Trajectory tracking of full‐state constrained random nonlinear systems by nonlinear transformation functions

Abstract This paper addresses the tracking problem for full‐state constrained random nonlinear systems without imposing traditional feasibility conditions on virtual controllers. Such systems are challenging due to inherent nonlinearity, randomness, and constrained states. A novel approach is used to map constrained states to unconstrained ones by introducing state‐dependent nonlinear transformation functions, and to ensure that states remain within the constraint set by analyzing the performance of unconstrained states. It can be proven that all signals of the closed‐loop system are finite almost surely, state constraints are not violated almost surely, and the tracking error converges to a small neighborhood near zero. A simulation example with a robotic arm system demonstrates the effectiveness of the proposed control approach.