Incremental Adaptive Control of a Class of Nonlinear Nonaffine Systems

As a class of familiar nonlinear systems, nonaffine systems are frequently encountered in practical applications. Currently, in the context of learning control, there is a lack of research results about such general class of nonlinear systems, especially for the case of performing infinite interval tasks. This article focuses on the incremental adaptive control for nonlinear systems in nonaffine form, without requiring periodicity or repeatability. Instead of using the integral adaptation, incremental adaptive mechanisms are developed and the corresponding control schemes are presented, by which the numerical integration for implementation can be avoided. With the proposed incremental adaptation, the implicit function theorem is introduced to solve the intractability problem of the nonaffine structure. The robustness (robust convergence) of the tracking error is characterized, with the aid of a proposed key lemma, while the boundedness of all the variables is examined. Numerical results are presented to verify the effectiveness of the proposed control design.