Asymptotic approximation method of force reconstruction: Proof of concept

An important problem in engineering is the determination of the system input based on the system response. This type of problem is difficult to solve as it is often ill-defined, and produces inaccurate or non-unique results. Current reconstruction techniques typically involve the employment of optimization methods or additional constraints to regularize the problem, but these methods are not without their flaws as they may be sub-optimally applied and produce inadequate results. An alternative approach is developed that draws upon concepts from control systems theory, the equilibrium analysis of linear dynamical systems with time-dependent inputs, and asymptotic approximation analysis. This paper presents the theoretical development of the proposed method. A simple application of the method is presented to demonstrate the procedure. A more complex application to a continuous system is performed to demonstrate the applicability of the method.