Re: Control Function With NDsolve

• To: mathgroup at smc.vnet.net
• Subject: [mg19367] Re: [mg19323] Control Function With NDsolve
• From: "Richard Finley" <rfinley at medicine.umsmed.edu>
• Date: Fri, 20 Aug 1999 23:09:41 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```Don,
Perhaps what you are asking is obvious to those that work in systems
control theory, but I don't think you have given us enough information to
be able to make a general statement.  What are a and b for example?  Are
they real and positive?
If so, then since you start out with f = 1 the ODE has the solution:
y[t]==(a/b)(1 - Exp[-b t]
and it tends towards the maximum a/b as t->Infinity which of course it
never actually reaches, so f will never change.  On the other hand, if b
is complex, what maximum value of y[t] do you mean...Real, Abs ??  Or
perhaps the solution only has to reach within a certain fraction of ymax
before f changes?

regards,
RF

In solving a control type dif eq with NDSolve I have the following
question. Suppose the eq is of the following simplified form

y'[t]==a*f[y[t]]-b*y[t]
y[0]==0

How to define f so that it starts at f=1, and changes to f=0 when y
reaches ymax, and then changes back to f=1 when y reaches ymin, and
so
on in oscilatory fashion?

```

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