Attractive Surface-Based State-Attracted Control for Uncertain Nonlinear Systems

Designing model-free controllers to achieve desired control performance often leads to reduced real-time performance, diminished robustness, or increased complexity. This paper proposes an attractive surface-based state-attracted control (SAC) method for uncertain nonlinear systems, where the attractive surface is designed through a performance-based state-attracted function (SAF) with global boundedness and convergence. This method ensures that the tracking error convergence direction and rate are consistent with the output of the SAF, so that the tracking error converges along the attractive surface to a small neighborhood of the origin. Notably, the SAC method eliminates model dependence and maintains low controller complexity while achieving desired control performance, robustness, and real-time performance in a complementary way. Furthermore, three types of SAC are developed: a fast SAC (FSAC) for rapid convergence, a convex SAC (CSAC) for smooth convergence, and a switched SAC (SSAC) for multi-phase convergence. Finally, the stability of the closed-loop system is analyzed by using Lyapunov theory, and its performance is validated through simulations.