Practically finite-time <i>H</i> _∞ deployment of large-scale multi-agent systems with sequence-dependent switching topology: a fuzzy PDE-based approach

In this paper, for large-scale nonlinear first-order and second-order multi-agent systems (MASs) with external disturbance, the practically finite-time [Formula: see text] deployment (PFTHD) problem is studied via the approach based on partial differential equations (PDEs). First of all, it is assumed that the number of first-order agents (FOAs) and second-order agents (SOAs) is sufficient, then, by designing two class of special network communication protocols (NCPs) and combining T-S fuzzy technology, the tracking errors of large-scale nonlinear FOAs and SOAs can be modelled as a first-order fuzzy PDE and a second-order fuzzy PDE, respectively, through the continuum method of discrete systems. It should be pointed out that to consistent with actual communication situations, the topological weights of the NCPs are designed as sequence-dependent and Markovian switched. In addition, two fuzzy boundary control strategies are designed, and the corresponding design criteria of controller gains are obtained based on the Lyapunov method, which could ensure the PFTHD of the considered large-scale MASs with external disturbance. Finally, numerical examples are given to illustrate the effectiveness of the designed NCPs and control strategies.