Re: A question on contral parameters in dynamical systems

Hi Peter,

Actually I am from the engineering field. So my guess would be that it
is in vector space. Would the constraint set be compact after adding
the constraint set A<= \dot{\beta} <= B?

Many thanks,

Fan


On Apr 1, 6:35 am, spellu...@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx (Peter
Spellucci) wrote:
In article <3c80dd7b-8417-4e6c-be25-37c8fc129...@xxxxxxxxxxxxxxxxxxxxxxxxxxx>, Fan <fyan...@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?
 >
 >
 >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????
 >
    in the definition of convexity , the parameter \lambda isn't dependent
    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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