Probabilistic analysis and control of systems with uncertain parameters over non-hypercube domain

Generalized polynomial chaos expansion provides a computationally efficient way of quantifying the influence of stochastic parametric uncertainty on the states and outputs of a system. In this study, a polynomial chaos-based method was proposed for an analysis and design of control systems with parametric uncertainty over a non-hypercube support domain. In the proposed method, the polynomial chaos for the hypercube domain was extended to non-hypercube domains through proper parameterization to transform the non-hypercube domains to hypercube domains. Based on the proposed polynomial chaos framework, a constrained optimization problem minimizing the mean under the maximum allowable variance was formulated for a robust controller design of dynamic systems with the parametric uncertainties of the non-hypercube domain. Several numerical examples ranging from integer to fractional order systems were considered to validate the proposed method. The proposed method provided superior control performance by avoiding the over-bounds from a hypercube assumption in a computationally efficient manner. From the simulation examples, the computation time by gPC analysis was approximately 10-100 times lower than the traditional approach.