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.