# Event

### M.S. Defense: Reza Hadadi

Tuesday, November 30, 2021

2:00 p.m.

AVW 2328

Maria Hoo

301 405 3681

mch@umd.edu

**ANNOUNCEMENT**: M.S. Defense

**Name:**Reza Hadadi

**Committee Members:**

Professor Eyad H. Abed, Chair

Professor Andre Tits

Professor Radu V. Balan

Professor Derek Paley

Professor Andre Tits

Professor Radu V. Balan

Professor Derek Paley

**Date/Time**: Tuesday, November 30, 2021 at 2 pm

**Location**: AVW 2328

**Title:**Controllability and Tracking of Ensembles: An Optimal Transport Theory Viewpoint

**Abstract:**

Ensembles are considered that are collections of elements, agents, particles, systems, or the like, in which the evolution of each component system is governed by the same dynamical equation, but with different initial conditions. In the context of controlling ensembles, it is assumed that the control inputs are uniformly applied to all of the systems within an ensemble (usually referred to as broadcast control). It is also assumed that the systems are not individually distinguishable. Instead, collections of their outputs are observed at certain time instants, without identifying indices or labels.

In this regard, the notion of ensemble observability and its relationship with the classical notion of observability for dynamical systems is studied first. In addition, by characterizing the deterministic state distributions of ensembles as probability distributions over the state space, the state tracking problem for ensembles with linear dynamics which are optimal with respect to some cost function is cast as an optimization problem over probability distributions. Then an optimal transport (OT) theory viewpoint is adopted to transform the problem into a linear programming problem to which numerical algorithms are applied, and the time-varying state distribution of the ensemble states is interpolated over the time.

The controllability of linear ensembles is also investigated, and ideas are explored on how optimal transport theory sheds light on the optimal control of ensembles utilizing stochastic feedback laws.

The controllability of linear ensembles is also investigated, and ideas are explored on how optimal transport theory sheds light on the optimal control of ensembles utilizing stochastic feedback laws.