Forward/backward adaptation law for nonlinearly parameterized systems

Linear parameterizations is a central assumption in adaptive estimation and control strategies and it in turn becomes a bottleneck for prevalent applications of adaptive control in many nonlinearly parameterized systems encountered in practice. In literature, there have been some attempts to breakthrough this bottleneck by investigating the characteristics of nonlinearities in artistic arguments. However, it is still open for an implementable strategy that is powerful for nonlinearly parameterized systems as the certainty equivalence principle for linearly parameterized systems. This paper aims to contribute a novel attempt to this open problem by proposing an adaptation algorithm which does not explicitly rely on the expression of the nonlinearities and allows blind tuning for satisfactory performance. The algorithm is supported by rigorous analysis on asymptotic stability and parameter convergence as well as numerical simulation.