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There is now a CONTENT FREEZE for Mercury while we switch to a new platform. It began on Friday, March 10 at 6pm and will end on Wednesday, March 15 at noon. No new content can be created during this time, but all material in the system as of the beginning of the freeze will be migrated to the new platform, including users and groups. Functionally the new site is identical to the old one. webteam@gatech.edu
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You are invited to hear
give a lecture
on Friday, November 11 at 11 a.m.
Montgomery Knight 317
About this talk
In the first part of this talk I will present distributed algorithms for partitioning and locational optimization problems involving networks of agents with planar rigid body dynamics in the presence of communication constraints. First, I will discuss a solution technique for the computation of a Voronoi-like partition of a three-dimensional non-flat manifold embedded in a six-dimensional state space based on a proximity metric that is a non-quadratic function. The proposed approach is based on a special embedding technique with which the original partitioning problem is associated with a one-parameter family of partitioning problems, whose domains are two-dimensional flat sub-manifolds of the original three-dimensional manifold and their proximity metrics are (parametric) quadratic functions. In contrast with the original problem, the parametric problems have a special structure that allows one to solve them by means of exact and finite steps algorithms. Subsequently, I will utilize the proposed class of Voronoi-like partitions to develop distributed locational optimization algorithms, which are based on a “divide and conquer’’ philosophy.
In the second part of the talk, I will present control algorithms that are intended to steer the macroscopic state of a multi-agent network, when the latter is described in terms of a probability distribution, to a goal state/distribution. I will focus on finite-horizon distribution steering problems for discrete-time stochastic linear systems with either complete or incomplete state information using a stochastic optimal control framework. I will show that in the special case in which the marginal distributions are multi-variate Gaussian distributions, the stochastic optimal control problem can be essentially reduced to a finite-dimensional, deterministic nonlinear program, whose only obstruction from being a convex program is the non-convexity of a terminal equality constraint imposed on the state covariance. Subsequently, I will show that the nonlinear program can be associated, via a simple convex relaxation technique, with a convex program which can be addressed by means of robust and efficient algorithms.