HOPF BIFURCATIONS AND NONLINEAR STUDIES OF GAIN MARGINS IN PATH CONTROL OF MARINE VEHICLES

The problem of loss of stability of marine vehicles under cross-track error control in the presence of a mathematical model versus actual sy stem mismatch is analyzed. Emphasis is placed on studying the response of the system after the initial loss of stability of straight line mo tion. Center manifold reduction and integral averaging methods are use d in order to study bifurcations to periodic solutions and stability o f the resulting limit cycles. Numerical integrations are used to confi rm the theoretical results and to establish regions of asymptotic stab ility. The methods used in this work demonstrate the significance of n onlinear terms in assessing the response of the system.