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Quadratic optimal control of graphon Q-noise linear systems
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DOI：10.1016/j.automatica.2026.113024.png)
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Abstract
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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 is defined and shown to be the limit of the corresponding finite graph optimal control problem. The theory is extended to finite rank systems, and a fully worked special case is presented. In addition, the worst-case long-range average optimal control performance with respect to some example Q-noise distributions is computed for a small set of standard graphon limits.
Keywords:
graphon theory
optimal control
Q-noise
linear quadratic systems
large networks
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