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Control Oriented Nonlinear Model Reduction For Distributed Parameter Systems, Samir Sahyoun

Doctoral Dissertations

The development of model reduction techniques for physical systems modeled by partial differential equations (PDEs) has been a very active research area. Large number of states is needed to accurately capture the dynamics of such systems which makes them unsuitable for control design. The order of the system must be reduced prior to control design. In this dissertation, new methods that generalize the popular proper orthogonal decomposition (POD) to nonlinear PDEs are investigated. In particular, cluster based POD algorithms are developed and applied to the one and two dimensional Burgers equations that govern a nonlinear convective ow. Each cluster contains …