Nonlinear Ship Control: An Opportunity for Applied Mathematicians

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This research addresses some fundamental design issues in the theory of nonlinear control for underactuated mechanical systems. On the basis of our recent work on underactuated ship control, we will take a further step toward the problem of controlling a surface ship with incomplete state information and in the presence of environmental disturbances. Under these constraints, achieving robustness of global stability is hard because the ship often is underactuated, and is highly non-linear. The lack of the separation principle, the general nonlinear observer design, and general robustification tools make this problem challenging. To make advances on this issue, we will use analytical techniques from ordinary and partial differential equations, together with recent results in nonholonomic mechanics and nonlinear control. This research project will pay particular attention to stabilization with incomplete state information and trajectory tracking with robustness to environmental disturbances. Underactuated mechanical systems are systems with less number of actuators than the degrees of freedom. They appear in ocean ships and many other aerospace and marine systems such as satellites and underwater vehicles. A major goal of this project is to develop a mathematical framework of high-performance control for practical applications involving these systems. Performance-oriented controllers derived from this research will be validated via computer simulations and experiments.