IEEE - Institute of Electrical and Electronics Engineers, Inc. - Comments on "On the Necessity of Diffusive Couplings in Linear Synchronization Problems With Quadratic Cost"
|Author(s):||Henk J. van Waarde ; M. Kanat Camlibel ; Harry L. Trentelman|
|Sponsor(s):||IEEE Control Systems Society|
|Publisher:||IEEE - Institute of Electrical and Electronics Engineers, Inc.|
In this note we want to comment on the recent paper  by Montenbruck, Schmidt, Seyboth and Allg¨ower on the necessity of difusiveness of optimal control laws in linear quadratic control problems... View More
In this note we want to comment on the recent paper  by Montenbruck, Schmidt, Seyboth and Allg¨ower on the necessity of difusiveness of optimal control laws in linear quadratic control problems in the context of synchronization. In the paper  the authors concentrate on the optimal feedback law associated with the maximal solution of the underlying algebraic Riccati equation (ARE). In this comment we argue that it is more natural to use the smallest positive semidefinite solution of the ARE. Our approach generalizes the results in  to the case in which the agent dynamics is allowed to have eigenvalues in the open right half plane. Moreover, our proof considerably simplifies the one in  as it avoids the analysis of the Riccati differential equation. In addition, we propose and solve the zero endpoint version of the linear quadratic problem studied in .View Less