Real-Time Nonlinear Quadratic Trajectory Tracking Control for Polynomial Nonlinear Systems

This paper presents a real-time nonlinear quadratic trajectory tracking control (NLQTC) method for polynomial nonlinear state-space systems. Building on prior regulator designs, a stacked feedback control structure is developed, incorporating an additional term to enable trajectory tracking. The proposed approach guarantees fixed computational costs per control cycle, making it suitable for real-time applications. Validation on a nonlinear mass-spring-damper system demonstrates effective trajectory tracking. Comparative simulations against nonlinear model predictive control (NMPC) show that NLQTC achieves equivalent tracking accuracy while significantly improving computational efficiency.