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Scalar parameter values as well as initial condition values are to be identified in initial value problems for ordinary differential equations (ODE). To achieve this goal, computer algebra tools are combined with numerical tools in the MATLAB environment. The best fit is obtained through the minimization of the summed squares of the difference between measured data and ODE solution. The minimization is based on a gradient algorithm where the gradient of the summed squares is calculated either numerically...
We consider a class of second-gradient elasticity models for which the internal potential energy is taken as the sum of a convex function of the second gradient of the deformation and a general function of the gradient. However, in consonance with classical nonlinear elasticity, the latter is assumed to grow unboundedly as the determinant of the gradient approaches zero. While the existence of a minimizer is routine, the existence of weak solutions is not, and we focus our efforts on that question...
We consider a class of second-gradient elasticity models for which the internal potential energy is taken as the sum of a convex function of the second gradient of the deformation and a general function of the gradient. However, in consonance with classical nonlinear elasticity, the latter is assumed to grow unboundedly as the determinant of the gradient approaches zero. While the existence of a minimizer is routine, the existence of weak solutions is not, and we focus our efforts on that question...
This paper studies the attainable set at time T>0 for the control system showing that, under suitable assumptions on f, such a set satisfies a uniform interior sphere
condition. The interior sphere property is
then applied to recover a semiconcavity result for the value
function of time optimal control problems with a general target, and to
deduce C1,1-regularity for boundaries of attainable sets.
This paper presents the role of vector relative degree in the
formulation of stationarity conditions of optimal control problems
for affine control systems. After translating the dynamics into a
normal form, we study the Hamiltonian structure. Stationarity
conditions are rewritten with a limited number of variables. The
approach is demonstrated on two and three inputs systems, then, we
prove a formal result in the general case. A mechanical system
example serves as illustration.
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