Find pairings with integrity (findICI)

Finds pairings for decentralized control which satisfy necessary conditions for integrity.

function [CC,criteria]=findICI(G)

Returns in CC all the pairings which satisfy the necessary condition for integrity (ICI) derived fron the Niederlinski Index. This function can be applied to square systems with a maximum size of 8x8.

The input "G" must be a square matrix of real values which represents the dc-gain of the system.

"CC" is a matrix, where each of the rows represents a pairing. For a given row, the value of the i-th element is the index of the input which is paired with the i-th output (see example below).

"criteria" is a quantification of the level of the interaction of the pairings. The k-th element in the criteria vector is associated to the pairing represented by the k-th row of CC. For each pairing, the quantification used is the sum of all the considered elements in the Relative Interaction Array accumulated for all the possible partially controlled systems.

Example: Consider the following DC-gain system fot a Petlyuk distillation column used in by K.E. Haeggblom (1997)with four inputs u1,u2,u3,u4 and four outputs y1,y2,y3,y4.

G=[153.45, -179.34, 0.23, 0.03;

-157.67, 184.75, -0.10, 21.63;

24.63, -28.97, -0.23, -0.1;

-4.8, 6.09, 0.13, -2.41];

Calling to these function returns the calue of "CC":

CC= [3 4 1 2;

1 2 3 4]

The first row of CC represents the paring y1-u3, y2-u4, y3-u1, y4-u2. The second row of CC represents the diagonal pairing y1-u1, y2-u2, y3-u3, y4-u4.

The returned value of criteria is: criteria= [29.2847, 117.7139], indicating that the first pairing is

preferred, since the second pairing presents a larger amount of interaction.