A viability approach for the stabilization of an underactuated underwater vehicle in the presence of current disturbances

In this paper we present a viability-based formulation for the stabilization of an underactuated underwater vehicle under the influence of a known, constant current and state constraints. The stabilization problem is described by three problems in terms of viability theory. We present a solution to the first problem which addresses the safety of the system, i.e. guarantees that there exists a control law such that the vehicle always remains into the safe set of state constraints. In order to overcome the computational limitations due to the high dimension of the system we develop a two-stage approach, based on forward reachability and game theory. The control law is thus the safety controller when the system viability is at stake, i.e. close to the boundary of the safe set. The viability kernel and the control law are numerically computed.