Adaptive Tracking Control of Nonlinear Multi-Agent Systems Subject to Multiple Constraints via Multi-Dimensional Taylor Network

This paper investigates the adaptive tracking control problem for nonlinear multi-agent systems operating under simultaneous input saturation and output performance constraints. To address asymmetric input saturation, an innovative auxiliary system is developed that generates compensatory signals based on the discrepancy between the input signal and the saturation function output. A central contribution is the introduction of a novel dynamic performance function (DPF), this function leverages signals from the auxiliary system to adaptively adjust performance boundaries, critically activating this adjustment only when input saturation occurs concurrently with synchronization errors exceeding predefined safety limits, thereby effectively resolving conflicts between the input and performance constraints. Furthermore, a first-order filter is employed within the backstepping control design to approximate virtual control derivatives, mitigating the "computational explosion" issue. An adaptive controller incorporating multi-dimensional Taylor network (MTN) is then synthesized based on this framework. Rigorous Lyapunov stability analysis confirms the boundedness of all signals within the closed-loop system. Supporting this theoretical finding, simulation results confirm the proposed control strategy’s effectiveness and feasibility, demonstrating enhanced synchronization performance and robustness under these multiple, potentially conflicting constraints.