Distributed optimization problem for double-integrator systems with the presence of the exogenous disturbance

Optimal Output Consensus of Heterogeneous Linear Multi-Agent Systems Over Weight-Unbalanced Directed Networks

“…The main feature of this paper is that both general high-order dynamics and weight-unbalanced directed graphs can be handled via our proposed controllers. On one hand, different from existing works that require the agent dynamics to be integrator-type [14], [18] or high-order but minimum phase systems [22]- [24], the general dynamics considered in this work are allowed to be non-minimum phase. On the other hand, in contrary to most existing works where undirected graphs [7], [13] or balanced directed graphs [14], [15] are considered, the proposed controller ( 6) is able to tackle weight-unbalanced directed graphs without a prior knowledge of the left eigenvector corresponding to the eigenvalue zero of the Laplacian matrix L. It is worth noting that the left eigenvector is a kind of global information, which is required in [17], but may be unavailable in practical applications.…”

“…However, there are quite a few engineering tasks in practice that could be reformulated as the OOC problem for more general agent dynamics, such as the economic dispatch in power systems [19], rigid body attitude formation control [20] and source seeking in multi-robot systems [21]. Recently, many efforts are dedicated to solving the OOC for double integrators [22], high-order linear systems [23], [24] and nonlinear systems [25], [26], over undirected graphs. It can be noted that the control design in such scenarios is much more challenging.…”

Optimal Output Consensus of Second-Order Uncertain Nonlinear Systems on Weight-Unbalanced Directed Networks

“…seeking in multi-robot systems [20]. Some works have been reported recently in solving the OOC problem of multi-agent systems with double integrators agent dynamics [12]- [14] and high-order linear agent dynamics [15]- [17] over undirected graphs.…”

Distributed finite‐time optimisation algorithm for second‐order multi‐agent systems subject to mismatched disturbances

“…Currently, some results have been presented on distributed optimisation of multi‐agent systems subject to disturbances [27–30]. By using the internal model approach, some distributed asymptotic optimisation algorithms were proposed for first‐order [27, 28] and second‐order [29] multi‐agent systems subject to disturbances generated from exogeneous systems. In [30], to achieve asymptotic distributed optimisation for multiple uncertain Euler–Lagrange systems, an adaptive distributed control scheme was designed.…”