Su alcuni problemi fortemente ben posti di controllo ottimo

Summary Let P_n be a sequence of optimal control problems with fixed end times (described by ordinary differential equations, with pointwise and norm (of controls) constraints, and with general functional). Let P₀ be an ? unperturbed ? problem (of the same type). In this paper theorems are obtained about the strong convergence (in some L^p) of optimal controls of P_n to some optimal control of P₀, about the uniform convergence x_n → x₀ of states, and the property thatmin P_n min P₀. As corollaries, convergence theorems for some calculus of variations problems can be derived. Weak convergence theorems of optimal controls of P_n to an optimal one of P₀ were considered in7]. A general abstract theorem about strong convergence of minimum points, generalizing a result in5], is proved.

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Indirizzo dell'autore: Istituto di Matematica, via L. B. Alberti 4 - 16132 Genova. Lavoro eseguito nell'ambito del Centro di Matematica e di Fisica Teorica del C.N.R. presso l'Università di Genova.

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Entrata in Redazione il 4 maggio 1972.