Adaptive Control of Feedback Linearizable Systems with Finite-time Convergence

Adaptive control enables the online adjustment of system parameters that are subject to variations and uncertainties to achieve the desired level of performance. The feedback linearization combines an appropriate transformation with a proper control law to linearize the input-output nonlinear system dynamics (NSD). Substantial parametric variations result in the improper cancellation of nonlinear terms in the control law, resulting in an erroneous linear plant. A comprehensive framework of adaptive control is thus proposed using Dynamic Regression Extension and Mixing (DREM) without any prior knowledge of the system’s parameters, simplifications, and assumptions. The proposed DREM-based MRAC and feedback linearization scheme demonstrates the global parameter convergence with improved transient response under a condition strictly weaker than the Persistence of Excitation (PE) of the regressor. Furthermore, in adaptive control, the system states are estimated using the High gain Observer (HGO), and the issues associated with HGO are resolved by the LMI observer. The usefulness of the proposed methodology is validated using MATLAB/simulation on a joint manipulator.