21d4139a-cc32-4f13-b3b0-dbb12a852ddd 9 4 5 false false 0 decimal
&[DATE] &[TIME] - &[FILENAME]
&[PAGENUM] / &[COUNT]

Pseudo Inverse Matrices

For the overdetermined case (pg50):

For example representing two resistor networks connected to two soures.

 1 1000 / 1 150 / 1 100 / 1 500 / 1 100 / 1 200 / 2 3 mat 1 1000 / 1 500 / 1 150 / 1 100 / 1 100 / 1 200 / 3 2 mat * ( 1 - ^ 1 1000 / 1 150 / 1 100 / 1 500 / 1 100 / 1 200 / 2 3 mat *

Left Pseudo-Inverse

 23.1454 - 69.7923 - 148.8427 36.7953 141.7211 98.1602 - 2 3 mat

The Left Pseudo-Inverse / Overdetermined case contains redundant information, so if the data contains errors, LPI performs an averaging process that minimizes mean- square error in the estimate of x.

For the undetermined case (pg51):

For example representing three valves connected to same tank.

 1 1 1 3 1 mat 1 1 1 1 3 mat 1 1 1 3 1 mat * ( 1 - ^ *

Right Pseudo-Inverse

 0.3333 0.3333 0.3333 3 1 mat

The Right Pseudo-Inverse case does not contain enough information to provide a unique solution for x. According to the book, does provide a feasible solution that minimizes the quadratic norm of x.

Optimal Control and Estimation by Robert Stengel