Conditions for Complete Decentralization of the Linear Quadratic Regulator
For control theorists and engineers, this work provides a step toward understanding when optimal control can be decentralized, though the results are limited to specific simple cases.
This paper identifies conditions under which the optimal Linear Quadratic Regulator (LQR) can be implemented in a completely decentralized manner, where each subsystem's controller uses only local information. The conditions are derived for simple cases and extended to more complex systems, with physical interpretations provided through examples.
An unconstrained optimal control policy is completely decentralized if computing actuation for each subsystem only requires information directly available to its own subcontroller. Parameters that admit a completely decentralized optimal controller have been characterized in a variety of systems, but attempts to physically explain the phenomenon have been limited. As a step toward a general characterization of complete decentralization, this paper presents conditions for complete decentralization of Linear Quadratic Regulators for several simple cases and physically interprets these conditions with illustrative examples. These simple cases are then leveraged to characterize complete decentralization of more complex systems.