Prescribed Performance Control of Nonlinear Multi-Agent Systems under Switching Topologies: An Indirect and Singularity-Free Approach

This paper addresses the distributed leader-follower consensus prescribed performance control (PPC) problem for uncertain nonlinear strict-feedback multi-agent systems (MASs) under a switching communication topology. To avoid the potential singularity issues arising from topology switching in PPC, an innovative indirect prescribed performance design framework suitable for both directed and undirected topologies is proposed. This framework encompasses three pivotal steps. Firstly, the relationship between the performance bounds on output tracking errors and those on neighborhood tracking errors is established. Secondly, to avoid singularity, the performance functions are reconfigured during each time interval by analyzing the upper and lower bounds of neighborhood and virtual tracking errors at switching instants. Thirdly, to ensure performance guarantees, the performance function for neighborhood errors is reconstructed across the entire time domain by appropriately governing the reconfiguration at switching times. Based on this framework, a singularity-free, distributed, and low-complexity (model-, approximation-, adaptation-free, and non-recursive) control scheme is developed, capable of steering the output errors into an arbitrarily prescribed residual set at a user-predefined convergence rate. Furthermore, it is demonstrated that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB). The effectiveness of the theoretical findings is validated through simulations on a group of single-link robotic manipulators.