A question on contral parameters in dynamical systems?

Hi gurus,

I have an urgent question on contral parameters in dynamical systems.
I would greatly appreciate your help!

Suppose we have a dynamic system as

\dot = f (x, \beta), where x is nx1 vector and \beta is a vector
of
continuous-time control variables (with the same dimension as x).

Consider the following optimization problem:

min g(x, \beta)
subject to
\dot = f (x, \beta)
0 <= \beta <= UB

Since the objetive function is continuous, and the constraint set is
convex and compact, the solution of \beta must exist.

My questions is:  if we add one more constraint,  A<= \dot <=
B, then whether can we say  the constraint set is still convex and
compact????

Thank you very much,

Fan