A NEW NECESSARY CONDITION OF OPTIMALITY FOR SINGULAR CONTROL PROBLEMS.
HARVARD UNIV CAMBRIDGE MASS DIV OF ENGINEERING AND APPLIED PHYSICS
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A variation in the form of a rectangular pulse of short duration, is introduced into the singular control function. The technique of Differential Dynamic Programming is used to obtain an expression for the change in cost produced by the control variation, and a new necessary condition of optimality is deduced by requiring that this change in cost be non-negative. When terminal equality constraints are present, the control variation takes the form of a rectangular pulse followed by a special variation which is chosen to keep the terminal equality constraints satisfied to first-order. Simple control problems are used to illustrate the non-equivalence of the new necessary condition and the generalized Legendre-Clebsch condition. Author
- Theoretical Mathematics