Stochastic consensus of single-integrator multi-agent systems under relative state-dependent measurement noises and time delays

Abstract

This paper proposes a consensus algorithm for continuous-time single-integrator multi-agent systems with relative state-dependent measurement noises and time delays in directed fixed and switching topologies. Each agent's control input relies on its own information state and its neighbors' information states, which are delayed and corrupted by measurement noises whose intensities are considered a function of the agents' relative states. The time delays are considered time-varying and uniform. For directed fixed topologies, condition to ensure mean square linear -consensus (average consensus, respectively) are derived for digraphs having spanning tree (balanced digraphs having spanning tree, respectively). For directed switching topologies, conditions on both time delays and dwell time have been given to extend the mean square linear -consensus (average consensus, respectively) of fixed topologies to switching topologies. 861In references [1][2][3][4][5][6][7][8][9], the noises are considered additive noises whose intensities are constant and independent of the agents states. Recently, some research [10-12] considered a more reliable and practical model for the noises, which relies on the fact that the noises intensities are time-varying and dependent on the agents' states. [10] obtained sufficient conditions to ensure both mean square and almost sure consensus of high-dimensional first-order dynamics under relative state-depending measurement noises in undirected topologies, where the noise intensities are assumed a vector or a matrix function of agents' relative states.[11] studied the single-integrator consensus with measurement noises in directed topologies. The measurement noise intensities are considered a linear function proportional to the absolute agents' relative states. Conditions to achieve mean square convergence and strong convergence have been obtained for both fixed and time-varying topologies.[12] extended the results of [11] to the leader-following consensus in directed fixed and switching topologies and derived conditions to ensure the tracking in mean square.Motivations and contributions: The authors in [10][11][12] assumed that the information states obtained by an agent from its neighbors are undelayed. However, this statement is not practical because the communication in real physical systems is always subject to time delays caused by the limitation of the speed of acquisition and transmission [13]. Therefore, it is of great importance if one studies the problem of consensus under relative state-dependent measurement noises and time delays. To the best of our knowledge, this problem is not investigated in the literature. In fact, solving this problem is more challenging and is not trivial, because the closed-loop equation that describes the system is a stochastic delay differential equation that is difficult to analyze, because its perturbed term is also a function of the delayed relative states, and therefore, the usual techniques that are typically used with non-state depending measurement...

Output feedback semiglobal practical consensus of linear systems with relative state‐dependent uncertainties

“…Uncertainties of this kind are common in multiagent systems, which may be caused by communication noises, actuator failures, or inherent couplings between agents. For example, assume that there are continuous‐time relative state‐dependent noises in the communication channels of where relative output information is available. Let ξ i denote the internal state estimate generated by the i th distributed observer.…”

“…Uncertainties of this kind are common in multiagent systems, which may be caused by communication noises, actuator failures, or inherent couplings between agents. For example, assume that there are continuous-time relative state-dependent noises 16 in the communication channels oḟ…”

“…The synchronizability will be influenced if the relative state‐dependent uncertainties are ignored. To fill this gap, Ni and Li, Li et al, and Djaidja et al investigated the consensus problem of single‐integrator networks with communication noises, where the noise intensity functions are assumed to be linear functions or globally Lipschitz functions of relative states. On the other hand, since communication noises, actuator failures, and inherent couplings between agents widely exist in networked multiagent systems, relative state‐dependent uncertainties are common in various multiagent systems.…”

Leader‐following mean square consensus of stochastic multi‐agent systems with input delay via event‐triggered control

“…In actuality, when a agent moves in practice environment, stochastic disturbance is unavoidable. Therefore, the consensus problems of stochastic MASs (SMASs) are more applicable in some sense, and it has aroused interest of many researchers [18][19][20][21][22][23][24][25][26][27][28][29][30]. For instance, in [22], the authors have presented an averageconsensus control strategy the average-consensus control strategy for discrete-time MASs in uncertain communication environments, where a type of distributed stochastic approximation control strategy is used to deal with communication noises.…”

Synchronised trajectory tracking for a network of MIMO non‐minimum phase systems with application to aircraft control

“…In the nature, synchronisation behaviours in the form of flocking of birds, schooling of fish, and swarming of bacteria can be observed, and the advantages of these behaviours, such as aerodynamic or hydrodynamic drag reduction and fighting together against predators, lead to increasing interests in synchronised control of multiple vehicle systems in the past decade. In existing works, various vehicle models have been considered for synchronisation control studies, such as single/double integrator systems [1, 2], general linear systems [3], and general non‐linear systems [4]. Extensive applications of synchronisation control have been presented, including attitude synchronisation of spacecraft [5] and three degrees of freedom helicopter [6], autopilot of unmanned aerial vehicles [7], yaw and sideslip angle synchronisation of ships [8], consensus trajectory tracking of mobile robots [9], and so on.…”