Combined direct and indirect adaptive control for a class of nonlinear systems

A new adaptive control methodology is proposed for a class of state feedback linearisable nonlinear systems. The new scheme combines direct and indirect adaptive control regimes in an effort to improve speed and accuracy of the adaptation which would lead to increased tracking performance. The adaptive scheme is a certainty equivalence-based methodology and can be viewed as the modified version of a direct adaptive controller. The parameter update dynamics is driven both by the identification error and the tracking error. Closed-loop error dynamics is shown to be stable by using Lyapunov analysis with tracking error and identification error convergence. The proposed method is applied for the control of a typical auto catalysed chemical reaction in order to demonstrate the efficient use of the algorithm when compared with a direct adaptive scheme.