Abstract
Existing results on dealing with unknown high-frequency gain signs (UHFGSs) mainly adopt the Nussbaum-type functions. A new kind of control algorithms with nonlinear PI functions are presented to cope with UHFGSs. It is rigorously proven that the proposed algorithms with properly selected nonlinear PI functions can guarantee consensus for high-order multi-agent systems (MASs) under switching topologies with uniformly quasi-strongly $\delta $ -connected graphs (UQSGs). Furthermore, we also investigate the output leaderless consensus of heterogeneous agents with UHFGSs. Finally, the numerical examples are illustrated to show the validity of the proposed results.
Highlights
For the last several decades, the cooperative control problems of designing algorithms that achieve consensus in multiagent systems (MASs) have attracted much attention in the field of system control [1]–[4]
We first introduce nonlinear PI control algorithms for MASs under uniformly quasi-strongly δ-connected graphs (UQSGs), and the results are extended to output leaderless consensus of heterogeneous agents
Remark 2: In view of Theorem 2, we deal with the output consensus of heterogeneous MASs with unknown high-frequency gain signs (UHFGSs) under UQSGs, which extends the results in Theorem 1 to the more general case
Summary
For the last several decades, the cooperative control problems of designing algorithms that achieve consensus in multiagent systems (MASs) have attracted much attention in the field of system control [1]–[4]. For the nonidentical UHFGSs in some of the literature, partially known UHFGSs are required in [19], and global network information is used in [20] To break this limit, the work of [21] can construct a partial Lyapunov function in which one Nussbaum-type function exists for each agent, and the problem of multiple Nussbaum-type functions is solved. The work of [21] can construct a partial Lyapunov function in which one Nussbaum-type function exists for each agent, and the problem of multiple Nussbaum-type functions is solved According to this method, the leaderless consensus of MASs with nonidentical UHFGSs was achieved for linear MASs under switching topologies [22] and for nonlinear MASs [23].
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