Calendar

Posted August 23, 2025
Last modified August 26, 2025

Control and Optimization Seminar Questions or comments?

Alex Olshevsky, Boston University AFOSR YIP and NSF CAREER Awardee
The Connection Between Reinforcement Learning and Gradient Descent

Temporal difference (TD) learning with linear function approximation is one of the earliest methods in reinforcement learning and the basis of many modern methods. We revisit the analysis of TD learning through a new lens and show that TD may be viewed as a modification of gradient descent. This leads not only to a better explanation of what TD does but also improved convergence times guarantees. We discuss applications of this result to more involved reinforcement learning methods, such as actor-critic and neural-network based methods.

Posted August 11, 2025
Last modified September 2, 2025

Control and Optimization Seminar Questions or comments?

Gabriela Gonzalez, Louisiana State University Member, US National Academy of Sciences
Feedback Loops in the LIGO Gravitational Wave Detectors

The Laser Interferometric Gravitational-wave Observatory (LIGO) operates two detectors in Livingston, LA and Hanford, WA to detect perturbations of space time produced by astrophysical events like the collision of black holes. The detectors have an amazing sensitivity, using laser beams traveling in vacuum detecting differences in two 4km long arms smaller than a thousandth of a proton diameter in a frequency band between 10 Hz and 5 kHz. To achieve this sensitivity, a large number of feedback control systems are used to damp suspended mirrors, to reduce the effect of ground motion, to keep optical cavities resonant, and much more. I will briefly describe these systems and the challenges for current and future detectors.

Posted August 14, 2025
Last modified September 26, 2025

Control and Optimization Seminar Questions or comments?

Xin Zhang, New York University
Exciting Games and Monge-Ampère Equations

We consider a competition between d+1 players, and aim to identify the “most exciting game” of this kind. This is translated, mathematically, into a stochastic optimization problem over martingales that live on the d-dimensional sub-probability simplex and terminate on the vertices of the simplex, with a cost function related to a scaling limit of Shannon entropies. We uncover a surprising connection between this problem and the seemingly unrelated field of Monge-Ampère equations, and identify the optimal martingale via a detailed analysis of boundary asymptotics of a Monge-Ampère equation.

Posted August 1, 2025
Last modified October 3, 2025

Control and Optimization Seminar Questions or comments?

Felix Schwenninger, University of Twente, The Netherlands
Infinite-Dimensional Input-to-State Stability (ISS) -- Peculiarities of Sup-Norms

E. Sontag’s input-to-state stability (ISS), dating back to the late 80ies, is a cornerstone of modern mathematical control theory. While originally studied for finite-dimensional systems, the theory about infinite-dimensional systems, and in particular models involving partial differential equations, has been developed in the past 15 years. Somewhat surprisingly, the linear case, which is trivial in finite-dimensions, even offered challenges with respect to the mutual relations of several variants of ISS. In this talk we will focus in particular on “integral ISS” for linear and bilinear systems and discuss established results as well as more recent findings. The underlying reason for these subtleties is primarily due to the nontrivial interplay of supremum-norms, which naturally arise in ISS), and the (Banach space) geometry of the state spaces.

Posted September 5, 2025

Control and Optimization Seminar Questions or comments?

Naira Hovakimyan, University of Illinois Urbana-Champaign Fellow of AIAA, ASME, IEEE, and IFAC
Safe Learning in Autonomous Systems

Learning-based control paradigms have seen many success stories with autonomous systems and robots in recent years. However, as these robots prepare to enter the real world, operating safely in the presence of imperfect model knowledge and external disturbances is going to be vital to ensure mission success. We introduce a class of distributionally robust adaptive control architectures that ensure robustness to distribution shifts and enable the development of certificates for validation and verification of learning-enabled systems. An overview of different projects at our lab that build upon this framework will be demonstrated to show different applications.

Posted October 7, 2025
Last modified October 9, 2025

Control and Optimization Seminar Questions or comments?

Alexandre Mauroy, Université de Namur
Dual Koopman Operator Formulation in Reproducing Kernel Hilbert Spaces for State Estimation

The Koopman operator acts on observable functions defined over the state space of a dynamical system, thereby providing a linear global description of the system dynamics. A pointwise description of the system is recovered through a weak formulation, i.e. via the pointwise evaluation of observables at specific states. In this context, the use of reproducing kernel Hilbert spaces (RKHS) is of interest since the above evaluation can be represented as the duality pairing between the observables and bounded evaluation functionals. This representation emphasizes the relevance of a dual formulation for the Koopman operator, where a dual Koopman system governs the evolution of linear evaluation functionals. In this talk, we will leverage the dual formulation to build a Luenberger observer that estimates the (infinite-dimensional) state of the Koopman dual system, and equivalently the (finite-dimensional) state of the nonlinear dynamics. The method will be complemented with theoretical convergence results that support numerical Koopman operator-based estimation techniques known from the literature. Finally, we will extend the framework to a probabilistic approach by solving the problem of moments in the RKHS setting.

Posted October 8, 2025
Last modified October 28, 2025

Control and Optimization Seminar Questions or comments?

Umesh Vaidya, Clemson University
Koopman Meets Hamilton and Jacobi: Data-Driven Control Beyond Linearity

In this talk, we present recent advances in operator-theoretic methods for controlling nonlinear dynamical systems. We begin by establishing a novel connection between the spectral properties of the Koopman operator and solutions of the Hamilton–Jacobi (HJ) equation. Since the HJ equation lies at the core of optimal control, robust control, dissipativity theory, input–output analysis, and reachability, this connection provides a new pathway for leveraging Koopman spectral representations to address control problems in a data-driven setting. In particular, we show how Koopman coordinates can shift the classical curse of dimensionality associated with solving the HJ equation into a curse of complexity that is more manageable through modern computational tools. In the second part of the talk, we discuss safe control synthesis using the Perron–Frobenius operator. A key contribution is the analytical construction of a navigation density function that enables safe motion planning in both static and dynamic environments. We further present a convex optimization formulation of safety-constrained optimal control in the dual (density) space, allowing safety constraints to be incorporated systematically. Finally, we demonstrate the application of this unified operator-theoretic framework to the control of autonomous ground vehicles operating in off-road environments.

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

Control and Optimization Seminar Questions or comments?

Thinh Doan, University of Texas at Austin AFOSR YIP and NSF CAREER Awardee
TBA

Posted July 13, 2025
Last modified July 18, 2025

Control and Optimization Seminar Questions or comments?

Dimitra Panagou, University of Michigan AFOSR YIP, NASA Early Career Faculty, and NSF CAREER Awardee
TBA

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