Finite-time Bipartite Synchronization of Homogeneous and Heterogeneous Multiple Agents with Input Saturation: A TVRE-based Gain Approach

Pursuing faster convergence rates and smaller input magnitudes seem to be two conflicting goals in studying multi-agent systems. To give a trade-off between the two, this paper focuses on the bipartite synchronization problems over signed topologies and aims to achieve finite-time control for general linear agents subject to input saturation constraints. Firstly, this paper considers homogeneous agents and presents a class of bipartite synchronization protocols with saturation constraint, which exploits the solution of the time-varying Riccati equation (TVRE) to design the control gain. Then, a time-varying parameter scheduler is tactically designed for TVRE and achieves finite-time bipartite synchronization. Note that the design uses the solution computed online and brings a bit of conservatism in determining the settling time. So, for heterogeneous agents, this paper constructs a modified parameter scheduler computed off-line to reduce the conservatism. A class of finite-time bipartite synchronization generators and generator-based finite-time protocols are proposed. It shows that, in both designs, the control input subjects to the bound saturation during convergence even if the gain escapes to infinity towards the settling time. Moreover, the trade-off among the finite convergence time, the saturation bound of the input, and the initial domain are analyzed explicitly in theory. Finally, two simulations verify the validity of the theoretical results.