Overcoming the detectability obstacle in certainty equivalence adaptive control
This paper concerns global adaptive stabilization of nonlinear systems where both a linearly parameterized stabilizer and a Lyapunov function are known for the ideal closed-loop system. Although the standard estimator is implementable, the Lyapunov function is not assumed to be strict (i.e., with a derivative that is only negative semidefinite). The motivation behind this work derives from physical systems where the natural Lyapunov function is the total energy, which is not always strict. In prior work, completing the stability proof in these circumstances has required a rather restrictive detectability condition. Here, the authors take an alternate approach by adding to the parameter estimator an identification error coming from an incorrect identifier. The detectability assumption is then replaced by a new condition that requires that the negative definite terms in the Lyapunov function dominate.
scientific article; zbMATH DE number 1797091