We consider optimal control problems for several classes of control systems, in particular for a system governed by a semilinear differential equation y ' (t)=Ay(t)+f(t,y(t),u(t)), y(0)=ξ, in Hilbert space, with a cost functional y 0 (t,y,u). The target condition is y(t)=y ¯· Let u ¯ be an optimal control corresponding to an initial condition ξ ¯ and to a minimum m=y 0 (t ¯,y ¯,u ¯) of the cost
... [Show full abstract] functional and let u be an arbitrary control, y(t,ξ,u) the trajectory corresponding to u and to an initial condition ξ. We study the problem of estimating explicitly the difference u ¯(t)-u(t) (in a suitable weighted L 2 norm) in terms of ∥ξ ¯-ξ∥,∥y(t ¯,ξ ¯,u ¯)-y(t,ξ,u)∥ and y 0 (t,y,u)-m.