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In this paper a control law for tracking of underactuated surface vessels is presented. Optimal trajectories for surface vessels are given as combinations of arcs of circles and line segments. It is shown how optimal trajectories can be made smooth by a technique called splines, and how these trajectories can be stabilized by backstepping. The control law depends on that the forward velocity of the surface vessel always is positive, which is not a major limitation for tracking urposes.It is also shown how this work can be parts o f a hierarchical hybrid system for control of surface vessels.

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this note a continuous feedback control law with time-periodic terms is derived for the control of nonholonomic systems in power form. The control law is derived by Lyapunov design from a homogeneous Lyapunov function. Global asymptotic stability is shown by applying the principle of invariance for time-periodic systems. Exponential convergence follows since the vector elds are homogeneous of degree zero.

Summary Automatic control solutions for drilling are expected to become widely used in the future. Both basic and more advanced control tools are well established in other communities such as offshore processing facilities and oil refineries. Drilling systems, however, have traditionally been operated manually. There is a great economic potential for the introduction of automatic control providing reduced drilling time, increased regularity, and improved performance, especially for wells with very narrow pressure margins. One example of automated drilling is automatic control of the downhole pressure by topside choking in managed-pressure-drilling (MPD) operations. Narrow drilling margins, especially in depleted reservoirs, ask for highly accurate pressure control. Statoil applied automatic MPD successfully offshore at the Kvitebjørn field in the North Sea in 2007. This paper presents some MPD results from Kvitebjøm and discusses automatic control requirements for drilling operations. The requirements for MPD operations include a specified accuracy for a set of normal operations, such as rate changes and set point ramping during connections, surge and swab, and some failure operations, such as power loss, gas kicks, and blocked choke. The paper also includes some ideas for the future of intelligent-drilling operations with increasing automation.

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