# Question:Using pdsolve to find a potential function, with constraints

## Question:Using pdsolve to find a potential function, with constraints

Maple

Greetings All,

This is an application for control theory, specifially using Maple to solve control problems in the area of Interconnection and Damping Assignment Passivity Based Control (IDA-PBC).

- Assuming two variables (iL and Vo), there is a potential function that I am trying to solve for called "Ha".  I have two equations here, and I want to solve for Ha using the pdsolve() command:

eq1 := diff(Ha(iL, Vo), iL) = rhs(result[1]);
eq2 := diff(Ha(iL, Vo), Vo) = rhs(result[2]);
pdsolve( {eq1, eq2  } );

Once I do this, Maple gives me an expression for Ha that has arbitrary functions in it (I understand where these are coming from).  So far, so good.

--> In order to get help solving for these arbitrary functions, I also want to tell Maple some constraints.  For example:

"the Hessian matrix of Ha must be positive definite"

Is there a way to do this?

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