Posted January 16, 2024
Last modified March 4, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Jorge Poveda, University of California, San Diego
Donald P. Eckman, NSF CAREER, and AFOSR Young Investigator Program Awardee
Multi-Time Scale Hybrid Dynamical Systems for Model-Free Control and Optimization
Hybrid dynamical systems, which combine continuous-time and discrete-time dynamics, are prevalent in various engineering applications such as robotics, manufacturing systems, power grids, and transportation networks. Effectively analyzing and controlling these systems is crucial for developing autonomous and efficient engineering systems capable of real-time adaptation and self-optimization. This talk will delve into recent advancements in controlling and optimizing hybrid dynamical systems using multi-time scale techniques. These methods facilitate the systematic incorporation and analysis of both "exploration and exploitation" behaviors within complex control systems through singular perturbation and averaging theory, resulting in a range of provably stable and robust algorithms suitable for model-free control and optimization. Practical engineering system examples will be used to illustrate these theoretical tools.
Posted May 3, 2024
Probability Seminar Questions or comments?
11:00 am – 12:00 pm Zoom
Olga Iziumtseva, University of Nottingham
Asymptotic and geometric properties of Volterra Gaussian processes
In this talk we discuss asymptotic and geometric properties of Gaussian processes defined as $U(t) = \int_0^t K(t, s)dW(s),\ t \geq 0$, where $W$ is a Wiener process and $K$ is a continuous kernel. Such processes are called Volterra Gaussian processes. It forms an important class of stochastic processes with a wide range of applications in turbulence, cancer tumours, energy markets and epidemic models. Le Gall’s asymptotic expansion for the volume of Wiener Sausage shows that local times and self-intersection local times can be considered as the geometric characteristics of stochastic processes that look like a Wiener process. In this talk we discuss the law of the iterated logarithm, existence of local times and construct Rosen renormalized self-intersection local times for Volterra Gaussian processes.
Posted March 21, 2024
Last modified May 3, 2024
Order, Algebra, Logic, and Real Algebraic Geometry (Day 1 of 3)
https://www.math.lsu.edu/OAL-RAG2024
Posted March 21, 2024
Last modified May 3, 2024
Order, Algebra, Logic, and Real Algebraic Geometry (Day 2 of 3)
https://www.math.lsu.edu/OAL-RAG2024
Posted March 21, 2024
Last modified May 3, 2024
Order, Algebra, Logic, and Real Algebraic Geometry (Day 3 of 3)
https://www.math.lsu.edu/OAL-RAG2024
Posted April 29, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Giovanni Fusco, Università degli Studi di Padova
A Lie-Bracket-Based Notion of Stabilizing Feedback in Optimal Control
With reference to an optimal control problem where the state has to asymptotically approach a closed target while paying a non-negative integral cost, we propose a generalization of the classical dissipative relation that defines a control Lyapunov function by a weaker differential inequality. The latter involves both the cost and the iterated Lie brackets of the vector fields in the dynamics up to a certain degree $k\ge 1$, and we call any of its (suitably defined) solutions a degree-k minimum restraint function. We prove that the existence of a degree-k minimum restraint function allows us to build a Lie-bracket-based feedback which sample stabilizes the system to the target while regulating (i.e., uniformly bounding) the cost.
Posted January 22, 2024
1:00 pm – 4:00 pm Lockett Hall 232Written Qualifier Exam on Applied Mathematics
Posted January 22, 2024
1:00 pm – 4:00 pm Lockett Hall 232Written Qualifier Exam on Topology
Posted January 22, 2024
1:00 pm – 4:00 pm Lockett Hall 232Written Qualifier Exam on Analysis
Posted January 22, 2024
1:00 pm – 4:00 pm Lockett Hall 232Written Qualifier Exam on Algebra