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Re: optimal control
*To*: mathgroup at smc.vnet.net
*Subject*: [mg4888] Re: [mg4839] optimal control
*From*: Andrei Constantinescu <constant at athena.polytechnique.fr>
*Date*: Fri, 4 Oct 1996 00:17:30 -0400
*Sender*: owner-wri-mathgroup at wolfram.com
Hi George !
There is a little remark I'd like to make: Its more
practical to define just expression at the beginning
and arrive at a function as late as possible, i.e:
v = BetaDistribution[9,3];
r = PDF[v,t];
h = NormalDistribution[0,.1];
e = NormalDistribution[.3,.1];
g = CDF[h ,u];
b = CDF[e ,u];
w[u_,t_] := g+(1-b)r - b r - (1- g);
te= Simplify[ D[w[u,t],t]];
This gives :
In[9]:= te= Simplify[ D[w[u,t],t]]
7 2
Out[9]= 990 t (-4 + 9 t - 5 t ) Erf[5. Sqrt[2] (-0.3 + u)]
In[10]:= hamiltonian = w[u,t] + lambda te;
In[11]:= D[hamiltonian, lambda]
7 2
Out[11]= 990 t (-4 + 9 t - 5 t ) Erf[5. Sqrt[2] (-0.3 + u)]
So at this moment, there is no sense to make:
In[13]:= Solve[ D[hamiltonian,lambda]==0, lambda]
Out[13]= {{}}
... as there is no lambda depence in D[hamiltonian, lambda]
I hope that helps !
Regards,
Andrei
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