TY - JOUR
T1 - Regular Synthesis and Sufficiency Conditions for Optimality
JF - SIAM J. Control Optim. 39 (2000) 359-410
Y1 - 2000
A1 - Benedetto Piccoli
A1 - Hector J. Sussmann
AB - We propose a definition of \\\"regular synthesis\\\" that is more general than those suggested by other authors such as Boltyanskii and Brunovsky, and an even more general notion of \\\"regular presynthesis.\\\" We give a complete proof of the corresponding sufficiency theorem, a slightly weaker version of which had been stated in an earlier article, with only a rough outline of the proof. We illustrate the strength of our result by showing that the optimal synthesis for the famous Fuller problem satisfies our hypotheses. We also compare our concept of synthesis with the simpler notion of a \\\"family of solutions of the closed-loop equation arising from an optimal feedback law,\\\" and show by means of examples why the latter is inadequate, and why the difficulty cannot be resolved byusing other concepts of solution--such as Filippov solutions, or the limits of sample-and-hold solutions recently proposed as feedback solutions by Clarke, Ledyaev, Subbotin and Sontag -for equations with a non-Lipschitz and possibly discontinuous right-hand side.
PB - SIAM
UR - http://hdl.handle.net/1963/3213
U1 - 1088
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -