53 research outputs found
On Structured Realizability and Stabilizability of Linear Systems
We study the notion of structured realizability for linear systems defined
over graphs. A stabilizable and detectable realization is structured if the
state-space matrices inherit the sparsity pattern of the adjacency matrix of
the associated graph. In this paper, we demonstrate that not every structured
transfer matrix has a structured realization and we reveal the practical
meaning of this fact. We also uncover a close connection between the structured
realizability of a plant and whether the plant can be stabilized by a
structured controller. In particular, we show that a structured stabilizing
controller can only exist when the plant admits a structured realization.
Finally, we give a parameterization of all structured stabilizing controllers
and show that they always have structured realizations
Realizability and Internal Model Control on Networks
It is proved that network realizability of controllers can be enforced
without conservatism using convex constraints on the closed loop transfer
function. Once a network realizable closed loop transfer matrix has been found,
a corresponding controller can be implemented using a network structured
version of Internal Model Control.Comment: 3 page
Optimal Decentralized State-Feedback Control with Sparsity and Delays
This work presents the solution to a class of decentralized linear quadratic
state-feedback control problems, in which the plant and controller must satisfy
the same combination of delay and sparsity constraints. Using a novel
decomposition of the noise history, the control problem is split into
independent subproblems that are solved using dynamic programming. The approach
presented herein both unifies and generalizes many existing results
A System Level Approach to Controller Synthesis
Biological and advanced cyber-physical control systems often have limited, sparse, uncertain, and distributed communication and computing in addition to sensing and actuation. Fortunately, the corresponding plants and performance requirements are also sparse and structured, and this must be exploited to make constrained controller design feasible and tractable. We introduce a new “system level” (SL) approach involving three complementary SL elements. SL parameterizations (SLPs) provide an alternative to the Youla parameterization of all stabilizing controllers and the responses they achieve, and combine with SL constraints (SLCs) to parameterize the largest known class of constrained stabilizing controllers that admit a convex characterization, generalizing quadratic invariance. SLPs also lead to a generalization of detectability and stabilizability, suggesting the existence of a rich separation structure, that when combined with SLCs is naturally applicable to structurally constrained controllers and systems. We further provide a catalog of useful SLCs, most importantly including sparsity, delay, and locality constraints on both communication and computing internal to the controller, and external system performance. Finally, we formulate SL synthesis problems, which define the broadest known class of constrained optimal control problems that can be solved using convex programming
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