# Registered Data

## [00675] New trends in (optimal) control theory

**Session Date & Time**:- 00675 (1/2) : 4E (Aug.24, 17:40-19:20)
- 00675 (2/2) : 5B (Aug.25, 10:40-12:20)

**Type**: Proposal of Minisymposium**Abstract**: The goal of this mini-symposium is to bring together experts in several fields of interest in control and optimal control theory, including controllability, stabilization, and large-time behavior of optimal controls, in order to foster scientific interactions. This mini-symposium also aims to be at the intersection between theoretical issues and applications, notably to machine learning, traffic flow and microswimmers.**Organizer(s)**: Pierre Lissy, Idriss Mazari**Classification**:__49K15__,__49K20__,__93B05__,__93B52__**Speakers Info**:- Laetitia Giraldi (INRIA Sophia Antipolis)
- Roberto Guglielmi (University of Waterloo)
- Teresa Scarinci (Università di Cassino)
- Borjan Geshkovski (Massachusetts Institute of Technology)
- Rémi Robin (INRIA Paris)
- Thibault Liard (Université de Limoges)
- Michael Schuster (Friedrich-Alexander-Universität Erlangen-Nürnberg)
- Carlos Esteve-Yagüe (University of Cambridge)

**Talks in Minisymposium**:**[01794] On the intersection of control and machine learning****Author(s)**:**Borjan Geshkovski**(MIT)

**Abstract**: I will survey recent results on the neural ODE perspective of learning. This point of view is compelling since tasks in learning find a natural counterpart in control theory. I'll focus on the optimal control perspective and present convergence results for the optimal error and controls in long time. Implications to generalization and the required depth for the corresponding ResNet will be discussed. Based on works with Carlos Esteve-Yague, Dario Pighin, and Enrique Zuazua.

**[01796] Surveillance-evasion games with visibility constraints****Author(s)**:**Carlos Esteve-Yague**(University of Cambridge)

**Abstract**: In this talk, I consider a two-player zero-sum game in which the payoff involves the visibility of the players. First, I will present a new analysis of the boundary conditions for the associated Hamilton-Jacobi-Isaacs HJI equation. As we shall see, these boundary conditions turn out to be non-trivial, and the regularity is related to the curvature of the obstacles. Then, using a new notion of visibility, I will introduce suboptimal feedback strategies for the players which can be proven to approximate the optimal feedback given by the solution of the HJI equation. The main advantage of using these suboptimal feedback controls is that they are computationally efficient and are scalable to the case of multiple players.

**[01818] Turnpike phenomena in optimal control****Author(s)**:**Roberto Guglielmi**(University of Waterloo)

**Abstract**: We provide a characterization of the exponential turnpike property for infinite dimensional generalized linear-quadratic optimal control problems in terms of structural properties of the control system, such as exponential stabilizability and detectability. The proof relies on the analysis of the exponential convergence of solutions to the differential Riccati equations to the algebraic counterpart, and on a necessary condition for exponential stabilizability in terms of a closed range test.

**[01823] Steering undulatory micro-swimmers in a fluid flow through reinforcement learning****Author(s)**:- Zakarya El-Khiyati (Université Côte d’Azur, Inria, CNRS, Sophia-Antipolis)
- Raphaël Chesneaux (Université Côte d’Azur, Inria, CNRS, Sophia-Antipolis)
**Laetitia Giraldi**(Université Côte d’Azur, Inria, CNRS, Sophia-Antipolis)- Jérémie Bec (Université Côte d’Azur, Inria, CNRS, Sophia-Antipolis)

**Abstract**: The talk deals with optimal navigation policies for thin, deformable microswimmers, which progress in a viscous fluid flow by propagating a sinusoidal undulation along their slender body. The swimmer has to compete with the drifts, strains, and deformations inflicted by the external flow. Such an intricate situation, where swimming and navigation are tightly bonded, is addressed using various methods of reinforcement learning. A study of the swimming strategies selected set will be provided.

**[01828] Stability of open quantum systems designed by reservoir engineering.****Author(s)**:**Rémi Robin**(Laboratoire de Physique de l’école Normale Supérieure, Mines Paris, Inria, CNRS, ENS-PSL, Sorbonne Université, PSL Research University)- Pierre Rouchon (Laboratoire de Physique de l’école Normale Supérieure, Mines Paris, Inria, CNRS, ENS-PSL, Sorbonne Université, PSL Research University)
- Lev-Arcady Sellem (Laboratoire de Physique de l’Ecole Normale Supérieure, Mines Paris, CNRS, ENS-PSL, Inria, Sorbonne Université, PSL Research University, Paris, France)

**Abstract**: Dynamically protected cat-qubits are an open quantum system that stabilizes a finite dimensional subspace of a quantum harmonic oscillator. Such a process is achieved through reservoir engineering, a method of coupling a high-quality cavity with a dissipative one. In this talk, we will present a new generalized LaSalle's invariance principle to prove the long time convergence of this system towards the finite dimensional subspace of interest.

**[02530] Optimal Boundary Control for the semilinear Transport Equation under Uncertainty: A Turnpike Result****Author(s)**:**Michael Schuster**(FAU Erlangen-Nuremberg)- Noboru Sakamoto (Nanzan University Nagoya)

**Abstract**: We show an integral turnpike result for an optimal Dirichlet boundary control problem with a semilinear transport equation in the sense that if the time horizon goes to infinity, then the dynamic optimal control converges to the corresponding steady state optimal control. Further we show that the integral turnpike result also holds if the initial data and/or the source term is uncertain with respect to a random variable

**[02571] Stabilization of traffic flow using fixed bottlenecks****Author(s)**:**Thibault Liard**(University of Limoges)

**Abstract**: We study the asymptotic behavior of scalar conservation laws with local side constraints. Our aim is to construct a boundary feedback law, based on a sliding mode procedure, which globally stabilizes G-solutions of scalar conservation laws around a given stationary solutions. To that end, we will extend the notion of generalized characteristics to G-solutions. In the context of vehicular traffic, this leads to control the flow of cars at the tolls of a highway to reach a given target function. Thus, some bottlenecks could be created. Simulations using particle methods will be given to illustrate our results.

**[02637] Optimization problems under uncertainty****Author(s)**:**teresa scarinci**(Università di Cassino e del Lazio Meridionale)

**Abstract**: The study of models with uncertainty plays an important role in scientific numerical simulations. This class of problems is strongly utilized in engineering, biology, and finance. In this talk, we discuss the importance of including uncertainty in optimal control. Randomness can be utilised to model applications where the data of the problem -- such as the dynamic, the coefficients, or the time delay -- are not known a priori and one knows only statistical information.