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MathGroup Archive 1996

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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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