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Cross‐country sailplane flight as a dynamic optimization problem
Author(s) -
Pierson Bion L.,
De Jong Jan L.
Publication year - 1978
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620121111
Subject(s) - bounded function , optimization problem , optimal control , projection (relational algebra) , mathematics , trajectory , mathematical optimization , trajectory optimization , thermal , control theory (sociology) , process (computing) , computer science , control (management) , mathematical analysis , algorithm , physics , astronomy , artificial intelligence , meteorology , operating system
A minimum−time, thermal−to−thermal sailplane trajectory optimization problem is formulated as a non−linear optimal control problem. Numerical solutions are obtained using a gradiaent projection algorithm which incorporates conjugate directions of search. Further insight into the nature of the solutions and the computational process is ontained through an analysis of the linearized sailplane dynamics and the necessary conditions for optimality. Numerical results are presented for two sailplane types and various values of thermal strength and distance between thermals. An additional problem is formulated and solved for the case of bounded control rate.