Viability control for a class of underactuated systems

This paper addresses the feedback control design for a class of nonholonomic systems which are subject to inequality state constraints defining a constrained (viability) set KK. Based on concepts from viability theory, the necessary conditions for selecting viable controls for a nonholonomic system are given, so that system trajectories starting in KK always remain in KK. Furthermore, a class of state feedback control solutions for nonholonomic systems are redesigned by means of switching control, so that system trajectories starting in KK converge to a goal set GG in KK, without ever leaving KK. The proposed approach can be applied in various problems, whose objective can be recast as controlling a nonholonomic system so that the resulting trajectories remain forever in a subset KK of the state space, until they converge into a goal (target) set GG in KK. The motion control for an underactuated marine vehicle in a constrained configuration set KK is treated as a case study; the set KK essentially describes the limited sensing area of a vision-based sensor system, and viable control laws which establish convergence to a goal set GG in KK are constructed. The robustness of the proposed control approach under a class of bounded external perturbations is also considered. The efficacy of the methodology is demonstrated through simulation results.