A question on contral parameters in dynamical systems?
- From: Fan <fyanguw@xxxxxxxxx>
- Date: Sun, 30 Mar 2008 19:01:16 -0700 (PDT)
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{x} = 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{x} = 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{\beta} <=
B, then whether can we say the constraint set is still convex and
compact????
Thank you very much,
Fan
.
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