based Newton's method to find the optimal localized gain. To investigate the performance of localized controllers, we examine how the coherence of large-scale stochastically forced formations scales with the number of vehicles. We establish several explicit scaling relationships and show that the best performance is achieved by a localized controller that is both non-symmetric and spatially-varying.

Affiliated with

Also associated with

No associations

Rating

Optimal Control of Vehicular Formations with Nearest Neighbor Interactions 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 Optimal Control of Vehicular Formations with Nearest Neighbor Interactions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Optimal Control of Vehicular Formations with Nearest Neighbor Interactions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-25676