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GRASP Student Seminar Series: Spring 2006
March 22, 5:00 PM, 307 Levine Hall
Nader Motee
"Receding Horizon Control of Spatially
Distributed Systems Over Arbitrary Graphs"
Abstract: In this talk, I will present
the problem of receding horizon control of spatially distributed systems
with input and state constraints. Specifically, we extend our earlier
results on distributed receding horizon control of spatially invariant
systems to the case of heterogeneous systems with arbitrary interconnection
topologies; i.e., without any assumption on spatial invariance. Our
approach is based on tools from operator theory and Multi Parametric
Quadratic Programming (MPQP). The key idea is the introduction of spatially
decaying operators (SD) which serve as the main ingredient in the cost
function that couples the state and control of individual agents with
those of others. It is shown that coupling between subsystems of many
well-known spatially distributed systems such as some of the recently
studied models of distributed motion coordination with nearest neighbor
interactions as well as spatially invariant systems can be characterized
using such operators. The dynamics of individual agents are uncoupled
with the coupling appearing through a finite horizon cost function.
Furthermore, agents are assumed to be heterogeneous. We prove that for
spatially distributed systems with input and state constraints in which
the coupling is through an SD operator, optimal receding horizon controllers
are piece-wise affine (represented as a convolution sum plus an offset).
More importantly, we prove that the kernel of each convolution sum decays
exponentially in the spatial domain, thereby providing evidence that
even centralized solutions to the receding horizon control problems
for such systems has an inherent spatial locality.
Biography: Nader is a Ph.D. student in ESE,
working with Ali Jadbabaie, whose research interests include distributed
receding horizon control of multi-agent systems; optimal control of
spatially invariant systems; algebraic methods in optimization and applications;
and nonlinear control of mechanical systems.
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