TY - JOUR
T1 - Verification and validation of convex optimization algorithms for model predictive control
AU - Cohen, Raphael
AU - Feron, Eric
AU - Garoche, Pierre Loïc
N1 - Generated from Scopus record by KAUST IRTS on 2021-02-18
PY - 2020/1/1
Y1 - 2020/1/1
N2 - 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 paper 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.
AB - 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 paper 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.
UR - https://arc.aiaa.org/doi/10.2514/1.I010686
UR - http://www.scopus.com/inward/record.url?scp=85083995793&partnerID=8YFLogxK
U2 - 10.2514/1.I010686
DO - 10.2514/1.I010686
M3 - Article
SN - 2327-3097
VL - 17
SP - 257
EP - 270
JO - Journal of Aerospace Information Systems
JF - Journal of Aerospace Information Systems
IS - 5
ER -