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MathGroup Archive 1996

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optimal control

  • To: mathgroup at smc.vnet.net
  • Subject: [mg4839] optimal control
  • From: George Melikian <melikian at ups.edu>
  • Date: Fri, 20 Sep 1996 01:12:52 -0400
  • Sender: owner-wri-mathgroup at wolfram.com

 Hello,
I am having some difficulty setting up an optimal control problem on
Mathematica. The problem is as follows:
The control variable (u) denotes a threshold setting (0<u<1) that is placed
between 2 probability densities (h & t). The objective is to maxize the
payoff (w) while considering changing risks over time (r(t)). Here is the
code:

v = BetaDistribution[9,3];
r[t_] := PDF[v,t];
h = NormalDistribution[0,.1];
e = NormalDistribution[.3,.1];
g[u_] := CDF[h ,u];
b[u_] := CDF[e ,u];
w[u_,t_] := g[u]+(1-b[u])r[t]- b[u]r[t]- (1-g[u]);
te= Simplify[ D[w[u,t],t]];

hamiltonian = w[u,t] + lambda te;


The problem comes when I attempt to solve for the partial derivatives of
the hamiltonian with respect to: each  (u,t,lambda). 

i.e. 
D[Hamiltonian, lambda]
or
Solve[ D[Hamiltonian,lambda]==0, lambda] 

I get an error telling me either 1/0 encountered or that the function
cannot be solved. Any help here would be greatly appreciated.

Thanks in advance,
George Melikian
Melikian at ups.edu

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