Calendar

Posted September 6, 2024
Last modified October 11, 2024

Control and Optimization Seminar Questions or comments?

Laura Menini, Università degli Studi di Roma Tor Vergata
Distance to Instability for LTI Systems under Structured Perturbations

The talk will present a procedure to compute the distance to instability for linear systems subject to structured perturbations, in particular perturbations that affect polynomially the dynamics of the system. The procedure is based on classical notions from stability of linear systems, optimization and algebraic geometry, some of which will be reviewed briefly. The application to the design of fixed-structure controllers to deal with robust control problems will also be outlined, with the goal of choosing the controller which obtains the best conservative estimate of the region of stability. The results will be illustrated on some academic examples.

Posted August 29, 2024
Last modified October 22, 2024

Control and Optimization Seminar Questions or comments?

Piernicola Bettiol, Université de Bretagne Occidentale, France
Average Cost Minimization Problems Subject to State Constraints

Optimal control problems involving parameters appear to be a natural framework for some models arising in applications such as aerospace engineering, machine learning, and biology, among many others. According to the nature of the problem (or the model), we may have different minimization criteria; in some circumstances it is more convenient to provide the performance criterion in terms of an average cost, providing a paradigm which differs from the more traditional minimax or robust optimization criteria. In this talk, we shall consider pathwise state constraint optimal control problems in which unknown parameters intervene in the dynamics, the cost, the endpoint constraint, and the state constraint. The cost criteria to minimize take the integral form of a given endpoint cost function with respect to a reference probability measure that is defined on the set of unknown parameters. For this class of problems, we shall present the necessary optimality conditions.

Posted August 21, 2024
Last modified September 12, 2024

Control and Optimization Seminar Questions or comments?

Benedetto Piccoli, Rutgers University, Camden AMS Fellow, SIAM W. T. and Idalia Reid Prize Awardee
Control Theory in Traffic Applications: 100 Years of Traffic Models

In 1924, in The Quarterly Journal of Economics, Frank H. Knight debated on social costs using an example of two roads, which was the base of the Wardrop’s principle. The author suggested the use of road tolls and it was probably the first traffic model ever. A few other milestones of a long history include the traffic measurements by Greenshields in 1934, the Lighthill-Whitham-Richards model in late 1950s, and follow-the-leader microscopic models. After describing some of these milestones, we will turn to modern theory of conservation laws on topological graphs with application to traffic monitoring. The theory required advance mathematics such as BV spaces and Finsler-type metrics on L1. In the late 2000s, this theory was combined with Kalman filtering to deal with traffic monitoring using data from cell phones and other devices. Then we will turn to measure-theoretic approaches for multi-agent systems, which encompass follow-the-leader-type models. Tools from optimal transport allow us to deal with the mean-field limit of controlled equations, representing the action of autonomous vehicles. We will conclude by discussing how autonomy can dissipate traffic waves and reduce fuel consumption, then illustrating the results of a 2022 experiment with 100 autonomous vehicles on an open highway in Nashville.

Posted August 13, 2024

Control and Optimization Seminar Questions or comments?

Karl Johansson, KTH Royal Institute of Technology, Sweden Fellow of IEEE, IEEE CSS Hendrik W. Bode Lecture Prize Awardee
TBA

Posted September 4, 2024

Control and Optimization Seminar Questions or comments?

María Soledad Aronna, Escola de Matematica Aplicada, Brazil
TBA

Posted November 1, 2024

Control and Optimization Seminar Questions or comments?

Ali Zemouche, University of Lorraine, France
TBA

Posted November 7, 2024

Control and Optimization Seminar Questions or comments?

Irena Lasiecka, University of Memphis AACC Bellman Control Heritage Awardee, AMS Fellow, SIAM Fellow, and SIAM Reid Prize Awardee
TBA