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:

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.