Calendar

Posted August 31, 2024

Control and Optimization Seminar Questions or comments?

Ugo Boscain, Sorbonne University, France
3D Optimal Control Problems Constrained on Surfaces

In this talk I consider a surface embedded in a 3D contact sub-Riemannian manifold (i.e., an optimal control problem in dimension 3 with 2 controls which is linear with respect to the controls and with quadratic cost; we will also make a natural controllability assumption). Such a surface inherits a field of direction (with norm) from the ambient space. This field of directions is singular at characteristic points (i.e., where the surface is tangent to the set of admissible directions). In this talk we will study when the problem restricted to the surface is controllable, in other words when the normed field of directions permits to give to the surface the structure of metric space (of SNCF type). We will also study how to define the heat and the Schroedinger equation on such a structure and if the singular points are “accessible” or not by the evolution.

Posted September 3, 2024

Control and Optimization Seminar Questions or comments?

Denis Efimov, University of Lille
Homogeneity with Respect to a Part of Variables and Accelerated Stabilization

The presentation addresses the problem of transforming a locally asymptotically stabilizing time-varying control law to a global one with accelerated finite/fixed-time convergence rates. The approach relies on an extension of the theory of homogeneous systems to homogeneity only with respect to a part of the state variables and on the associated partial stability properties. The proposed control design builds upon the kind of approaches first studied in [MCloskey and Murray,1997] and uses the implicit Lyapunov function framework. A sampled-time implementation scheme of the control law is also presented and its properties are characterized. The method is illustrated by finite-time and nearly fixed-time stabilization of a nonholonomic integrator.

Posted August 27, 2024

Control and Optimization Seminar Questions or comments?

Jean Auriol, CNRS Researcher, L2S, CentraleSupélec
Robust Stabilization of Networks of Hyperbolic Systems with Chain Structure

In this talk, we focus on recent developments for the stabilization of networks of elementary hyperbolic systems with a chain structure. Such a structure arises in multiple industrial processes such as electric power transmission systems, traffic networks, or torsional vibrations in drilling devices. The objective is to design feedback control laws that stabilize the chain using the available actuators and sensors. The different systems composing the network are called elementary in the sense that when taken alone, we know how to design stabilizing output-feedback control laws. We will first consider the case where the actuators and sensors are available at one end of the chain. Using appropriate state predictors, we will present a recursive approach to stabilize the whole chain. Then, we will focus on the case where the actuators and sensors are only available at the junction between two subsystems composing the chain. We will show that such a configuration does not always guarantee the controllability of the chain. Under appropriate controllability/observability conditions, we will design simple stabilizing control laws. Our approach will be based on rewriting the system as Integral Delay Equations (IDEs) with pointwise and distributed control terms. Finally, we will show how the proposed techniques can be used to develop output feedback control laws for traffic flow on two cascaded freeway segments connected by a junction.

Posted August 11, 2024
Last modified September 22, 2024

Control and Optimization Seminar Questions or comments?

Panagiotis Tsiotras, Georgia Institute of Technology AIAA and IEEE Fellow
From Covariance Control to Covariance Steering: The First 40 Years

Uncertainty propagation and mitigation is at the core of all robotic and control systems. The standard approach so far has followed the spirit of control of a system “with uncertainties,” as opposed to the direct control “of uncertainties.” Covariance control, developed by Bob Skelton and his colleagues in the early 80’s, was introduced as a principled approach to handle uncertainty with guarantees in the asymptotic case. The finite-time case has only been recently addressed, and borrowing ideas from the classical optimal mass transport and the Schrödinger Bridge problems, provides a new tool to control stochastic systems with strict performance guarantees that go beyond classical controllability results that only hold for deterministic systems. In this talk, I will review recent results on covariance and distribution control for discrete stochastic systems, subject to probabilistic (chance) constraints, and will demonstrate the application of the approach on control and robot motion planning problems under uncertainty. I will also discuss current trends and potential directions for future work.

Posted October 8, 2024

Control and Optimization Seminar Questions or comments?

