A nonlinear H-infinity control approach for autonomous navigation of underactuated vessels

Abstract

A new nonlinear optimal control approach is proposed for autonomous navigation of unmanned surface vessels. The dynamic model of the surface vessels undergoes approximate linearization round local operating points which are redefined at each iteration of the control algorithm. These temporary equilibria consist of the last value of the vessel's state vector and of the last value of the control signal that was exerted on it. For the approximate linearization of the system's dynamics Taylor series expansion is performed through the computation of the associated Jacobian matrices. The modelling errors are compensated by the robustness of the control algorithm. Next, for the linearized equivalent model of the vessel an H-infinity feedback controller is designed. This requires the solution of an algebraic Riccati equation at each iteration of the computer control program. It is shown that the control scheme achieves H-infinity tracking performance, which implies maximum robustness to modelling errors and external perturbations. Moreover, the asymptotic stability of the control loop is proven through Lyapunov analysis.