Uncertainty Modeling Using a Dimension Search and a Genetic Algorithm With Application to Robust Stability Analysis

Abstract

This work uses a new method of determining a parameterization, resampling, and dimension search of an uncertainty model that can be used for efficient engineering models in control design. An algorithm using the Cayley–Menger determinant as a measure of the dimension test geometry (volume/area/length) of the parametric data points is presented to search for a reduced number of dimensions that can be used to represent the parameters of a model that captures the uncertainty in a dynamic system (uncertainty model). A genetic algorithm (GA) is utilized to solve the nonconvex problem of finding the coefficients of a parameterization of the uncertainty model. A resampling approach for the uncertainty model is also presented. The methods presented here are demonstrated on an electrohydraulic valve control system problem. This demonstration includes consideration of the dimensional search, data resampling, and parameterizing of an uncertainty class determined from test data for 30 replications of an electrohydraulic flow control valve which were experimentally modeled in the lab. The suggested resampling method and the parameterization of the uncertainty are used to analyze the robust stability of a control system for the class of valves using both frequency domain h-infinity methods and analysis of closed-loop poles for the resampled uncertainty model.