The paper is concerned with the problem of adaptive tracking system control synthesis. It is assumed that a nonlinear, feedback linearizable object dynamics (model structure) is (partially) unknown and some of its nonlinear characteristics can be approximated by a sort of functional approximators. It has been proven that proportional state feedback plus parameter adaptation are able to assure its asymptotic stability. This form of controller permits online compensation of unknown model nonlinearities and exogenous disturbances, which results in satisfactory tracking performance. An interesting feature of the system is that the whole process control is performed without requisite asymptotic convergence of approximator parameters to the postulated 'true' values. It has been noticed that the parameters play rather a role of slack variables on which potential errors (that otherwise would affect the state variables) cumulate. The system's performance has been tested via Matlab/Simulink simulations via an example of ship path-following problem.

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The design of a vessel path-following control system based on a full, realistic, nonlinear model is considered. The control objective is to force a surface, course-unstable vessel to track a predefined geometric path. We study an underactuated ship characterized only by a surge control force and yaw control moment, typical of many supply vessels. The assumption is made that the ship's model parameters are unknown, while significant external disturbances and unmodeled dynamics exist. Therefore, the design procedures make use of robust and adaptive control techniques. The controller synthesis uses adaptive output feedback linearization and H  optimal control techniques. In this way, the proposed control scheme assures position tracking despite various uncertainties. Because the considered design method leads to a nonminimum phase system, the problem of how to stabilize unstable zero dynamics arises. The presented simulations are based on a realistic ship model in terms of the structure and experimentally identified parameters. The simulations illustrate the effectiveness of the proposed algorithms.

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