Recently, distributed coordination control of the unmanned aerial vehicle (UAV) swarms has been a particularly active topic in intelligent system field. In this paper, through understanding the emergent mechanism of the complex system, further research on the flocking and the dynamic characteristic of UAV swarms will be given. Firstly, this paper analyzes the current researches and existent problems of UAV swarms. Afterwards, by the theory of stochastic process and supplemented variables, a differential-integral model is established, converting the system model into Volterra integral equation. The existence and uniqueness of the solution of the system are discussed. Then the flocking control law is given based on artificial potential with system consensus. At last, we analyze the stability of the proposed flocking control algorithm based on the Lyapunov approach and prove that the system in a limited time can converge to the consensus direction of the velocity. Simulation results are provided to verify the conclusion.

UAV is an advanced system with high autonomy for intelligent combat [

In this paper, we consider models for flocking swarms. Firstly, a mathematical model of cooperative system is established by using Markov stochastic process and calculus analysis. Then, the control law for UAV swarm is established based on artificial potential field. At last, we analyze the stability of the proposed flocking control algorithm based on the Lyapunov approach and prove the conclusion that the system in a limited time can converge to the consensus direction of the velocity. Simulation results are provided to verify the conclusion.

Let

In order to obtain Markov random process, the new state of process is derived by supplement of variable [

The probability of state transition after

Differentiate the expression for state transition probability to derive its limit. Then the mathematical model can be described using integral-differential equations as follows:

The reliability of coordination system has uniqueness and nonnegative solution on

According to the initial conditions we can get the analytic solution of the partial differential equation [

Set

So we can get the following equation:

then, the solution of the system can be converted into vectors format as follows:

Any component of

The behavior evolution of the UAV swarm system is a limited Markov decision process. Suppose that the probability distribution of the system state is

And the time derivative of the

In this section, first we design a distributed flocking control law. Assuming that each UAV senses its own position and velocity and is able to obtain its neighbors’ position and velocity, the UAV swarms form flocking behaviour model structure control law as follows:

Consider the following positive semidefinite function:

Consider the UAV swarms consisting of

Consider

By making the variable replacement

Finally, select Lyapunov function

Time derivative can be obtained:

According to the UAV’s physical characteristics, this paper will discretize the time with high frequency. Thus, a UAV

The movement of the individual is not only controlled by itself but also affected by the state of other individuals. Therefore, the individual direction of movement at a certain time is not only relative to its direction one moment before, but also relative to the directions of its surrounding individuals’ movements. The influence of all the individuals to the individual

Then, the speed direction of the UAV

We consider the swarms of 100 UAVs with six degrees of freedom. The weights of the cost function are set to

Velocities with respect to time.

Trajectories with respect to time.

From Figure

Figure

Figures

Angle of the Pitch with respect to time.

Angle of the Roll with respect to time.

Angle of the Attack with respect to time.

Figure

Angle of the Sideslip with respect to time.

This paper analyzed current researches and existent problems of UAV swarms. Afterwards, by the theory of stochastic process and supplemented variables, a differential-integral model was established. The existence and uniqueness of the solution of the system were discussed. The flocking control law is given based on artificial potential with system consensus. At last, we analyzed the stability of the proposed flocking control algorithm based on the Lyapunov approach and proved the conclusion that the system in 28 s can converge to the consensus direction of the velocity. And we performed simulation tests to verify the conclusion.

This paper is supported by The National Defense Pre-Research Foundation of China (Grant no. B222011XXXX).