This article contains a continuous-time optimal and adaptive control s
cheme for underwater vehicles moving in six degrees of freedom. The co
ntrol scheme is an extension of the algorithm of Johansson (1990) and
a modification of the algorithm found in Sagatun (1992). The algorithm
is optimal in the sense that it minimizes the state errors and the fo
rces which contribute to the vehicle's kinetic energy that is spent to
correct these errors. The performance measure does also contain a ter
m which penalizes the quadratic tracking errors proportional to the ra
te of energy which dissipates from the system due to damping.