IEEE Decision and Control Conference Sydney , Australia , Dec 2000 H ∞-Optimal Tracking Control Techniques for Nonlinear Underactuated Systems

This paper presents new techniques for controlling the motion of an underactuated vehicle when disturbances are present and only imperfect state measurements are availabl e for feedback. A state feedback controller is developed and then it is converted to an imperfect state measurement feedback controller. The state feedback tracking control law us es anH∞-optimal design and produces a locally exponentially stable closed-loop system. The imperfect state measuremen t feedback controller combines the state feedback control la w with anH∞-£lter to estimate the states and achieves a modi£ed form of disturbance attenuation. The state estimator exploits a unique structure in the nonlinear equations of mo tion to develop a direct solution. The M ATLAB simulations illustrate both control algorithms for an underactuated sh ip model.