Sensitivity Analysis for Nonsmooth Dynamic Systems

Dr. Kamil Khan, Mathematics,Computer Science Division, Argonne National Laboratory Argonne


18 March 2015 at 10:00

Location: JHE 342

Nonsmoothness in chemical process models can hinder conventional numerical methods for simulation, sensitivity analysis, and optimization, since these methods often depend heavily on differentiability assumptions. Nonsmoothness can be introduced into process models through a number of sources, such as discrete changes in flow regime, thermodynamic phase, or operating mode.  Embedded optimization problems represent a further source of nonsmoothness, and are employed, for example, in pinch analysis and models of cellular metabolism. While dedicated numerical methods exist for nonsmooth problems, these methods typically require generalized derivative information at each iteration, which can be difficult to furnish. This talk presents the first methods for computing useful parametric generalized derivatives for nonsmooth dynamic systems. These methods exploit several intermediate theoretical and numerical advances in automatic differentiation, nonsmooth analysis, and the theory of ordinary differential equations. As an incidental result, sufficient conditions are also developed for smoothness of ostensibly nonsmooth dynamic systems.

 

 


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