Addie McCurdy

Addie McCurdy, Isabel Collins, Emily Jensen

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.

Addie McCurdy, Andrew Gusty, Emily Jensen

The optimal controller design problem for a linear, first-order spatially-invariant distributed parameter system is considered. Through a case study of the Linear Quadratic Regulator (LQR) problem for the diffusion equation over the torus, it is illustrated that the optimal controller design problem can be equivalently formulated as an optimization problem over the system's closed-loop mappings, analogous to the System Level Synthesis framework. This reformulation is solved analytically to recover the LQR for the diffusion equation, and an internally stable implementation of this controller is recovered from the optimal closed-loop mappings. It is further demonstrated that a class of spatio-temporal constraints on the closed-loop maps can be imposed on this closed-loop formulation while preserving convexity.