Sayan Basu Roy

Adaptive–Robust Control of Euler–Lagrange Systems With Linearly Parametrizable Uncertainty Bound

This brief proposes a new adaptive–robust control (ARC) architecture for a class of uncertain Euler–Lagrange (EL) systems where the upper bound of the uncertainty satisfies linear in the parameters structure. Conventional ARC strategies either require structural knowledge of the system or presume that the overall uncertainties or its time derivative are norm bounded by a constant. Due to the unmodeled dynamics and modeling imperfection, true structural knowledge of the system is not always available. Furthermore, for the class of systems under consideration, prior assumption, regarding the uncertainties (or its time derivative) being upper bounded by a constant, puts a restriction on the states beforehand. Conventional ARC laws invite overestimation–underestimation problem of switching gain. Toward this front, adaptive switching-gain-based robust control (ASRC) is proposed, which alleviates the overestimation–underestimation problem of switching gain. Moreover, ASRC avoids any presumption of constant upper bound on the overall uncertainties and can negotiate uncertainties regardless of being linear or nonlinear in parameters. Experimental results of ASRC using a wheeled mobile robot note improved control performance in comparison with the adaptive sliding mode control.

Robust Gradient-Based Adaptive Control of Nonlinearly Parametrized Plants

Most of the contributions in adaptive control literature assume that the system dynamics is linearly parametrizable, and a certainty equivalence principle is exploited to guarantee global stability and asymptotic convergence of tracking error to zero. Although linear-in-the-parameters (LIP) assumption is reasonable for a large class of dynamics, there exists a considerable number of real world systems, involving complex dynamics, where nonlinear parametrizations are inevitable. Previous research has shown that classical gradient-based adaptive designs with the certainty equivalence principle do not perform satisfactorily for nonlinear-in-the-parameter (NLIP) systems, and may, in fact, cause instability in many situations. This letter is an attempt toward addressing this issue by a novel non-certainty equivalence adaptive control design, where the classical gradient-based adaptive algorithm is used to tackle the LIP component of the NLIP dynamics, while a robust compensator, appended to the controller, accounts for the linearization error. The designed controller ensures global uniformly ultimately bounded stability of the error dynamics. Simulation results on a model of biochemical process, involving NLIP dynamics, are provided to validate the theoretical development.

Parameter convergence via a novel PI-like composite adaptive controller for uncertain Euler-Lagrange systems

This work proposes a novel PI-like composite adaptive control architecture for the uncertain Euler-Lagrange (EL) systems. The composite adaptive law is strategically designed to be proportional to the parameter estimation error in addition to the tracking error, leading to parameter convergence. Unlike conventional adaptive control laws which require the regressor function to be persistently exciting (PE) for parameter convergence, the proposed method guarantees parameter convergence from a milder initially exciting (IE) condition on the regressor. The IE condition is significantly less restrictive than PE, since it does not rely on the future values of the signal and that it can be verified online. Further, the design methodology does not assume the knowledge of acceleration in the adaptive update law development. As far as the authors are aware, this is the first work on EL dynamics that achieves exponential convergence of the tracking and the parameter estimation errors to zero once the sufficient IE condition is met.