Protocol selection for second-order consensus against disturbance

Noticing that both the absolute and relative velocity protocols can solve the second-order consensus of multi-agent systems, this paper aims to investigate which of the above two protocols has better anti-disturbance capability, in which the anti-disturbance capability is measured by the L2 gain from the disturbance to the consensus error. More specifically, by the orthogonal transformation technique, the analytic expression of the L2 gain of the second-order multi-agent system with absolute velocity protocol is firstly derived, followed by the counterpart with relative velocity protocol. It is shown that both the L2 gains for absolute and relative velocity protocols are determined only by the minimum non-zero eigenvalue of Laplacian matrix and the tunable gains of the state and velocity. Then, we establish the graph conditions to tell which protocol has better anti-disturbance capability. Moreover, we propose a two-step scheme to improve the anti-disturbance capability of second-order multi-agent systems. Finally, simulations are given to illustrate the effectiveness of our findings

Formation Control and Reconfiguration Strategy of Multi-Agent Systems

Multi-agent systems consist of multiple agents, which detect and interact with their local environments. The formation control strategy is studied to drive multi-agent systems to predefined formations. The process is important because the objective formation is designed such that the group achieves more than the sum of its individuals. In this thesis, we consider formation control strategies and reconfiguration strategy for multi-agent systems. The main research contents are as follows. A formation control scheme is proposed for a group of elliptical agents to achieve a predefined formation. The agents are assumed to have the same dynamics, and communication among the agents limited. The desired formation is realized based on the reference formation and the mapping decision. In the controller design, searching algorithms for both cases of minimum distance and tangents are established for each agent and its neighbors. In order to avoid collision, an optimal path planning algorithm based on collision angles, and a self-center-based rotation algorithm are also proposed. Moreover, randomized method is used to provide the optimal mapping decision for the underlying system. To optimize the former formation control scheme, an adaptive formation control strategy is developed. The multiple elliptical agents can form a predefined formation in any 2D space. The controller is based on the neighborhood of each agent and the optimal mapping decision for the whole group. The collision-free algorithm is built based on direction and distance of avoidance group of each agent. The controller for each agent is adaptive based on the number of elements in its avoidance group, the minimum distance it has and its desired moving distance. The proposed adaptive mapping scheme calculates the repetition rate of optimal mappings in screening group of mapping decisions. The new optimal mapping is constructed by the fixed repeating elements in former mappings and the reorganized elements which are not the same in each optimal mappings based on the screening group. An event-triggered probability-driven control scheme is also investigated for a group of elliptical agents to achieve a predefined formation. The agents are assumed to have the same dynamics, and the control law for each agent is only updated at its event sequence based on its own minimum collision time and deviation time. The collision time of each agent is obtained based on the position and velocity of the others, and the deviation time is linked with the distance between its current position and desired position. The probabilitydriven controller is designed to prevent the stuck problem among agents. The stuck problem for the group means that when the distance between vi agents is too close and their moving directions are crossed, the control input with deterministic direction will cause the agents not to move or to move slowly. To optimize the event-triggered probability-driven controller, a mappingadaptive strategy and an angle-adaptive scheme are also developed. The mapping-adaptive strategy is used to find the optimal mapping to decrease the sum of the moving distance for the whole group, while the angle-adaptive scheme is employed to let the distance between any two elliptical agents is large enough to further ensure there is no collision existed during execution. Reconfiguration strategy is considered for multiple predefined formations. A two-stage reconfiguration strategy is proposed for a group of agents to find its special formation, which can be seen as transition of the predefined formations, during idle time in order to minimize the reconfiguration time. The basic reconfiguration strategy combines with a random mapping algorithm to find optimal special formation. To meet the practical requirements, agents are modeled as circles or ellipses. The anti-overlapping strategies are built to construct the achievable special formation based on the geometric properties of circle and ellipse.Thesis (Ph.D.) -- University of Adelaide, School of Electrical & Electronic Engineering, 202