DQCR:

Path: Common/Control

% Create a quadratic regulator.

   Create a quadratic regulator of the form

   u = -Kx minimizing the cost functional

   J = †(1/2){u'ru + x'qx + u'nx + x'nu}dt.

   Given the constraint:
    
   x(k+1) = a x(k) + b u(k)

--------------------------------------------------------------------------
   Form:
   k = DQCR( a, b, q, r, n )
--------------------------------------------------------------------------

   ------
   Inputs
   ------
   a                   Plant matrix
   b                   Input matrix
   q                   State cost matrix
   r                   Input cost matrix
   n                   State/input cost cross-coupling matrix

   -------
   Outputs
   -------
   k		            Optimal gain

--------------------------------------------------------------------------
   References:	Franklin, G.F., J.D. Powell, M.L. Workman, Digital Control
               of Dynamic Systems, 2nd Edition, Addison-Wesley, 1990,
               pp. 435-438.
--------------------------------------------------------------------------

Children:

Common: Control/DRiccati
Math: MathUtils/Odd

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