## Date et Lieu

Jeudi 15 Mars 2018 — LIX, Ecole Polytechnique, Palaiseau

**Salle:** Grace Hopper

## Programme

### 9h00 – Accueil Café

### 9h30 – Eric Goubault

#### Inner and Outer Approximating Flowpipes for Delay Differential Equations

#### Abstract

Delay differential equations are fundamental for modeling networked control systems where the underlying network induces delay for retrieving values from sensors or delivering orders to actuators

They are notoriously difficult to integrate as these are actually functional equations, the initial state being a function.

We propose a scheme to compute inner and outer-approximating flowpipes for such equations with uncertain initial states and parameters.

Inner-approximating flowpipes are guaranteed to contain only reachable states, while outer-approximating flowpipes enclose all reachable states. We also introduce a notion of robust inner-approximation, which we believe opens promising perspectives for verification, beyond property falsification.

The efficiency of our approach relies on the combination of Taylor models in time, with an abstraction or parameterization in space based on affine forms, or zonotopes.

It also relies on an extension of the mean-value theorem, which allows us to deduce inner-approximating flowpipes, from flowpipes outer-approximating the solution of the DDE and its Jacobian with respect to constant but uncertain parameters and initial conditions.

[slides]

### 10h30 – Uli Fahrenberg

#### Distributed Computing by Oblivious Mobile Robots

#### Abstract

I’ll try to give an overview about the new and exciting field of distributed robotics.

More precisely the question is: What can I do with a bunch of cheap and stupid mobile robots (depending on the definition of « cheap and stupid »)?

Disclaimer: This is not precisely my research area; it’s just something I find exciting.

### 11h30 – Didier Henrion (LAAS-CNRS, Univ Toulouse, FR and Czech Tech Univ Prague, CZ)

#### Performance guarantees with the Lasserre hierarchy for polynomial optimal control

#### Abstract

We consider non-linear optimal control problems with polynomial data (Lagrangian, vector field, state and control constraints). We explain how the Lasserre hierarchy (also known as the moment-sums-of-squares or LMI relaxation hierarchy) can be used to generate guaranteed bounds on the value function (i.e. on the best achievable performance) with uniform convergence guarantees where the relaxation order tends to infinity. The talk is a tutorial introduction to optimal control and the Lasserre hierarchy, with a sketch of the main ideas. For more details, see here.

### 12h30 – Repas

### 14h00 – Café

### 14h30 – Damien Massé

#### From paths to traces: advantages and drawbacks of Eulerian discretization

#### Abstract

Eulerian discretization can be used to compute inner and outer approximations of invariant sets and viability kernels for differential inclusions.

This approach, developed by Thomas Le Mezo and Luc Jaulin, relies on the connection between continuous paths (as solutions of differential inclusions) and discrete traces (which enable to use program analysis techniques).

In this talk, I explore the advantages and limits of this connection, and the possibility of getting unsound results. Finally, I discuss the opportunity to adapt recent fixpoint-computation techniques for this approach.

[slides]

### 15h30 – Luc Jaulin

#### Kleene algebra to compute with invariant sets of dynamical systems

#### Abstract

Consider sets X1,…,Xm of invariant sets associated to a continuous-time dynamical system. We want to compute an approximation of a set X defined as an expression of the Xi’s and linked by the operators union, intersection, complementation. It will be shown that the problem can be formalized in a Kleene algebra the elements of which are set-valued functions. This formalization could help us to build efficient and simple algorithms to compute with invariant sets.

[slides]

### 16h30 – Thomas Le Mézo

#### Application of invariant set approach to control law validation

#### Abstract

### 17h30 – Discussion

## Social Event

Mardi 14 Mars 2018 — 19h30 — Restaurant L’entrepôt, Paris 14

### Participants

- Olivier Mullier
- Sylvie Putot
- Benjamin Martin
- David Filliat
- Luc Jaulin
- Eric Goubault
- Damien Massé
- Uli Fahrenberg
- Adina Panchea
- Thibault Toralba
- Didier Henrion

## Précédentes réunions

Réunion du 7 Novembre 2017

Réunion du 22 Juin 2017

Réunion du 28 Mars 2017

Réunion du 24 Novembre 2016

Réunion du 28 Juin 2016