Research on Improved Adaptive Control Methods for High-Order Nonlinear System Using Finite-Time Techniques

Abstract

This study develops four enhanced adaptive finite-time control strategies for high-order nonlinear maritime systems, addressing critical limitations in conventional backstepping controllers when applied to vehicles operating under uncertain oceanic conditions. The research proposes four advanced control strategies: multilayer adaptive control, neural network-based adaptive control, model predictive control (MPC) combined with backstepping, and event-triggered control employing barrier Lyapunov functions. These methods have been validated through simulations on a third-order nonlinear system and a cart-pendulum system. Comprehensive MATLAB simulations on third-order nonlinear systems demonstrate substantial performance improvements: the neural network controller achieves 88% faster convergence with 93.4% higher tracking accuracy, the MPC-backstepping approach reduces control energy by 32.7%, and the event-triggered method cuts computational load by 93% while maintaining strict state constraints. Quantitative analysis reveals steady-state error reductions from 0.085 to 0.014 (83.5% improvement) and settling time decreases from 1.2 s to 0.144 s (88% improvement) compared to conventional finite-time backstepping controllers. Furthermore, the proposed controllers were experimentally validated on practical applications, including robotic manipulators, quadrotor UAVs, and industrial hydraulic systems, exhibiting outstanding performance in highly nonlinear and noisy environments. © The Author(s) 2025