Abstract. Variational convergence is developed for optimal control problems depending on time-varying parameters. Systems with chattering parameters serve then s variational limits when the parameters are rapidly oscillating. Continuity of the value, robustness of controls and continuous dependence of optimal controls are examined. 1991 Mathematics Subject Classification: 49J45, 49N99. 1. Introduction This paper addresses the variational convergence problem of optimal control Systems. The form we choose to work with is a minimization problem with constraint equation depending on a time-varying parameter. The variational convergence of this parameter function is sought. Namely, we consider a family of control Systems minimize J Q (x, u, t, (f)) dt (VQ) -£=f(x,u,t,Q(ty)dt x( ) = x0. Each element in the family is determined by a parameter function = (·). We seek a convergence notion for the collection of parameter functions such that: (i) the cost functional with a fixed control depends continuously on , and (ii) the value of vary continuously with . Research supported by a grant from the Basic Research Fund, The Israel Academy of Science and Humanities. * Incumbent of the Hettie H. Heineman Professorial Chair in Mathematics. Zvi Artstein With these two properties, the following approximation scheine applies
Forum Mathematicum – de Gruyter
Published: Jan 1, 1993
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