A cyber-physical system (CPS) is defined as a distributed network of collaborating hybrid, dynamic devices that operate in real-time and abide the by laws of physics. CPS incorporate sensors to acquire data from their environment as well as actuators to influence physical processes. The concept encompasses intercommunicating mechatronic systems; popular civil implementations of this concept are wireless sensor actuator networks (WSAN) and cyber-physical production systems (CPPS). The combination of sensors and actuators within the physical domain effectively forms a hierarchy of operational/reactive and strategic/predictive closed control loops within the cyber and socio domains respectively. The feedback loop is fundamentally a measurement system. In a mathematical sense, the evaluation of a measurement is an inverse problem, whereby the system's perturbed output, i.e., the effect, is observed and the system's original input, i.e., the cause, is sought. The acquired data has a given significance depending on the context it is related to. An analytically correct solution requires adequate mathematical models of the physical phenomena, whereby models are simplified abstractions of reality. Incorporation of a-priori knowledge about the system enables the solution of the problem with respect to a maximum likelihood estimation in the presence of noise. Using model based design (MBD), the equations are formulated on abstract model level without the need of detailed knowledge about the intended target hardware platform or programming language. The dissertation focuses on the formulation of a robust algebraic framework for the description of physical models using discrete orthogonal polynomial (DOP) basis functions as numerical linear operators in regression analysis. Furthermore, a linear differential operator for the solution of perturbed ordinary and partial differential equations (ODE and PDE) has been derived. In this vein, inverse problems are solved using spectral regularization in a least squares sense with high numerical quality and stability. The use of linear operators is advantageous in terms of estimating the error propagation as well as their potential to be automatically translated to platform specific target code for embedded systems using MBD. In-the-loop verification techniques ensure the functional and numerical equivalence between model code and target code. The generic DOP concept has been expanded to weighted approximation, constrained basis functions and bivariate transformations to cover a wider range of possible applications. The theoretical framework has been implemented in CPS applications on heavy machinery from the mining and tunneling industry utilizing the presented system design approach. This encompasses the use of DOP basis functions for system level calibration in machine vision together with a-priori estimation of confidence intervals, uncertainty weighted multi-source data fusion as well as the automatic generation and deployment of target code on various embedded processor platforms. Extensive experimental verification has been carried out during these projects. The new methods are completely general and fully scalable. They bear immense potential for future applications, especially in temporal data mining where multi-channel streaming data emerging from large-scale CPS has to be analyzed in real-time for adaptive/predictive control of physical processes within the socio domain.