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rt54321

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Using pdsolve to find a potential functi...

rt54321 10 Maple
pde pdsolve differential-equations
February 05 2024
0 0

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?

Solving a system of equations that has a...

rt54321 10 Maple
December 04 2022
2 0

I have seen several examples of using Maple to numerically solve a PDE, but I'm looking for a "symbolic" method.

Very basic exampl - I have a system of differential equations with two state variables [x1 and x2] like so:
 
x1_prime = x2 + u*x1 + dH/dx1      <--- dH/dx1 is the partial deriv of H wrt x1
x2_prime = x1 + dH/dx2                 <--- dH/dx2 is the partial deriv of H wrt x2
 
H is the energy function that I'm trying to find.
--> I know the partial derivatives of the function H (from above), but I don't know what H itself is. Is there a Maple function or example that will help me find H symbollically?
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