On Composite Adaptive Continuous Finite-Time Control of a class of Euler-Lagrange systems
In this paper, we propose several set-point control schemes for achieving finite-time regulation in a class of Euler--Lagrange systems with $n$ degrees of freedom and uncertain potential energy. The proposed controllers are based on composite adaptive control approaches. Each control scheme consists of two main components: a Proportional--Derivative (PD)-based nonlinear feedback term and a finite-time parameter estimation law. The estimation laws rely on the Dynamic Regressor Extension and Mixing (DREM) technique, which can be designed using either the Kreisselmeier or the least-squares dynamic regressor extensions. These results extend recent advances in finite-time adaptive control for Euler-Lagrange systems. To the best of the authors' knowledge, the composite adaptive control formulation proposed here, which does not employ well-known Slotine and Li adaptive control structure, has not been studied in detail yet. The properties of the proposed controllers are rigorously analyzed using Lyapunov methods. The performance of the controllers is thoroughly evaluated through extensive simulation studies.