Guaranteed‐performance consensus tracking for one‐sided Lipschitz non‐linear multi‐agent systems with switching communication topologies

Abstract

The guaranteed-performance consensus tracking (GPCT) for non-linear multi-agent systems (MASs) with switching communication topologies is presented. Different from the existing work, the non-linear range of one-sided Lipschitz non-linear MASs is wider than the Lipschitz ones, and the upper bound of the tracking performance is given while achieving the consensus tracking. First, a guaranteed-performance tracking control protocol is proposed, where consensus tracking regulation performance is involved. Then, by the linear matrix inequality (LMI), sufficient conditions are provided to achieve the GPCT under the one-sided Lipschitz and quadratic inner bounded conditions. It is worth noting that a special LMI structure is directly constructed by introducing these two conditions to simplify the complexity of the derivation. Finally, two simulation examples are provided to demonstrate the effectiveness of the proposed results.

Robust consensus of uncertain multi agent systems with one‐sided Lipschitz nonlinearity

“…The proposed protocol considers a more general one‐sided Lipschitz condition. Existing works in the observer‐based protocol for OSL MAS 33,34,38 provides consensus solution for leader‐follower type problem. These works neither employs adaptive coupling nor is robust against the parametric uncertainties.…”

“…Note that (12) of Theorem 1 is a bilinear matrix inequality (BMI), credited to the constants $$$ {\epsilon}_j,j=1,\dots 4 $$$ and the decision matrices $$$ {P}_1 $$$ and $$$ {P}_2 $$$. Most of the available literature be it concerning a single‐agent system 43,44 or a multi‐agent system 35‐38 requires a guess for these constants, also some works 36,46 utilizes cone complementary linearization (CCL) technique 54 . There are two issues.…”

“…An output feedback approach which does not require the states for measurement was proposed in Reference 37. A guaranteed optimal cost index was developed by the authors in Reference 38 for a leader‐follower type consensus of OSL multi‐agent system. Other studies concerning quasi‐one‐sided systems 39 and p‐one‐sided systems 40 were also investigated.…”

Consensus based on output for nonlinear multi-agent systems with switching topologies

“…Therefore, we consider the mathematical model under switching topologies, so that the conclusions have more practical application value. In addition, the proposed model can describe many practical systems, such as the car formation by Kim and Seo (2012), the power system by Dai and Guo (2018), and the multiple motors system by Quan et al (2021).…”

Dynamic edge event‐triggered consensus for one‐sided Lipschitz multiagent systems with disturbances

“…21 Many results have studied on OSL systems. [22][23][24][25][26][27] For OSL MASs with switching topology, the guaranteed-performance consensus protocol is designed. 22 By virtue of the observer-based method, the distributed intermittent consensus protocol is considered to handle the problem of unavailable states for OSL MASs.…”