FINITE ELEMENTS AND TERMINAL PENALIZATION FOR QUADRATIC COST OPTIMAL CONTROL PROBLEMS GOVERNED BY ORDINARY DIFFERENTIAL EQUATIONS.
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The finite element method is used to compute optimal controls of systems governed by linear ordinary differential equations with a quadratic performance index. As an application the penalty technique is used to solve terminal state optimal controllability problems. Numerical instabilities, which are common in the use of penalty, are minimized when the finite element method is applied to solve this problem. Convergence theorems are given and error and penalty parameter estimates are presented. Concrete examples for various situations are given to illustrate the theory.
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