Stability analysis and control of multi-vibro-impact capsule systems with distributed interactions

The vibro-impact capsule system has been a focal point of extensive research over the past decade, owing to its inherent challenges as a piecewise-smooth dynamical system and its significant applications across engineering and healthcare technologies. In this groundbreaking study, we initiate the first comprehensive analysis aimed at understanding the dynamics and implementing chaos control within multiple vibro-impact capsules such that they can reach the desired steady-state consistency and are expected to be utilized in various medical examinations in the future. The nonlinear dynamical behavior of the system is analyzed by constructing a bifurcation diagram, which reveals the existence of multi-stability and complex chaotic phenomena. By exploiting the switching between attractors, a novel distributed feedback control method is proposed, facilitating information interaction among the multi-capsule robotic system, ensuring that all capsules can reach the target attractor under any initial condition. Furthermore, we mathematically prove the stability of the multi-capsule system. Finally, numerical analysis verifies the effectiveness of the proposed scheme.