Quadratic Optimal Control of Graphon Q-noise Linear Systems

Understand

The modelling of linear quadratic Gaussian optimal control problems on large complex networks is intractable computationally.

• Graphon theory provides an approach to overcome these issues by defining limit objects for infinite sequences of graphs permitting one to approximate arbitrarily large networks by infinite dimensional operators.
• This is extended to stochastic systems by the use of Q-noise, a generalization of Wiener processes in finite dimensional spaces to processes in function spaces.
• The optimal control of linear quadratic problems on graphon systems with Q-noise disturbances are defined and shown to be the limit of the corresponding finite graph optimal control problem.