Impulse capture basins of sets under impulse control systems

Hybrid Kernels and Capture Basins for Impulse Constrained Systems

We investigate, for constrained controlled systems with impulse, the subset of initial positions contained in a set K from which starts at least one run viable in K the hybrid viability kernel eventually until it reaches a given closed target in finite time the hybrid capture basin. We define a constructive algorithm which approximates this set. The knowledge of this set is essential for contro...

Viability Kernels and Capture Basins of Sets Under Differential Inclusions

This paper provides a characterization of viability kernels and capture basins of a target viable in a constrained subset as a unique closed subset between the target and the constrained subset satisfying tangential conditions or, by duality, normal conditions. It is based on a method devised by Hélène Frankowska for characterizing the value function of an optimal control problem as generalized...

Closed-loop impulse control of oscillating systems

Impulse control in pigeons.

Pigeons were given a small, immediate food reinforcement for pecking a key, and a larger, delayed reinforcement for not pecking this key. Most subjects pecked the key on more than 95% of trials. However, when pecking a differently colored key at an earlier time prevented this option from becoming available, three of 10 subjects consistently pecked it, thereby forcing themselves to wait for the ...

Impulse Control of Brownian Motion