Robust adaptive dynamic surface control of uncertain nonlinear systems

This paper studies the robust adaptive dynamic surface control of a class of nonlinear systems with unmatched uncertainties. The unmatched uncertainties consist of not only the linearly parameterized terms but also the nonlinearly parameterized terms. The bound of each nonlinearly parameterized uncertainty term is supposed to be expressed by a known nonnegative function multiplied by a constant called bound parameter. According to whether the bound parameters are known or not, two different kinds of robust adaptive dynamic surface control algorithms are proposed. It is proved that in each case all the states of the closed-loop system are kept uniformly ultimately bounded, and the output is driven to track a feasible desired output trajectory with an arbitrarily small error. An example is also employed to indicate the effect of the proposed methods.