Adaptive Learning Control Algorithms for Infinite-Duration Tracking

Learning control is applicable to systems that operate periodically or over finite time intervals. Currently, there is a lack of research results about learning control approaches to infinite-duration tracking, without requiring periodicity or repeatability. This article addresses the problem of adaptive learning control (ALC) for systems performing infinite-duration tasks. Instead of using integral adaptation, incremental adaptive mechanisms are exploited, by which the numerical integration for implementation can be avoided. The comparison with the conventional integral adaptive mechanisms indicates that the suggested methodology can be an alternative to the adaptive system designs. Using an error-tracking approach, the approximation-based backstepping design is carried out for systems in the strict-feedback form, where a novel integral Lyapunov function is shown to be efficient in the treatment of state-dependent control gain. Theoretical results for the performance analysis are presented in detail. In particular, the robust convergence of the tracking error is established, while the boundedness of the variables of the closed-loop system is characterized, with the aid of a key technical lemma. It is shown that the proposed control method can provide satisfactory tracking performance and simplify the controller designs. Numerical results are presented to demonstrate effectiveness of the learning control schemes.