Input-to-State Stability of a Bilevel Proximal Gradient Descent Algorithm

This paper studies convergence properties of inexact iterative solution schemes for bilevel optimization problems. Bilevel optimization problems emerge in control-aware design optimization, where the system design parameters are optimized in the outer loop and a discrete-time control trajectory is optimized in the inner loop, but also arise in other domains including machine learning. In the paper an interconnection of proximal gradient algorithms is proposed to solve the inner loop and outer loop optimization problems in the setting of control-aware design optimization and robustness is analyzed from a control-theoretic perspective. By employing input-to-state stability arguments, conditions are derived that ensure convergence of the interconnected scheme to the optimal solution for a class of the bilevel optimization problem.Comment: Submitted to 2023 IFAC World Congres

Sum-of-squares Flight Control Synthesis for Deep-stall Recovery

Under review for publication in the Journal of Guidance, Control, and Dynamics.In lieu of extensive Monte-Carlo simulations for flight control verification, sum-of-squares programming techniques provide an algebraic approach to the problem of nonlinear control synthesis and analysis. However, their reliance on polynomial models has hitherto limited the applicability to aeronautical control problems. Taking advantage of recently proposed piecewise polynomial models, this paper revisits sum-of-squares techniques for recovery of an aircraft from deep-stall conditions using a realistic yet tractable aerodynamic model. Local stability analysis of classical controllers is presented as well as synthesis of polynomial feedback laws with the objective of enlarging their nonlinear region of attraction. A newly developed synthesis algorithm for backwards-reachability facilitates the design of recovery control laws, ensuring stable recovery by design. The paper's results motivate future research in aeronautical sum-of-squares applications

Local stability analysis for large polynomial spline systems

International audiencePolynomial switching systems such as multivariate splines provide accurate fitting while retaining an algebraic representation and offering arbitrary degrees of smoothness; yet, application of sum-of-squares techniques for local stability analysis is computationally demanding for a large number of subdomains. This communiqué presents an algorithm for region of attraction estimation that is confined to those subdomains actually covered by the estimate, thereby significantly reducing computation time. Correctness of the results is subsequently proven and the run time is approximated in terms of the number of total and covered subdomains. Application to longitudinal aircraft motion concludes the study

Piecewise Polynomial Model of the Aerodynamic Coefficients of the Generic Transport Model and its Equations of Motion

Comment on Version 2: An appendix has been added to detail a polynomial spline model of the aircraft longitudinal motion.Comment on Version 3: The polynomials for low and high angles of attack and with respect to side-slip and surface deflections have been corrected.The purpose of this document is to illustrate the piecewise polynomial model which has been derived from wind-tunnel measurement data of the Generic Transport Model (GTM) using the pwpfit toolbox. For implementation details and use in MATLAB, please refer to the source code at https://github.com/pwpfit/GTMpw.Comment on Version 2: An appendix has been added to detail a polynomial spline model of the aircraft longitudinal motion.Comment on Version 3: The polynomials for low and high angles of attack and with respect to side-slip and surface deflections have been corrected

A Feasibility Governor for Enlarging the Region of Attraction of Linear Model Predictive Controllers

This paper proposes a method for enlarging the region of attraction of Linear Model Predictive Controllers (MPC) when tracking piecewise-constant references in the presence of pointwise-in-time constraints. It consists of an add-on unit, the Feasibility Governor (FG), that manipulates the reference command so as to ensure that the optimal control problem that underlies the MPC feedback law remains feasible. Offline polyhedral projection algorithms based on multi-objective linear programming are employed to compute the set of feasible states and reference commands. Online, the action of the FG is computed by solving a convex quadratic program. The closed-loop system is shown to satisfy constraints, be asymptotically stable, exhibit zero-offset tracking, and display finite-time convergence of the reference

Comments on the computation of multiple Lyapunov-like functions for switched hybrid systems

Preprint submitted to the International Journal of Robust and Nonlinear Control.This note exposes false claims of Zheng et al., "Computing multiple Lyapunov-like functions for inner estimates of domains of attraction of switched hybrid systems," Int. J. Robust Nonlinear Control 2018

Modélisation, analyse et commande pour la récupération d'un aéronef en situation de décrochage : de la théorie des systèmes au pilote automatique

Aircraft upset conditions have, in the past, led to rare but fatal accidents and to this day remain a severe threat to civil aviation. In response, considerable efforts contributed towards the prevention and detection of upset conditions as well as recovery of the aircraft into its desired flight regime. Despite these efforts made, comprehensive strategies including analysis of aircraft dynamics, recovery control, and verification of the implemented control over a large flight envelope have been missing for future aircraft safety. In this thesis, we apply and extend recently developed tools such as bifurcation theory, sum of squares analysis and control synthesis, and nonlinear model-predictive control, to a set of newly developed piecewise polynomial aircraft models, which provide a trade-off between modeling accuracy and computational complexity. Thus, we contribute to the development as well as certification of safer flight control systems.Dans le passé, le décrochage d’aéronefs a entraîné des accidents rares mais mortels et reste à ce jour une préoccupation importante pour l’aviation civile.Malgré les efforts déployés pour la prévention et la détection du décrochage ainsi que la récupération de l'avion, des stratégies telles que l'analyse de la dynamique, le contrôle de la récupération au décrochage et la vérification des lois de commande mises en oeuvre constituent un chaînon manquant pour la sécurité des avions à venir.Dans cette thèse, nous appliquons et étendons des outils récents de l'automatique, tels que la théorie de la bifurcation, les programmes de « sum of squares » et le contrôle prédictif modèle non-linéaire aux modèles d’avions polynomiaux par morceaux développés, qui offrent une bonne précision de modélisation et une faible capacité de calcul. Ainsi, nous contribuons au développement et à la certification de systèmes de contrôle de vol plus sûrs

EDURA: an Evolvable Demonstrator for Upset Recovery Approaches with a 3D-printed Launcher

International audienceAs in-flight loss of control has remained a severe threat to aviation, aeronautical research designed several approaches for upset recovery, few of which has been demonstrated in flight tests.The on-going success of micro air vehicles, however, rises the possibility of cheap and flexible flight demonstrations. In this paper, we present the concept of and first steps towards an aerial experimental platform for upset recovery: EDURA. EDURA is part of the CONVEX project to investigate,develop, and demonstrate non-linear upset recovery control laws in a fixed-wing MAV

Performances d'aéronefs sans pilote en cas de perte de contrôle

International audienceLoss of control is a severe and immediate consequence of faults in an unmanned aircraft system during flight. Without recovery, detection of admissible landing spots is necessary to avoid causalities. This case study considers exemplary the MAKO unmanned aircraft and discusses viable trim conditions for a drone system after faults of propulsion and elevator using continuation analysis. Furthermore, simple estimates of reachable zones for controlled flight into terrain are provided.La perte de contrôle est une conséquence grave et immédiate de pannes dans un système d'avion sans pilote pendant le vol. Sans récupération, la détection de points d'atterrissage admissibles est nécessaire pour éviter victimes. Cette étude de cas prend comme exemple l'avion sans pilote MAKO et discute de conditions viables de trim pour un système de drone après pannes de propulsion et de profondeur utilisant l'analyse de continuité. En outre, de simples estimations de zones accessibles d'atterrissage sont données