A Viability Problem for Control Affine Systems with Application to Collision Avoidance
Farid Fadaie, Mireille E. Broucke · 2006
Given a control affine system and a domain S which is a smooth manifold with boundary, we present results on explicit construction of a viability controller and viable kernel of S. Under a standard invariance condition on the viability domain, it is shown that there is a viability controller that takes a particularly simple form: it is a bang control. The proposed theory is applied to the problem of collision avoidance control of two vehicles