Techniques of Model-Based Control

Appendix C. Review of Linear Least-Squares Regression

Objectives

The objective of this appendix is to briefly review the theory of linear least-squares. Topics discussed include

• The concept of linear least-squares solution.

• Properties of the least-squares estimates.

• Overcoming collinearity problems with principal component and partial least-squares regression.

Derivation of the Linear Least-Squares Estimate

The problem of finding a least-squares solution to a set of linear equations arises at a number of places in this text.

• In process identification where we want to determine parameters in a linear model from empirical data.

• In model-predictive control where we want to determine the control moves that will minimize the future deviations of the output ...