Calendar

Posted July 26, 2025

Control and Optimization Seminar Questions or comments?

Rami Katz, Università degli Studi di Trento, Italy
Oscillations in Strongly 2-Cooperative Systems and their Applications in Systems Biology

The emergence of sustained oscillations (via convergence to periodic orbits) in high-dimensional nonlinear dynamical systems is a non-trivial question with important applications in control of biological systems, including the design of synthetic bio-molecular oscillators and the understanding of circadian rhythms governing hormone secretion, body temperature and metabolic functions. In systems biology, the mechanism underlying such widespread oscillatory biological motifs is still not fully understood. From a mathematical perspective, the study of sustained oscillations is comprised of two parts: (i) showing that at least one periodic orbit exists and (ii) studying the stability of periodic orbits and/or characterizing the initial conditions which yield solutions that converge to periodic trajectories. In this talk, we focus on a specific class of nonlinear dynamical systems that are strongly 2-cooperative. Using the theory of cones of rank k, the spectral theory of totally positive matrices and Perron-Frobenius theory, we will show that strongly 2-cooperative systems admit an explicit set of initial conditions of positive measure, such that every solution emanating from this set converges to a periodic orbit. We further demonstrate our results using the n-dimensional Goodwin oscillator and a 4-dimensional biological oscillator based on RNA–mediated regulation.

Posted August 1, 2025
Last modified November 3, 2025

Control and Optimization Seminar Questions or comments?

Thinh Doan, University of Texas at Austin AFOSR YIP and NSF CAREER Awardee
Multi-Time-Scale Stochastic Approximation as a Tool for Multi-Agent Learning and Distributed Optimization

Multi-time-scale stochastic approximation (SA) is a powerful generalization of the classic SA method for finding roots (or fixed points) of coupled nonlinear operators. It has attracted considerable attention due to its broad applications in multi-agent learning, control, and optimization. In this framework, multiple iterates are updated simultaneously but with different step sizes, whose ratios loosely define their time-scale separation. Empirical studies and theoretical insights have shown that such heterogeneous step sizes can lead to improved performance compared to single-time-scale (or classical) SA schemes. However, despite these advantages, existing results indicate that multi-time-scale SA typically achieves only a suboptimal convergence rate, slower than the optimal rate attainable by its single-time-scale counterpart. In this talk, I will present our recent work on characterizing the convergence complexity of multi-time-scale SA. We develop a novel variant of this method and establish new finite-sample guarantees that achieves the optimal (O(1/k)) convergence rate. Building upon these results, I will also discuss how these advances enable the design of efficient algorithms for key problems in multi-agent learning and distributed optimization over networks.

Posted July 13, 2025
Last modified November 4, 2025

Control and Optimization Seminar Questions or comments?

Dimitra Panagou, University of Michigan AFOSR YIP, NASA Early Career Faculty, and NSF CAREER Awardee
Safety-Critical Control via Control Barrier Functions: Theory and Applications

This seminar will focus on control barrier functions, as a tool for encoding and enforcing safety specifications, as well as their recent extensions (e.g., robust, adaptive, and predictive) to handle additive perturbations, parametric uncertainty and dynamic environments, with applications to (multi)-robot/vehicle motion planning and coordination. Time permitting, we will also cover how time constraints can be encoded as fixed-time control Lyapunov functions, and the trade-offs between safety and timed convergence.

Posted July 22, 2025

Control and Optimization Seminar Questions or comments?

Javad Velni, Clemson University
TBA

Posted August 18, 2025

Control and Optimization Seminar Questions or comments?

Zequn Zheng, Louisiana State University
TBA