State-constrained booster trajectory solutions via finite elements and shootingThis paper presents an extension of a FEM formulation based on variational principles. A general formulation for handling internal boundary conditions and discontinuities in the state equations is presented, and the general formulation is modified for optimal control problems subject to state-variable inequality constraints. Solutions which only touch the state constraint and solutions which have a boundary arc of finite length are considered. Suitable shape and test functions are chosen for a FEM discretization. All element quadrature (equivalent to one-point Gaussian quadrature over each element) may be done in closed form. The final form of the algebraic equations is then derived. A simple state-constrained problem is solved. Then, for a practical application of the use of the FEM formulation, a launch vehicle subject to a dynamic pressure constraint (a first-order state inequality constraint) is solved. The results presented for the launch-vehicle trajectory have some interesting features, including a touch-point solution.
Document ID
19930067346
Acquisition Source
Legacy CDMS
Document Type
Conference Paper
Authors
Bless, Robert R. (Lockheed Engineering and Sciences Co. Hampton, VA, United States)
Hodges, Dewey H. (Georgia Inst. of Technology Atlanta, United States)
Seywald, Hans (Analytical Mechanics Associates, Inc. Hampton, VA, United States)
Date Acquired
August 16, 2013
Publication Date
January 1, 1993
Publication Information
Publication: In: AIAA Guidance, Navigation and Control Conference, Monterey, CA, Aug. 9-11, 1993, Technical Papers. Pt. 1 (A93-51301 22-63)
Publisher: American Institute of Aeronautics and Astronautics