Av. Sarychev et Dfm. Torres, Lipschitzian regularity of minimizers for optimal control problems with control-affine dynamics, APPL MATH O, 41(2), 2000, pp. 237-254
We study the Lagrange Problem of Optimal Control with a functional integral
(a)(b) L (t, x (t), u (t)) dt and control-affine dynamics (x) over dot = f
(t, x) + g (t, x)u and (a priori) unconstrained control u is an element of
R-m. We obtain conditions under which the minimizing controls of the proble
m are bounded-a fact which is crucial for the applicability of many necessa
ry optimality conditions, like, for example, the Pontryagin Maximum Princip
le. As a corollary we obtain conditions for the Lipschitzian regularity of
minimizers of the Basic Problem of the Calculus of Variations and of the Pr
oblem of the Calculus of Variations with higher-order derivatives.