| In recent years,with the development and progress of society,the traditional single-machine model can no longer meet the needs of complex production practices.Scholars have begun to study high-efficiency,low-cost,and scalable cluster systems,and the research on cluster-related technologies has become a cutting-edge research direction.In this paper,based on the virtual ellipsoid proposed by Kurzhanski,the control problem of unmanned cluster with disturbance and moving targets is investigated from two aspects: theoretical basis and numerical algorithm.In order to realize the stable motion of unmanned cluster,the disturbance environment needs to be considered,and for the disturbance factors,two types of unmanned swarm control problems with bounded disturbances and random disturbances are investigated in this paper.Based on ellipsoidal calculus,the reachable sets of unmanned cluster under different disturbance conditions are studied,and the closed-loop reachable sets of unmanned cluster with bounded disturbances are obtained.Based on the theoretical foundation of virtual ellipsoid,the mathematical model of unmanned cluster control problem is given,the value function is solved by the Hamilton-Jacobi-Bellman equation,and the optimal control of the ellipsoid is obtained by an effective numerical method.On this basis,the disturbance term is added to the dynamic equation,the control problem of unmanned cluster with random disturbance is studied,and the ellipsoid motion trajectory is obtained and the results are analyzed.In order to realize the efficient movement of the unmanned cluster,the moving target needs to be taken into account.Aiming at the moving target,an unmanned cluster target control model is established in this paper.An appropriate objective function is defined,a value function in the form of a quadratic function is constructed,and the optimal control is obtained by solving the value function by using the Hamilton-Jacobi-Bellman equation.The simulation results of an example show that the cluster studied in this paper can follow the target and finally reach the target,which verifies the rationality of the proposed modeling and control method.This paper hopes that through the study of these types of problems,to a certain extent,it can provide ideas for dealing with unmanned cluster movements in wind fields,signal fields,and unmanned swarm search and rescue in complex areas. |
