Mesh stability of look-ahead interconnected systems

Adaptive control schemes for mobile robot formations with triangularised structures

“…This property is very important for formations in motion as it ensures that small perturbations on the leader robots do not cause collisions among follower robots. Pant et al [19] introduced the concept of mesh stability for interconnected systems. This idea may be explored in future work.…”

“…However, the transient response of each follower robot may differ depending on how far away it is from the leaders in terms of path length in the interaction graph. It remains an open interesting problem about how the transient response is amplified from the first follower to the nth follower as n tends to 1 and this is related to the notion of mesh stability [19].…”

Controlling across complex networks – Emerging links between networks and control

“…By appropriate control design, these disturbance signals are attenuated as they propagate through the string of interconnected systems, and stability is preserved. Mesh stability (Pant et al, 2002) generalizes this idea to multiple (physical) dimensions.…”

Leader and Predecessor Following Robust Controller Synthesis for String Stable Heterogeneous Vehicle Platoons

“…Reconsidering the definitions given by Swaroop and Hedrick (1996), Pant et al (2002), Ploeg et al (2014) and Shaw and Hedrick (2007b), the following generalized string stability definitions are proposed. Definition 1.…”

“…(Asymptotic) string stability in the sense of Lyapunov has been formalized by Swaroop and Hedrick (1996): for finite initial conditions the evaluation of spacing errors must be bounded (or must tend to zero). A generalization to 2D formations, called mesh stability (Pant et al (2002)), added the requirement of non-increasing spacing error bounds. These definitions consider the interconnected systems (IS) as autonomous systems without inputs.…”