Designing controllers necessitates having an accurate model of the system. However, in practice this is not feasible, regardless of whether the model is derived from first principles, through experimentation, or through the use of a linguistic model. Even if it were possible to develop an accurate model, wear or unknown inputs may cause changes in parameters. Therefore, the design process of a controller must include model uncertainty.

The goal of this research is to develop a controller design methodology that includes parametric uncertainty in its scheme, utilizing Polynomial Chaos Theory (PCT). First introduced in the form of Homogeneous Chaos Expansion in 1938, PCT is a spectral expansion of random variables that approximates the random process by a complete and orthogonal polynomial basis in terms of certain random variables. PCT can be used to formally apply uncertainty to a stochastic process. It has been applied to fluid dynamics, circuit simulation and even the field of measurement to study the effects of uncertainty.

This research endeavors to exploit the power of PCT in order to apply uncertainty to the modeling process and thereby create a probabilistic model of the system for the design of a robust controller.