Verification and Validation of Convex Optimization Algorithms for Model Predictive Control

Raphaël Cohen (1) , Eric Féron (1) , Pierre-Loïc Garoche (2)

1 School of Aerospace Engineering, Georgia Institute of Technology
2 DTIS, ONERA, Université de Toulouse [Toulouse]

Advanced embedded algorithms are growing in complexity and they are an essential contributor to the growth of autonomy in many areas. However, the promise held by these algorithms cannot be kept without proper attention to the considerably stronger design constraints that arise when the applications of interest, such as aerospace systems, are safety-critical. Formal verification is the process of proving or disproving the "correctness" of an algorithm with respect to a certain mathematical description of it by means of a computer. This article discusses the formal verification of the Ellipsoid method, a convex optimization algorithm, and its code implementation as it applies to receding horizon control. Options for encoding code properties and their proofs are detailed. The applicability and limitations of those code properties and proofs are presented as well. Finally, floating-point errors are taken into account in a numerical analysis of the Ellipsoid algorithm. Modifications to the algorithm are presented which can be used to control its numerical stability.

Mots clés: ALGORITHME; ALGORITHME OPTIMISATION

Domaines: Informatique et langage [cs.CL]; Systèmes embarqués; Théorie et langage formel [cs.FL]; Systèmes et contrôle [cs.SY]; Optimisation et contrôle [math.OC]

Raphaël Cohen, Eric Féron, Pierre-Loïc Garoche. Verification and Validation of Convex Optimization Algorithms for Model Predictive Control. Journal of Aerospace Information Systems, 2020, 17 (5), pp.257-270. ⟨10.2514/1.I010686⟩. ⟨hal-02617432⟩