For energy conservation, nonlinear-optimal-control-law design for marine surface vessels has become a crucial ocean technology for the current ship industry. A well-controlled marine surface vessel with optimal properties must possess accurate tracking capability for accomplishing sailing missions. To achieve this design target, a closed-form nonlinear optimal control law for the trajectory- and waypoint-tracking problem of autonomous marine surface vessels (AUSVs) is presented in this investigation. The proposed approach, based on the optimal control concept, can be effectively applied to generate control commands on marine surface vessels operating in sailing scenarios where ocean environmental disturbances are random and unpredictable. In general, it is difficult to directly obtain a closed-form solution from this optimal tracking problem. Fortunately, by having the adequate choice of state-variable transformation, the nonlinear optimal tracking problem of autonomous marine surface vessels can be converted into a solvable nonlinear time-varying differential equation. The solved closed-form solution can also be acquired with an easy-to-implement control structure for energy-saving purposes.
Closed-form solution of optimal control problem of a fractional order system
