First-Order and Second-Order Numerical Methods for Optimal Control Problems.
RICE UNIV HOUSTON TEX DEPT OF MECHANICAL ENGINEERING
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This lecture summarizes recent advances in the area of numerical methods for optimal control problems, with particular emphasis on the work performed by the Aero-Astronautics Group of Rice University. The following basic problems are considered problems with general boundary conditions, problem with nondifferential constraints, and problem with multiple subarcs. First-order alogrithms are reviewed, in particular, the sequential ordinary gradient-restoration algorithm and the sequential conjugate gradient-restoration algorithm. Second-order algorithms are also reviewed, in particular, the modified quasilinearization algorithm. Here, the optimal initial choice of the multipliers is discussed. Transformation techniques are presented by means of which a great variety of problems of optimal control can be reduced to one of the formulations presented. Specifically, the following topics are treated time normalization, free initial state, problems with bounded control, problems with bounded state, and Chebyshev minimax problems. Author
- Theoretical Mathematics