2019/05/23 by Han Feng, Feng, Han, Javad Lavaei +1 · 1 citation
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #math.OC
paper · pdf · doi:10.48550/arxiv.1905.09915
20 pages, 9 figures
arxiv created 2019/05/23 · arxiv updated 2019/05/27
We study the evolution of locally optimal decentralized controllers with the damping of the control system. Empirically it is shown that even for instances with an exponential number of connected components, damping merges all local solutions to the one global solution. We characterize the evolution of locally optimal solutions with the notion of hemi-continuity and further derive asymptotic properties of the objective function and of the locally optimal controllers as the damping becomes large. Especially, we prove that with enough damping, there is no spurious locally optimal controller with favorable control structures. The convoluted behavior of the locally optimal trajectory is illustrated with numerical examples.