Re: A question on contral parameters in dynamical systems
- From: spellucci@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (Peter Spellucci)
- Date: Tue, 1 Apr 2008 12:35:02 +0200 (CEST)
In article <3c80dd7b-8417-4e6c-be25-37c8fc129659@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Fan <fyanguw@xxxxxxxxx> writes:
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.
you are dealing with \beta as functions !
which property to you require for \beta (?measurable and essentially
bounded? in wich topology you want compactness?
which smoothness do you assume from g and f?
in the definition of convexity , the parameter \lambda isn't dependent
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????
on t . where is the problem concerning convexity?
but again : in which function space do you want to work?
hth
peter
.
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