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Abstract: Combining recent moment and sparse semidefinite programming SDP relaxationtechniques, we propose an approach to find smooth approximations for solutionsof problems involving nonlinear differential equations. Given a system ofnonlinear differential equations, we apply a technique based on finitedifferences and sparse SDP relaxations for polynomial optimization problemsPOP to obtain a discrete approximation of its solution. In a second step weapply maximum entropy estimation using moments of a Borel measure associatedwith the discrete solution to obtain a smooth closed-form approximation. Theapproach is illustrated on a variety of linear and nonlinear ordinarydifferential equations ODE, partial differential equations PDE and optimalcontrol problems OCP, and preliminary numerical results are reported.



Author: Martin Mevissen, Jean-Bernard Lasserre LAAS, Didier Henrion LAAS, CTU-FEE

Source: https://arxiv.org/



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