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Posted January 16, 2025
Last modified April 5, 2025

Control and Optimization Seminar Questions or comments?

Bahman Gharesifard, Queen's University
Structural Average Controllability of Ensembles

In ensemble control, the goal is to steer a parametrized collection of independent systems using a single control input. A key technical challenge arises from the fact that this control input must be designed without relying on the specific parameters of the individual systems. Broadly speaking, as the space of possible system parameters grows, so does the size and diversity of the ensemble — making it increasingly difficult to control all members simultaneously. In fact, an important result among the recent advances on this topic states that when the underlying parameterization spaces are multidimensional, real-analytic linear ensemble systems are not L^p-controllable for p>=2. Therefore, one has to relax the notion of controllability and seek more flexible controllability characteristics. In this talk, I consider continuum ensembles of linear time-invariant control systems with single inputs, featuring a sparsity pattern, and study structural average controllability as a relaxation of structural ensemble controllability. I then provide a necessary and sufficient condition for a sparsity pattern to be structurally average controllable.

Posted April 18, 2025

Combinatorics Seminar Questions or comments?

Mark Ellingham, Vanderbilt University
Maximum genus directed embeddings of digraphs

In topological graph theory we often want to find embeddings of a given connected graph with minimum genus, so that the underlying compact surface of the embedding is as simple as possible. If we restrict ourselves to cellular embeddings, where all faces are homeomorphic to disks, then it is also of interest to find embeddings with maximum genus. For undirected graphs this is a very well-solved problem. For digraphs we can consider directed embeddings, where each face is bounded by a directed walk in the digraph. The maximum genus problem for digraphs is related to self-assembly problems for models of graphs built from DNA or polypeptides. Previous work by other people determined the maximum genus for the very special case of regular tournaments, and in some cases of directed 4-regular graphs the maximum genus can be found using an algorithm for the representable delta-matroid parity problem. We describe some recent work, joint with Joanna Ellis-Monaghan of the University of Amsterdam, where we have solved the maximum directed genus problem in some reasonably general situations.

Posted February 19, 2025
Last modified April 24, 2025

Control and Optimization Seminar Questions or comments?

Nina Amini, Laboratory of Signals and Systems, CentraleSupélec
Feedback Control of Open Quantum Systems

First, we provide an overview of control strategies for open quantum systems, that is, quantum systems interacting with an environment. This interaction leads to a loss of information to the environment, a phenomenon commonly referred to as decoherence. One of the principal challenges in controlling open quantum systems is compensating for decoherence. To address robustness issues, feedback control methods are considered. Secondly, we consider the feedback stabilization of open quantum systems under repeated indirect measurements, where the evolution is described by quantum trajectories. I will present our recent results concerning the asymptotic behavior, convergence speed, and stabilization of these trajectories.