An algorithmic guide for finite-dimensional optimal control problems

JB Caillau, R Ferretti, E Trélat, H Zidani - Handbook of Numerical Analysis, 2023 - Elsevier
We survey the main numerical techniques for finite-dimensional nonlinear optimal control.
The chapter is written as a guide to practitioners who wish to get rapidly acquainted with the …

Optimistic planning algorithms for state-constrained optimal control problems

O Bokanowski, N Gammoudi, H Zidani - Computers & Mathematics with …, 2022 - Elsevier
In this work, we study optimistic planning methods to solve some state-constrained optimal
control problems in finite horizon. While classical methods for calculating the value function …

Pareto Front Characterization for Multiobjective Optimal Control Problems Using Hamilton--Jacobi Approach

A Désilles, H Zidani - SIAM Journal on Control and Optimization, 2019 - SIAM
In this work we present a new approach for the characterization of Pareto fronts for
multiobjective optimal control problems. Our approach is based on the Hamilton--Jacobi …

Neural networks for first order HJB equations and application to front propagation with obstacle terms

O Bokanowski, A Prost, X Warin - Partial Differential Equations and …, 2023 - Springer
We consider a deterministic optimal control problem, focusing on a finite horizon scenario.
Our proposal involves employing deep neural network approximations to capture Bellman's …

Least-violating symbolic controller synthesis for safety, reachability and attractivity specifications

A Girard, A Eqtami - Automatica, 2021 - Elsevier
Specifications considered in symbolic control are often interpreted qualitatively and
controllers are usually classified as correct if they enforce the specification or as incorrect if …

A differential game control problem with state constraints

N Gammoudi, H Zidani - Mathematical Control and Related Fields, 2022 - hal.science
We study the Hamilton-Jacobi (HJ) approach for a two-person zero-sum differential game
with state constraints and where controls of the two players are coupled within the dynamics …

Representation Results and Error Estimates for Differential Games with Applications Using Neural Networks

O Bokanowski, X Warin - Dynamic Games and Applications, 2024 - Springer
We study deterministic optimal control problems for differential games with finite horizon. We
propose new approximations of the strategies in feedback form and show error estimates …

Neural networks for differential games

O Bokanowski, X Warin - arXiv preprint arXiv:2402.02792, 2024 - arxiv.org
We study deterministic optimal control problems for differential games with finite horizon. We
propose new approximations of the strategies in feedback form, and show error estimates …

Stability and reachability analysis for a controlled heterogeneous population of cells

C Carrère, H Zidani - Optimal Control Applications and Methods, 2020 - Wiley Online Library
This article is devoted to the study of a controlled population of cells. The modeling of the
problem leads to a mathematical formulation of stability and reachability properties of some …

A model for a vector-borne disease with control based on mosquito repellents: A viability analysis

P Rashkov - Journal of Mathematical Analysis and Applications, 2021 - Elsevier
We investigate a model for a vector-borne disease of susceptible-infected-removed type for
the hosts in the presence of control measures and state constraints. The control is based on …