Reduced Order Modeling of High Dimensional Nonlinear Control Systems

University Of California-Davis, Davis CA

Investigators

Abstract

There are well-developed methods for the control and estimation of low dimensional nonlinear systems. There are also well-developed methods for the control and estimation of high or infinite dimensional linear systems. But methods for the control and estimation of high or infinite dimensional nonlinear systems are much less developed. The goal of this research project is to develop model reduction techniques for high or infinite dimensional nonlinear control systems so that low dimensional methodologies and intuition can be utilized. The project will be based on new generalizations to nonlinear systems of balanced realizations and proper orthogonal decompositions. The world is growing more complex as are the mathematical models that are used to describe, control and measure it. Not only are the sizes of the models growing but also their complex nonlinear behaviors. We need methods to capture their essential behaviors in simpler descriptions. An example is modeling of climate on a regional level. Such phenomena are modeled by nonlinear partial differential equations in time and three space variables. Moreover there are inputs from other climate regions, oceans, etc. Moreover it is only possible to measure the climate at discrete times and locations. Such models are discretized into very high dimensional control systems that strain our current computing capacity and our abilities to interpret the resulting data. What is needed are methods for reducing the complexity of models while maintaining their ability to mirror reality. The goal of this project is to develop such methods.