Abstract
An important engineering problem is the recovery of the input of a system given its output. This is a difficult problem to solve in that it is often an ill-defined problem. Such ill-posedness is problematic since noise becomes very influential and results in inaccurate or non-unique solutions. To combat this ill-posedness, additional constraints are typically applied to redefine the problem, leading to a well-defined problem with a unique solution. Current input reconstruction methods span the spectrum of analysis and computation, and we have grouped them into three categories: Direct, Regularization, and Probabilistic/Statistical. Each of these groups is divided into several subsets that offer different perspectives in which to view the reconstruction problem. Our primary interests lie in the behavior of mechanical systems and, as such, we have focused on the literature in these fields. However, applicability includes other fields with the same and similar governing equations.