Composite Adaptive Control of Uncertain Euler‐Lagrange Systems with Parameter Convergence without PE Condition

Abstract

This work proposes a novel composite adaptive controller for 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. The proposed adaptive controller ensures exponential convergence of the tracking and the parameter estimation errors to zero once the sufficient IE condition is met. Simulation results corroborate the efficacy of the proposed technique and also establishes it's robustness property in the presence of unmodeled bounded disturbance.

Relaxation for online frequency estimator of bias‐affected damped sinusoidal signals based on Dynamic Regressor Extension and Mixing

“…The results described in other works 25,[27][28][29] relay on initial excitation. These methods do not require the knowledge of window length for integration since it determines online by checking the determinant.…”

“…The first proposed relaxation method and those in other works [24][25][26][27][28][29] store information via integration. The second method uses delay, which is more close to concurrent learning [20][21][22][23] with direct using of the previous measurements in the estimator.…”

“…A detailed comparison with composite learning and concurrent learning can be found in the work of Basu Roy et al 28 In this paper, we propose two relaxation methods combined with Dynamic Regressor Extension and Mixing (DREM), 30,31 which can be applied to a linear regression model and bring necessary excitation to the estimates convergence. These methods do not require the knowledge of window length for integration since it determines online by checking the determinant.…”

“…These methods do not require the knowledge of window length for integration since it determines online by checking the determinant. A detailed comparison with composite learning and concurrent learning can be found in the work of Basu Roy et al 28 In this paper, we propose two relaxation methods combined with Dynamic Regressor Extension and Mixing (DREM), 30,31 which can be applied to a linear regression model and bring necessary excitation to the estimates convergence. The described relaxations are simple but restricted to the first-order regression models.…”

Robust Adaptive Identification of Linear Time-Varying Systems Under Relaxed Excitation Conditions

“…Furthermore, bounded time-varying disturbances can also be estimated along with system parameters as mentioned in [12]- [15] under the assumption of PE condition. A milder exciting condition that the regressor is sufficiently excited over a finite time interval is introduced to develop an adaptive law for estimation of unknown constant parameters under the influence of bounded disturbances [24]. However, the milder initially exciting condition is also difficult to satisfy in the case of adaptive control.…”