摘要
多无人机(Unmanned Aerial Vehicle, UAV)协同作战是未来战场上UAV的主要作战样式和发展趋势。随着网络技术的发展成熟与广泛应用,网络环境下的多UAV协同作战将极大地提高了作战效能,但也给多机控制和决策技术带来了重大挑战,需要考虑网络时延、网络拓扑变化和不确定性扰动等通信条件带来的影响。受限网络条件下的多机协同作战是研究多UAV协同控制和决策技术的直接推动力,同时也是提升UAV系统自主能力的重要体现。论文在网络约束条件下的多智能体一致性理论方面作了一些探索性工作,并以此为基础讨论了多UAV协同对地打击过程中的任务区集结和目标观测两个问题,主要工作及创新点如下：
(1)在网络时延和时变拓扑约束下,提出并理论证明了多智能体实现平均一致性的时延相关收敛判据。应用状态分解和空间变换思想,将平均一致性的收敛性等价为相应子系统的稳定性问题。进而,采用构造公共Lyapunov-Krasovskii泛函的方式来分析稳定性问题。为确保收敛判据具有较小的保守性(即偏离理论值的程度,保守性越低,越接近理论值),在Lyapunov-Krasovskii泛函导数负定性的判定过程中引入了自由权矩阵。进一步,获得关于线性矩阵不等式(Linear Matrix Inequalities, LMI)可行解的存在性判据。在此基础上,假定一致性控制协议的系数项满足多项式Hurwitzs稳定,可得到具有l阶链式积分器型多智能体平均一致性的收敛判据。新判据能够克服频域方法在构造公共或多个Lyapunov泛函所表现出的难度,易借助数学软件包获得多智能体实现平均一致性所允许的最大网络时延上界。数值实例和仿真结果验证了判据的有效性,且在保守性方面较已有文献结果有较大改善。
(2)在网络时延、扰动和时变拓扑结构不确定性等复杂约束下,提出并理论证明了多智能体实现鲁棒一致性的时延相关收敛判据。应用状态分解和空间变换思想,将鲁棒一致性的收敛性等价为相应子系统的鲁棒稳定性问题,即零扰动稳定性和非零扰动稳定性。进而,采用构造公共Lyapunov-Krasovskii泛函的方式来分析鲁棒稳定性问题,利用自由权矩阵方法获得关于非线性矩阵不等式(Nonlinear Matrix Inequalities, NLMI)可行解的存在性判据；在此基础之上,借鉴求解锥补问题的思想,对NLMI判据作非线性最小化处理,提出了LMI迭代求解算法,进而可获得多智能体实现鲁棒一致性所允许的最大网络时延上界。进一步,所得结论扩展至离散多智能体鲁棒一致性问题。新判据揭示了网络时延、时延变化率、鲁棒一致性控制协议系数以及给定H∞性能之间的相互关系。这为复杂网络约束条件下,满足给定H∞性能的鲁棒一致性控制协议设计提供了理论依据。数值实例和仿真结果验证了判据的有效性,且保守性优于已有文献结果。
(3)应用时延相关平均一致性理论,提出了面向网络化多UAV系统任务区集结问题的分布式协同控制方法。建立了集结问题的数学模型,提出了基于协调变量和协调函数的分布式求解框架。在减少冗余信息传递的同时,最大限度地降低了受限网络条件对集结任务的影响。从任务特征出发,改进了多智能体时延相关平均一致性算法：针对“自私型”多UAV系统,提出了满足个体代价最小的非合作优化一致性(Non-cooperative Optimal Consensus, NCOC)算法。利用Hamilton-Jacobi-Bellman方程及其边界条件,从理论上给出了NCOC控制协议的表达形式；在此基础上,针对“合作型”多UAV系统,提出了满足整体代价最小的合作博弈优化一致性(Cooperative Game based Optimal Consensus, CGOC)算法。根据合作博弈理论和灵敏度参数方法,从理论上给出了CGOC的控制协议的表达形式。进一步,提出了求解集结问题的两种分布式协同控制方法,即NCOC方法和CGOC方法。新方法更强调平台的轨迹控制,弱化了UAV对路径规划算法的要求。不仅能够降低集结问题的求解难度,且使多UAV系统具有较强的动态响应能力。仿真结果表明两种分布式协同控制方法均可用于求解网络化多UAV系统任务区集结问题,CGOC方法在最优性和动态响应性方面要优于NCOC方法。
(4)应用时延相关鲁棒一致性理论,提出了面向网络化多UAV系统协同目标观测问题的分布式状态估计方法。考虑到多UAV系统的松散通信结构和网络约束条件的复杂性,设计了“双时间窗”递推迭代机制,即预测／更新时间窗和一致性融合时间窗。进而,基于离散时间域下的鲁棒一致性算法,提出了分布式无色信息滤波(Robust Consensus based Distributed Unscented Information Filter, RC_DUIF)方法。从理论上分析了一致性融合算法收敛性对估计精度的影响,揭示了RC_DUIF方法的协方差大于集中式无色信息滤波方法的根本原因。RC_DUIF方法适用于网络时延、扰动和时变拓扑结构不确定性等复杂网络条件下的协同目标观测,算法计算复杂度和通信复杂度低,可实现性强。蒙特卡洛仿真实验表明,FRC_DUIF方法对复杂网络条件具有较强的鲁棒性,在平均估计误差、平均一致性误差以及平均协方差矩阵迹等方面表现出色,能够满足复杂网络条件下多UAV系统对非线性目标模型状态实时估算的要求。
Cooperative operation for multiple unmanned aerial vehicles(UAVs) is the main en-gagement manner and the trend of development in the future. With the rapid development and wide employment of the network technology, cooperative manner in networks may improve the operational efficiency greatly. There are also some significant challenges for distributed control and decision problems, such as the influence of the constraints condi-tions, i.e., network delays, time-varying network topologies and uncertain disturbances. It is not only the original impetus to cooperative control and decision of multi-UAV, but also it is an important manifestation of enhancing the autonomy of the UAV. This paper investigates some exploratory work on the multi-agent system consensus theory under the network constraints, and as a means to discuss the rendezvous in mission area and cooper-ative target observation during multi-UAV cooperative engagement. The main work and contributions are as follows:
(1) Under the constraint conditions including network delays and time-varying net-work topologies, the delay dependent convergence criteria are given and proved to achieve average consensus for multi-agent systems. By the idea of state decomposition and space transformation, the convergence property of average consensus is equivalent to the stabil-ity of the corresponding subsystem. Then, the common Lyapunov-Krasovskii functional is employed to analyze the stability. In order to get the criteria with lower conservativeness (that means the degree of deviation from the theoretical value, the lower the conservative-ness, the more close to the theoretical value), Free-weighting Matrices are used to verify the negative definite of the Lyapunov-Krasovskii functional. Further, the criteria are ob-tained through solving the corresponding feasible linear matrix inequality(LMI). Lastly, the convergence criteria for multi-agent systems with/th-order chain integrator dynamics are presented with the assumption that the coefficient parameters in the consensus protocol satisfying the Hurwitzs stable. The proposed criteria can overcome the difficulty of con-structing public or multiple Lyapunov functional by frequency-domain method, and the max tolerant upper bounds on network delays can be obtained conveniently using math-ematical package. Numerical examples and simulation results show the effectiveness of the proposed criteria, and the conservativeness is lower than the existing results.
