A Novel Feasibility Condition-Free Approach for Achieving Desired Precision and Unified Performance Within Prescribed Time

This paper proposes a low-complexity tracking control framework for uncertain nonlinear systems in strict feedback and normal forms, respectively. By leveraging a smooth scaling function, these control schemes ensure unified prescribed performance for the output tracking error of strict feedback nonlinear systems and the full-state tracking errors of normal form nonlinear systems. The notion of unified prescribed performance allows for different performance behaviors via performance functions, which can be either constant or time-varying with arbitrarily large initial values. The main contribution is achieving unified prescribed performance for full-state tracking errors without imposing feasibility conditions, a limitation of existing approaches. To eliminate these strict conditions, we introduce a uniform transformation independent of initial conditions. Additionally, the proposed control schemes are low-complexity since they do not require adaptive mechanisms or function approximation to deal with uncertainties and disturbances. The effectiveness of these frameworks is demonstrated through comparative analysis.