PENALTY METHODS IN OPTIMAL-CONTROL THEORY.
RESEARCH ANALYSIS CORP MCLEAN VA
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The recent appearance of a paper by A. V. Balakrishnan, in which a penalty function was used to remove the necessity of solving the dynamical equations in order to compute the solution of an optimal control problem, has motivated the developments presented here. Restricting ourselves to a fixed-end-point problem in optimal-control theory with special intermediate and control constraints, we prove that under certain restrictions one may replace this optimal-control problem by a sequence of unconstrained free variational problems by the use of a penalty function. This function incorporates the dynamical equations, intermediate-state constraints, and control constraints, as well as the initial-state constraint initial condition with appropriate penalties. Author
- Numerical Mathematics