(2) Under the constraint conditions including network delays, disturbances and time-varying network topologies, the delay dependent convergence criteria are given and proved to achieve robust consensus for multi-agent systems. By using the idea of state decompo-sition and space transformation, the condition for guaranteeing robust consensus is equiv-alent to the robust stability of the corresponding subsystem, i.e., stability with zero dis-turbance and nonzero disturbance. Then, the common Lyapunov-Krasovskii functional is built to analyze the robust stability, and the Free-weighting Matrices method is used to get the criteria which can be obtained through solving the corresponding feasible nonlin-ear matrix inequality(NLMI). Nonlinear minimization is employed to deal with the NLMI criteria like solving cone complementarity problem. Then, the iterative LMI algorithm is obtained, and the max tolerant upper bounds on network delays can be obtained. Further, the conclusions are expanded to the robust consensus for multi-agent systems with discrete dynamics. Convergence criteria reveal the relationship between the network delays, de-lay differential rate, control protocol for robust consensus and the index H∞performance. It is the theoretical basis to design the control protocol for robust consensus meeting the given H∞robust performance under complex network constraints. Numerical examples and simulation results show the effectiveness of the proposed criteria, and the conserva-tiveness is lower than the existing results.
(3) By delay dependent average consensus theory, distributed cooperative control methods are proposed to solve the rendezvous problem in mission area for multi-UAV system in network. The mathematical description of rendezvous problem is established, and the framework to be solved in distributed manner is provided based on the method of coordination variables and coordination function. It can be used to decrease the trans-mission of the redundant information, and reduce the influence of the limited network conditions on rendezvous task to some degree. Considering the characteristics of the task, delay dependent average consensus for multi-agent system is improved as follows: The non-cooperative optimal consensus(NCOC) algorithm, which can minimize the cost func-tion of each platform, is presented for the "selfish" UAVs. The expression of NCOC con-trol protocol is given theoretically by Hamilton-Jacobi-Bellman equation and its boundary condition; On the other hand, the cooperative game based optimal consensus(CGOC) al-gorithm, minimize the cost function of the whole multi-UAV system, is presented for the "cooperative" UAVs. The expression of CGOC control protocol is given theoretically by cooperative game and sensitivity parameter method. Moreover, two distributed coopera-tive control methods for rendezvous problem are proposed, i.e., NCOC method and CGOC method. The proposed methods emphasis on the trajectory control of the platform, thus weaken the requirements of the path planning algorithm for UAV. It can reduce the diffi-culty of solving rendezvous problem, and strengthen the dynamic response capabilities of the multi-UAV system. Simulation results show that the proposed two distributed cooper-ative control methods are valid for solving the rendezvous problem for multi-UAV system in network, and the CGOC method is better than NCOC method in terms of optimal and dynamic response.
(4) By delay dependent robust consensus, distributed state estimation method is pre-sented to solve the cooperative target observation for multi-UAV system in network. Con-sidering the loose communication structure of multi-UAV system and the complexity of the networks constraints, the iteration mechanism with double time-window is designed including local prediction/update window and consensus fusion window. The distributed unscented information filter (RC_DUIF) method is given base on the robust consensus un-der discrete time domain. The influence of the convergence property of consensus to the estimation precision is theoretically analyzed. That reveals the fundamental reason for the covariance error of RC_DUIF method is greater than the centralized information filtering method. RC_DUIF method is valid for cooperative target observation under the complex network constraints including network delay, disturbances and time-varying topologies uncertainty. It has the characteristics of lower computational complexity and communi-cation complexity. So it can be implemented easily. Lastly, the Monte Carlo simulation experiments indicate that RC_DUIF algorithm is robust to complex network constraints, and has the outstanding performance on average estimation error, average consistency er-ror and average trace of the covariance matrix, which can meet the requirement of the real time estimate of non-linear target for multi-UAV system under complex network.
引文
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