arXiv subjects

Emilien Flayac

Publications and source records attributed to Emilien Flayac.

9 recordsLinked to original sources

arXiv2026

Multi Impulse Low Earth Orbit Maneuver Synthesis Through Thrust Measure Primer Vector Conditions and Piecewise Multiple Shooting

This work sets out to apply primer vector theory to optimal impulse maneuvers in Low Earth Orbit (LEO) and adapt it to the types of perturbations encountered in this environment, which is not readily available in the literature. A review of the theory of optimal control and orbital maneuvering is made and in particular, primer vector theory is laid out in detail based on the extension of the thrust control to a measure, including its generalization to conservative and non-conservative perturbation models. An impulsive multiple shooting optimization scheme in Cartesian coordinates is presented, through a piecewise approach to the problem. Then, some maneuver scenarios with known solutions under the Keplerian model are solved under perturbed orbital dynamics with the help of the primer vector, and the resulting trajectories are compared. The perturbation models include a J2 model, representing the class of conservative perturbations by modeling Earth's nonspherical gravity field, and a J2+Drag model, representing the class of non-conservative perturbations by including the effects of atmospheric drag in LEO\@. For each model, some valid methods of primer vector calculation have been tried and validated between each other, and the primer vector is proven to be a useful tool in reducing the cost of orbital maneuvers.

math.OC↗

arXiv2024

Optimal Control of 1D Semilinear Heat Equations with Moment-SOS Relaxations

We use moment-SOS (Sum Of Squares) relaxations to address the optimal control problem of the 1D heat equation perturbed with a nonlinear term. We extend the current framework of moment-based optimal control of PDEs to consider a quadratic cost on the control. We develop a new method to extract a nonlinear controller from approximate moments of the solution. The control law acts on the boundary of the domain and depends on the solution over the whole domain. Our method is validated numerically and compared to a linear-quadratic controller.

math.OC↗

arXiv2023

Non-uniform Observability for Moving Horizon Estimation and stability with respect to additive perturbation

This paper formalises the concepts of weakly and weakly regularly persistent input trajectory as well as their link to the Observability Grammian and the existence and uniqueness of solutions of Moving Horizon Estimation (MHE) problems. Additionally, thanks to a new time-uniform Implicit Function Theorem, these notions are proved to imply the stability of MHE solutions with respect to small additive perturbation in the measurements and in the dynamics, both uniformly and non-uniformly in time. Finally, examples and counter-examples of weakly persistent and weakly regularly persistent input trajectories are given in the case of 2D bearing-only navigation.

math.OC↗

arXiv2023

Distributed Block Coordinate Moving Horizon Estimation for 2D Visual-Inertial-Odometry SLAM

This paper presents a Visual Inertial Odometry Landmark-based Simultaneous Localisation and Mapping algorithm based on a distributed block coordinate nonlinear Moving Horizon Estimation scheme. The main advantage of the proposed method is that the updates on the position of the landmarks are based on a Bundle Adjustment technique that can be parallelised over the landmarks. The performance of the method is demonstrated in simulations in different environments and with different types of robot trajectory. Circular and wiggling patterns in the trajectory lead to better estimation performance than straight ones, confirming what is expected from recent nonlinear observability theory.

cs.RO↗

arXiv2023

A unifying vision of Particle Filtering and Explicit dual Model Predictive Control

This paper presents a joint optimisation framework for optimal estimation and stochastic optimal control with imperfect information. It provides a estimation and control scheme that can be decomposed into a classical optimal estimation step and an optimal control step where a new term coming from optimal estimation is added to the cost. It is shown that a specific particle filter algorithm allows one to solve the first step approximately in the case of Mean Square Error minimisation and under suitable assumptions on the model. Then, it is shown that the estimation-based control step can justify formally the use of Explicit dual controllers which are most of the time derived from empirical matters. Finally, a relevant example from Aerospace engineering is presented.

math.OC↗

arXiv2023

Nonlinear Fisher Particle Output Feedback Control and its application to Terrain Aided Navigation

This paper presents state estimation and stochastic optimal control gathered in one global optimization problem generating dual effect i.e. the control can improve the future estimation. As the optimal policy is impossible to compute, a sub-optimal policy that preserves this coupling is constructed thanks to the Fisher Information Matrix (FIM) and a Particle Filter. This method has been applied to the localization and guidance of a drone over a known terrain with height measurements only. The results show that the new method improves the estimation accuracy compared to nominal trajectories.

math.OC↗

arXiv2023

Dual Particle Output Feedback Control based on Lyapunov drifts for nonlinear syst

This paper presents a dual receding horizon output feedback controller for a general non linear stochastic system with imperfect information. The novelty of this controller is that stabilization is treated, inside the optimization problem, as a negative drift constraint on the control that is taken from the theory of stability of Markov chains. The dual effect is then created by maximizing information over the stabilizing controls which makes the global algorithm easier to tune than our previous algorithm. We use a particle filter for state estimation to handle nonlinearities and multimodality. The performance of this method is demonstrated on the challenging problem of terrain aided navigation.

math.OC↗

arXiv2023

Nonlinear Dual control based on Fast Moving Horizon estimation and Model Predictive Control with an observability constraint

This paper proposes an algorithm that combines Fast Moving Horizon Parameter Estimation and Model Predictive Control subject to an observability constraint designed to ensure a lower bound on the performance of the parameter estimator. Output-feedback stability is proved through input-to-state stability of the state/error system under a small noise and initial error assumption. Numerical experiments have been carried out in the case of Active Simultaneous Localisation and Mapping (SLAM).

math.OC↗

arXiv2019

An MPC Approach to Transient Control of Liquid-Propellant Rocket Engines

The current context of launchers reusability requires the improvement of control algorithms for their liquid-propellant rocket engines. Their transient phases are generally still performed in open loop. In this paper, it is aimed at enhancing the control performance and robustness during the fully continuous phase of the start-up transient of a generic gas-generator cycle. The main control goals concern end-state tracking in terms of combustion-chamber pressure and chambers mixture ratios, as well as the verification of a set of hard operational constraints. A controller based on a nonlinear preprocessor and on linear MPC (Model-Predictive Control) has been synthesised, making use of nonlinear state-space models of the engine. The former generates the full-state reference to be tracked while the latter achieves the aforementioned goals with sufficient accuracy and verifying constraints for the required pressure levels. Robustness considerations are included in the MPC algorithm via an epigraph formulation of the minimax robust optimisation problem, where a finite set of perturbation scenarios is considered.

eess.SY↗