On the use of constraints in least squares estimation and control

In this article, we examine the effect of constraints on estimation and control methods based on quadratic penalty functions. We begin with estimation theory and analyze how constraints alter the statistical properties of the least squares estimates. It is shown that constraints can be used to formulate maximum likelihood (MLE) and maximum a posteriori (MAP) estimators for a variety of unimodal distributions. This provides greater flexibility over the assumption of normality inherent in the MLE and MAP interpretation of traditional least squares. We discuss how these ideas apply to state space models of dynamic systems. Possible applications for controllers that handle constraints are also discussed. A parameter estimation example is given to demonstrate the potential for improved performance over unconstrained least squares.