ISS-Based Cascade Analysis of Delay-Coupled Oscillator Coordination for Constrained Humanoid-Inspired Systems

This paper addresses a cascade control architecture for multi-degree-of-freedom mechanical systems in which coordination is generated by a network of delay-coupled regulated oscillators, while physical feasibility and closed-loop stability are enforced at the mechanical level. Time delays are confined to the coordination layer and encode relative timing relationships, whereas reference generation and mechanical tracking are delay-free. Each oscillator satisfies an input-to-state stability property, and boundedness of the delayed network is ensured under a small-gain condition. An admissibility layer enforces position, velocity, and acceleration constraints on the generated references, while the mechanical subsystem is assumed to satisfy an ISS tracking property under saturation and disturbances. A cascade stability result guarantees bounded trajectories and uniform ultimate boundedness of tracking errors. Simulation results with four regulated Van der Pol oscillators illustrate the effectiveness of the approach under delayed coordination and constrained mechanical operation.