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Comparison of the behavior of exact and approximate modelling of a nonlinear oscilator with one degree-of-freedom

Mesnier V., Lamarque C., Malasoma J., Awrejcewicz J.

Journal of Technical Physics

1999

Vol. 40, no 1

101-108

We consider a nonlinear mechanical system with one degree of freedom described by an exact model and then by a piecewise linear approximations of this model. We compare the global dynamic behavior of the exact model with that of the approximate model. An example shows that it is possible to describe complex behaviors with a rather reasonable accuracy.

Application of the classical implicit function theorem in sensitivity analysis of parametric optimal control

Malanowski K.

Control and Cybernetics

1998

Vol. 27, no 3

335-352

A family {(O[sub h])} of parametric optimal control problems for nonlinear ODEs is considered. The problems are subject to pointwise inequality type state constraints. It is assumed that the reference solution is regular. The original problems (O[sub h]) are substituted by problems [...] subject to equality type constraints with the sets of activity depending on the parameter. Using the classical implicit function theorem, conditions are derived under which stationary points of [...] are Frechet differentiable functions of the parameter. It is shown that, under additional conditions, the stationary points of [...] correspond to the solutions and Lagrange multipliers of (O[sub h]9).