projection-based consensus for linear dynamic system with state

By going through the study of consensus with linear dynamics from [57, 58], the consensus algorithm has been analyzed in different approaches for the linear dynamic system, which is widely apparent in the world for the current control systems, for example, the control in power system, the control protocol in factory manufacture process and etc,. Since the limitations also exist on the states in these systems, the constraint consensus applied on linear dynamic system is worthy to analyze.

A multi-agent system in a un-directed graph with N agents, for each agent i,

i∈(1,2, ..., N), the system dynamic is denoted by

˙ xi =Axi+Bui, (5.4) yi =Cxi (5.5) zi = 1 |Ni| X j∈Ni aij(xj −xi) (5.6)

where,xi ∈ Rm is multi-dimensional state of agent i, ui is the designed cooperative

control input, the yi is the system output, which can be considered as the state

measurement. zi is the the coupling measurement of the ith agent in system for

i = 1,2, ..., N. Matrices A,B,C are constant and in proper dimensions. Xi is the

constraint set for statexi of agent i. To keep xi inside its constraint set, we also use

the projection-based consensus algorithm to smoothly maneuver the state change. The P

j∈Ni(xj(t)− xi(t)) is the reference in a close loop system for the consensus

to be achieved, the input ui equals the difference between the reference and the

current state. Therefore, the control inputui =zi−xi = _|N1

i| P

j∈Niaij(xj−2xi), the

projection-based consensus protocol ˆui = (P rojxi)(xi(t), ui(t)) will be the focus on

the future work

Beside the theoretical analysis for projection-based consensus with state constraint in linear dynamic system, we will also validate the algorithm in a simulator. we will

take UAVs as the agents in linear dynamics; and apply the algorithm in simulator to complete a simultaneous arrival task with existence of velocity constraints. The MATLAB simulation tool is considered to be used as the simulator. The UAVs will be designed in close-loop systems and controlled by PID controllers. The destinations relates to the number of UAVs, will be carefully considered for all vehicles. Theses destinations can either be hovering points or landing locations. To make sure each path between its starting point and its destination is individual and non-repeated to its correlated UAV, we mark the starting points and ending points in pairs. The paths between all pairs of points will be simply considered as segments. To avoid the possible collision when flying on the paths, the segments should have no-intersections which means the height of the path will be carefully calculated.

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