Karl Worthmann, Institute of Mathematics, Technische Universität Ilmenau
Koopman-Based Control with Guarantees

Extended dynamic mode decomposition (EDMD), embedded in the Koopman framework, is a widely-applied technique to predict the evolution of an observable along the flow of a dynamical control system. However, despite its popularity, the error analysis is still fragmentary. We provide a complete and rigorous analysis for control-affine systems by splitting up the approximation error into the projection and estimation error resulting from the finite dictionary size and the finite amount of i.i.d. data used to generate the surrogate model. Further, we indicate extensions towards reproducible kernel Hilbert spaces to establish L∞-error bounds using kernel EDMD. Then, we demonstrate the applicability of the EDMD surrogate models for the control of nonlinear systems.

Posted August 19, 2024
Last modified September 27, 2024

Control and Optimization Seminar Questions or comments?

Andrii Mironchenko, University of Klagenfurt IEEE CSS George S. Axelby Outstanding Paper Awardee
Superposition Theorems for Input-to-State Stability of Time-Delay Systems

We characterize input-to-state stability (ISS) for nonlinear time-delay systems (TDS) in terms of stability and attractivity properties for systems with inputs. Using the specific structure of TDS, we obtain much tighter results than those possible for general infinite-dimensional systems. The subtle difference between forward completeness and boundedness of reachability sets (BRS) is essential for the understanding of the ISS characterizations. As BRS is important in numerous other contexts, we discuss this topic in detail as well. We shed light on the differences between the ISS theories for TDS, generic infinite-dimensional systems, and ODEs.

Posted August 26, 2024
Last modified October 24, 2024

Control and Optimization Seminar Questions or comments?

Angelia Nedich, Arizona State University
Resilient Distributed Optimization for Cyber-physical Systems

This talk considers the problem of resilient distributed multi-agent optimization for cyber-physical systems in the presence of malicious or non-cooperative agents. It is assumed that stochastic values of trust between agents are available which allows agents to learn their trustworthy neighbors simultaneously with performing updates to minimize their own local objective functions. The development of this trustworthy computational model combines the tools from statistical learning and distributed consensus-based optimization. Specifically, we derive a unified mathematical framework to characterize convergence, deviation of the consensus from the true consensus value, and expected convergence rate, when there exists additional information of trust between agents. We show that under certain conditions on the stochastic trust values and consensus protocol: 1) almost sure convergence to a common limit value is possible even when malicious agents constitute more than half of the network, 2) the deviation of the converged limit, from the nominal no attack case, i.e., the true consensus value, can be bounded with probability that approaches 1 exponentially, and 3) correct classification of malicious and legitimate agents can be attained in finite time almost surely. Further, the expected convergence rate decays exponentially with the quality of the trust observations between agents. We then combine this trust-learning model within a distributed gradient-based method for solving a multi-agent optimization problem and characterize its performance.

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 November 10, 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 basis of 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 the late 1950s, and follow-the-leader microscopic models. After describing some of these milestones, we will turn to the modern theory of conservation laws on topological graphs with applications to traffic monitoring. The theory requires advanced 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, and we will illustrate results of a 2022 experiment with 100 autonomous vehicles on an open highway in Nashville.

Posted August 13, 2024
Last modified November 24, 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
Machine Learning Components in Cyber-Physical Transport Systems

Advances in sensing, connectivity, computing, and electrification are reshaping the infrastructure for moving people and goods. Research in optimizing and enhancing the resilience of transport systems highlights the broader impact of control technology on mobility. This talk will explore the emerging field of learning-enabled cyber-physical-human systems and discuss some specific examples in intelligent transport. We will show how connected vehicles acting as mobile sensors and actuators can enable traffic predictions and control at a scale never before possible, by learning traffic models using physics-informed machine learning techniques. The complexities of safe interactions between automated and human-driven vehicles will be discussed, emphasizing the integration of formal reasoning methods and the use of tele-operation. The presentation highlights joint work with students, postdocs, and collaborators in academia and industry.

Posted September 4, 2024
Last modified December 10, 2024

Control and Optimization Seminar Questions or comments?

María Soledad Aronna, Escola de Matematica Aplicada, Brazil
Control of Pest and Disease Dynamics

In this talk, we will discuss some models related to disease control. These models include the optimization of vaccination and testing strategies, as well as systems for biological control of insects and pests. We will demonstrate how optimal control theory and other associated tools aid in analyzing the systems and provide answers to practical questions.