Signals Sensors and Systems
Royal Institute of Technology (KTH)
SE-100 44 Stockholm, Sweden
The synthesis of optimal decentralized controllers for complex
systems is a longstanding open problem. Conventional controls analysis
breaks down when multiple controllers have access to different information.
In the general case, this problem is notoriously difficult, even when the plant
and possible controllers are all LTI.
It is shown that when a simple condition holds, the optimal decentralized
control problem may be recast as a convex optimization problem. This
condition unified the few previously identified tractable problems, and has
elucidated many new ones. The implications for optimal control subject to
sparsity constraints will be shown, as will those for interconnected systems
subject to communication delays.
We then discuss recent work which considers all of the causal stabilizing
controllers for such systems. A new condition is introduced, under which we
may similarly parameterize all of the stabilizing decentralized controllers,
even if the plant or admissible controllers may be nonlinear time-varying.
In addition to extending LTI results to NLTV, we further see how this recent
result may allow this work to extend beyond the field of decentralized
control, to all types of constrained control problems.
These results all hinge on being able to show that certain constraints are
invariant under a feedback map. Time permitting, we'll discuss some of the
more technical aspects of this research which made these results possible,
including the development of a topology for operators on extended spaces, a
resulting not-so-small gain theorem, and a convergence theorem based on a
weak notion of contractiveness.