Path-constrained trajectory time-optimization in a three-dimensional steady flow field

• Type: Article in International Conference Proceedings Book
• Date: 2019

Authors

Roman Chertovskih (Author) FEUP; Dmitry Karamzin (Author) Other; Nathalie T. Khalil (Author) Other; Fernando Lobo Pereira (Author) FEUP

Conference proceedings International

Title: 2019 18TH EUROPEAN CONTROL CONFERENCE (ECC)

Pages: 3746-3751

18th European Control Conference (ECC)

Naples, ITALY, JUN 25-28, 2019

Indexing

ISI Web of Knowledge - 9 Citations

Scopus - 9 Citations

Other information

Authenticus ID: P-00R-1FB

DOI: 10.23919/ecc.2019.8796083

Abstract (EN): This work concerns a specific indirect method to solve an optimal control problem with state constraints in which the dynamics are driven by an ordinary differential equation involving a three-dimensional steady flow field. A moving object within this field is considered subject to a path constraint given by a cylinder. The given control system is linear, but the vector flow field may exhibit essential nonlinearity. An indirect numerical method is proposed based on the maximum principle in Gamkrelidze's form. This form of optimality conditions uses the concept of the extended Hamilton-Pontryagin function. The extended Hamilton-Pontryagin function differs from the conventional one in view of an additional term associated with the measure Lagrange multiplier. The proposed computational method essentially relies on the continuity of the measure multiplier, which is guaranteed under certain regularity conditions. Moreover, this property, together with the regularity condition, allows us to obtain an explicit expression for the measure multiplier. The application of the maximum principle yields a two-point boundary-value problem, which is solved by a variant of the shooting method.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 6