Control of underactuated systems with viability constraints

This paper addresses the control design for a class of nonholonomic systems which are subject to inequality state constraints defining a constrained (viability) set K. Based on concepts from viability theory, the necessary conditions for selecting viable controls for a nonholonomic system are given. Furthermore, a class of nonholonomic control solutions are redesigned by means of switching control, so that system trajectories are viable in K and converge to a goal set G in K. The motion control for an underactuated marine vehicle in a constrained configuration set K is treated as a case study. The set K essentially describes the limited sensing area of a vision-based sensor system, and viable control laws which establish convergence to a goal set G in K are constructed. The efficacy of the methodology is demonstrated through simulation results.