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 >>> Don Paddleford <don-paddleford at worldnet.att.net> 08/14/99 09:42PM >>> 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?