Robust and Optimal Control of Interconnected
Systems

Many systems consist of similar units which directly interact with their
nearest
neighbors. Even when these units have tractable models and interact
with their
neighbors in a simple and predictable fashion, when viewed as a whole
the resulting
system often displays rich and complex behavior. Examples include
vehicle platoons,
formation flight of unmanned aerial vehicles, and in the limit as the
size of the subsystems approach zero,
systems governed by partial differential equations. An important
aspect of many of these systems
is that sensing and actuation capabilities exist at every unit. In the
examples above, this is clearly the case for
vehicle platoons and aerial vehicle systems; with the rapid advances
in micro electro-mechanical
actuators and sensors, one may control systems governed by partial
differential equations
with a large number of distributed actuators and sensors as well.
If one attempts to control these systems using standard control design
techniques, severe limitations will be quickly
encountered as most optimal control techniques cannot handle systems of
high dimension and
with a large number of inputs and outputs. In addition, it is
typically
not feasible to control these systems with centralized schemes, as
these require
high levels of connectivity, impose a substantial computational burden,
and are typically
more sensitive to failures and modeling errors than decentralized
schemes.
In this talk, we investigate the use of multidimensional system
optimization to tackle the
above classes of problems. It is shown that semidefinite programming
algorithms can be used to synthesize
control systems for spatially distributed and interconnected systems.
From the point of implementation,
the resulting control strategies inherit the same structure as the
plant; in particular, the controllers are
distributed, with communication allowed between neighboring
controllers. Several examples are
presented which outline the strength of this approach.