Graphon Linear Quadratic Regulation of Large-scale Networks of Linear Systems
Shuang Gao, Peter E. Caines · 2018
We propose a graphon regulation methodology to solve linear quadratic regulator (LQR) problems for complex networks of dynamical systems following the formulation initiated in [1]. Conditions for the exact and approximate controllability of graphon dynamical systems are investigated. Approximation schemes are then developed to obtain finite dimensional LQR control laws which are utilized on large-scale network systems and for which the convergence properties are established. Finally, an example of the application of graphon-LQR control to networks of dynamical systems is given in which the Riccati equation of the limit graphon system is solved explicitly.