Design of Predefined-Time Convergence Parameter Estimator With Relaxed Excitation Conditions

Parameter estimation plays a significant role in the performance of adaptive controllers, yet its convergence relies on persistent excitation (PE) condition. In this paper, a novel design method of parameter estimator is proposed for a class of nonlinear systems with linear-in-parameter (LIP) uncertain parameters. The method achieves non-increasing monotonicity of parameter estimation error and predefined-time convergence. By utilizing historical data and instant data to expand the parameter regression matrix and introducing a perturbation matrix in this process, a novel parameter estimator is constructed. Through stability analysis of the parameter estimation error, it was verified that when a sufficiently small perturbation matrix is selected, the estimator can achieve predefined-time convergence of the parameter estimation error under the sufficient excitation (SE) condition, which is strictly weaker than the PE condition. Meanwhile, the numerical simulation results considering identification and control problems demonstrate the effectiveness and superiority of the proposed method. Note to Practitioners—Uncertainty parameters are ubiquitous in numerous systems, such as spacecraft, robotic arms, and ships. When designing controllers for these systems with uncertainties, it is often necessary to incorporate parameter estimators to approximate the uncertain parameters, thereby enhancing the performance of the control system. Traditional parameter estimators typically rely on persistent excitation conditions (e.g., requiring the controlled object to track periodic trajectories) to ensure the convergence of estimation errors. However, we aim to avoid imposing additional motions solely to achieve accurate estimation. Furthermore, apart from estimation accuracy, we require the estimation errors to exhibit monotonically non-increasing behavior and for the convergence time to be predefined. Motivated by these practical considerations, this paper presents a parameter estimator that guarantees predefined-time convergence of estimation errors under relaxed excitation conditions, along with non-increasing monotonicity of the estimation errors. Notably, this approach imposes no additional requirements on the controller design, allowing it to be seamlessly integrated with existing controllers or used independently as a system identification method. Finally, the effectiveness and superiority of the proposed method are validated through numerical simulations.