Open-loop viable control under uncertain initial state information (Q1301321)

The notions of contingent vector field, viability domain, and viability kernel are introduced in the case when the underlying space is a prescribed collection of sets endowed with the Hausdorff semimetric. As a motivation for this analysis, the problem of open-loop viable control of a nonlinear control system in \(R^n\), with uncertain state information is studied. The family of those initial sets for which a viable control is possible, is characterized. Moreover, an approximation scheme for the viability kernel is proposed. This scheme is numerically realizable in the case of low dimensions and of a simple collection of sets chosen for state estimation. A viability differential game where the uncertainty may enter also in the dynamics of the system, is also studied.