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This paper proposes a method to construct viability kernels for single output nonlinear control systems affine in the control. The safe set is a manifold with boundary and the control is constrained to take values in a compact polyhedron. The results make use of the Frankowska method and the notion of viable capture basins. Three examples illustrate the methodology: the inverted pendulum, a linear...
This paper presents results on the global structure of the time optimal trajectories of the planar pendulum on a cart. Relying on the geometric theory of time optimal synthesis, we provide a discontinuous feedback giving optimal solutions for any initial data.
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