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Regular synthesis and sufficiency conditions for optimality. (English) Zbl 0961.93014
The authors propose notions of “regular presynthesis and synthesis”. The relation between the introduced concepts and the other definitions of synthesis is discussed. Moreover, several examples for optimal regular synthesis are presented in order to illustrate the differences between the various definitions. The main result is a sufficiency condition for optimality. This result is based on the relation between the adjoint vector of the maximum principle and the gradient of the cost function. A technical result about differentiability of trajectories with respect to a parameter under weak differentiability assumptions is also presented separately in Appendix A.

MSC:
93B50 Synthesis problems
93C15 Control/observation systems governed by ordinary differential equations
49K15 Optimality conditions for problems involving ordinary differential equations
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