Iterative Learning Control for Unknown Nonlinear Systems Based on Data-Driven Model-Free Feedback Linearization

Inverse optimal control of general nonlinear systems based on adaptive dynamic programming

Robust Adaptive Neural Network-Based Backstepping Tracking for Second-Order Euler-Lagrange Systems with Unknown Parameters

This paper proposes a robust adaptive tracking control scheme for a class of second-order Euler–Lagrange systems with completely unknown parameters and nonlinear dynamics. System uncertainties, including unmodeled dynamics, parametric variations, and external disturbances, are formulated as a time-varying lumped perturbation. Radial Basis Function Neural Networks (RBFNNs) approximate the unknown state-dependent nonlinear component within the perturbation bound, while adaptive laws estimate the unknown bounding constants of input-dependent terms and disturbances. By integrating backstepping with a $\sigma$-modification mechanism, a continuous adaptive control law is developed that eliminates chattering typically caused by discontinuous robust terms. Lyapunov analysis proves that all closed-loop signals are uniformly ultimately bounded, achieving asymptotic trajectory tracking with smooth control inputs. Simulations on an underactuated Unmanned Surface Vehicle (USV) under complete model uncertainty and environmental disturbances validate the effectiveness and superiority of the proposed method.

Control Of Uncertain Nonlinear Systems Using Non-parametric Machine Learning

Accurately modeling nonlinear dynamical systems is challenging due to model inaccuracies and uncertainties, which can significantly degrade controller performance. Designing stabilizing controllers for nonlinear systems under such uncertainties remains a challenging problem. A wide range of stabilizing control algorithms have been proposed in the existing literature; however, their effectiveness relies on the accuracy of system dynamics. This manuscript addresses the issue of stabilizing controller design for nonlinear systems, particularly when the drift vector field is uncertain, by integrating non-parametric machine learning techniques to estimate the unknown component. In this work, a framework is proposed in which Gaussian process regression (GPR) is employed to estimate the unknown drift vector field and integrate it into the control synthesis. Moreover, an event-triggered condition is employed to collect data online as needed. The proposed approach enables the construction of control laws that practically stabilize the system, despite incomplete system knowledge. Rigorous theoretical guarantees for the proposed method are provided, and the effectiveness of the framework is demonstrated through numerical simulation studies.

Data-driven Robust Fixed-iteration Learning Control

Adaptive Compensation and Adaptive Optimal Control of a Single Link Manipulator

This paper presents an online solution to the finite-horizon optimal tracking control problem for continuous-time nonlinear systems with partially unknown dynamics, based on an Adaptive Dynamic Programming (ADP) approach. The method employs a dual-approximation identifier–critic neural network (NN) architecture, with both networks tuned simultaneously during online implementation. The unknown weights of the identifier and critic activation functions are estimated using a filter-based adaptive algorithm, which provides a simple online validation of the persistence of excitation (PE) condition required for convergence of the control parameters. The controller is evaluated in simulation on an ideal single-link robotic manipulator with partially unknown dynamics and is compared against two classical adaptive nonlinear control strategies: an adaptive Lyapunov-based nonlinear (ALN) controller and an adaptive backstepping (ABS) controller. Performance is assessed in terms of adaptive parameter convergence, tracking accuracy, control input smoothness, and tuning complexity. The ADP-based controller demonstrates the most intuitive tuning process, as its parameters are directly linked to observed system behaviour, and achieves superior tracking performance with the smoothest control input among the three controllers.

Koopman-based model predictive control for nonlinear systems with bounded model uncertainty