A Novel Control Approach Accommodating Dynamic Process and Steady-State Accuracy

This paper proposes an adaptive tracking control framework for nonlinear systems with unmodeled dynamics, ensuring both practical prescribed-time convergence and prescribed performance for full-state errors. Existing methods often depend on unbounded gains, focus only on output tracking error, or rely on initial conditions, restricting their practical applicability. To overcome these issues, we propose a novel adaptive control framework that constrains full-state errors independent of initial conditions and drives them to a prescribed region within a predefined time. This is achieved by using a bounded, continuously differentiable, prescribed-time gain. An adaptive mechanism with a dissipating term is designed to handle unmodeled dynamics and guarantee zero tracking error even under nonvanishing disturbances. Moreover, a smooth scaling function is introduced to enforce desired transient and steady-state performance while reducing large initial control effort. Numerical simulations demonstrate the superiority of the proposed method compared to existing approaches.