Adaptive Tracking Control for Unknown Dynamics Systems with SINDYc-based Sparse Identification

Abstract

Machine learning-based data-driven approaches have greatly improved system identification capabilities and facilitated the application of model-based control algorithms. However, techniques such as neural networks require significant amounts of training data and have limited generalization capabilities. To overcome this problem, we employ the sparse identification of nonlinear dynamics with control (SINDYc) for system identification, which considers both system states and control inputs. Based on the identified system, we design the controller using the backstepping control method. In order to make the algorithm more practical in real-world scenarios, we introduce an input saturation compensation system into the controller design. Additionally, we apply a command filter into the method to avoid deriving a virtual control signal and reduce the computational complexity of the controller. Through stability analysis, the proposed control algorithm ensures that the tracking error in the system is bounded. Finally, we verify the effectiveness of the proposed SINDYc-Backstepping framework by conducting simulations using a single-link robot arm.