Adaptive Prescribed Performance Control of Nonlinear Multi‐Agent Systems Based on Multi‐Dimensional Taylor Network Approach

ABSTRACT This paper presents an innovative adaptive tracking control approach that utilizes the multi‐dimensional Taylor network (MTN) for a class of nonlinear multi‐agent systems subject to input saturation, integrating prescribed performance control and the backstepping method. First, to address the prescribed performance problem in multi‐agent systems, a coordinate transformation of tracking errors is performed using performance and normalization functions, thus eliminating the constraints on system initial conditions imposed by conventional prescribed performance methods. Second, inspired by the concepts of horizontal and oblique asymptotes, an injective differentiable function is constructed to approximate the non‐smooth nonlinear input saturation function, offering a novel approach to addressing input saturation issues. Based on this foundation, a new adaptive tracking controller is developed by integrating adaptive control with MTN. Subsequently, the proposed control strategy is validated using Lyapunov stability theory, ensuring not only the semi‐global uniform ultimate boundedness of all signals in the closed‐loop system but also that the synchronization error remains within specified bounds and converges to prescribed neighborhoods within designated timeframes. Finally, simulation results validate the effectiveness and applicability of the proposed control scheme.