基于有限时间系统理论的多飞行器协同拦截问题研究
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摘要
随着空战环境日益复杂，作战武器性能日益提高，多飞行器协同作战已成为当今复杂空战中主要的作战方式。为了进一步扩大防御面积，提高防御能力，很多国家将多飞行器协同拦截作为一种新式的防御战术。现有的关于多飞行器协同拦截问题的研究大多存在顶层策略与底层方案脱节的问题。实际情况下，必须综合考虑各环节内的影响因素及各子任务之间的关联，才能满足复杂任务的需求。因此，有必要对该背景下关键问题进行归纳，充分考虑问题之间的耦合关系，采取行之有效的方法以提高任务的整体性能。本文以多飞行器协同拦截过程为研究对象，对其中的制导控制问题加以提炼并进行深入研究，主要研究内容包含以下几个方面。
首先，针对协同拦截问题是有限时间问题这一特点，对有限时间系统理论进行了研究。介绍了延拓Lp空间内系统性能的输入－输出信号度量及有限时间H∞控制方法；针对离散事件系统，给出了基于混合逻辑动态的有限时间二次型优化方法；另外，给出了多智能体网络的描述方法及一些重要性质，在此基础上，提出了输入约束下的有限时间一致性设计方法。
其次，针对多飞行器协同拦截过程中的协同探测问题，提出了基于混合逻辑动态优化的协同探测方法。结合末制导问题的特点，建立了目标－飞行器相对运动模型；引入目标兴趣值及目标年龄的概念，并在此基础上建立了考虑多飞行器信息交换的目标年龄修正模型；基于混合逻辑动态优化的思想，解决了协同探测中目标信息处理频率的优化问题；通过地面机器人实验对协同探测方法进行了验证。
再次，针对多飞行器协同拦截过程中的目标分配问题，提出了基于有限时间范数的目标分配方法。结合协同拦截中目标分配问题的特点，给出了目标分配的约束条件及目标分配准则；指出了中末交班误差及目标机动是导致飞行器能量消耗的主要因素，构造了反映能量需求的有限时间范数指标函数，并提出了基于有限时间范数的目标分配方法；给出了有限时间范数性能准则，在此基础上，给出了基于有限时间范数的目标分配问题求解方法。根据目标分配优化结果，多对多协同拦截中的协同制导问题被分解为一对一、一对多及多对一制导问题。
然后，针对多飞行器协同拦截过程中的协同制导律设计问题，提出了基于有限时间H∞控制理论的一对多制导方法及基于有限时间一致性的多对一制导方法。建立了一对多及多对一制导的数学模型。基于有限时间二次型最优控制，给出了一对多兼顾准则，并在此基础上，基于有限时间H∞控制理论设计了一对多制导律；此外，考虑飞行器控制输入受约束的情况下，基于有限时间一致性方法设计了多对一协同制导律，并分析了保证同时拦截的多飞行器网络连通条件。
最后，对多飞行器协同拦截高超声速目标的过程进行了制导控制设计。结合高超声速飞行器的运动特性，设定了多飞行器协同拦截的条件。在此基础上，针对协同拦截高超声速目标末制导过程中的协同探测、目标分配及协同制导问题进行了优化和制导律设计；仿真结果验证了本文提出协同拦截方法的有效性。
As the environment of air-combat is getting more and more complicated and theperformance of weapons is getting more and more improved, cooperative battle usingmultiple flight vehicles is becoming the main mode in the complex air-combat. In orderto expand defense area and improve defense power, lots of countries lay the defense tac-tics with cooperative interception using multiple flight vehicles. Most of existing worksignore the external relevance between top-level strategy and low-level design. In prac-tice, we have to synthesize relevance of all parts so that the requirement of cooperativebattle can be satisfied. Therefore, it’s necessary to sum up the subproblems under thisbackground and adopt efective methods to guarantee the integral performance of cooper-ative interception, considering the relevance among subproblems. Under the backgroundof cooperative interception, this dissertation mainly works on some guidance and controlproblems. The main contributions are summarized as follows.
First, aiming at the finite-time characteristic of cooperative interception, we studiedfinite-time system theory. An extended Lpspace and input-output signal measure of sys-tem performance are introduced. Finite-time H∞control is introduced. For discrete-eventsystem, finite-time quadratic optimizations are proposed based on mixed-logic dynamic.Besides, the description and characteristic of multi-agent network are introduced basedon which finite-time consensus is proposed under input constraints.
Second, aiming at cooperative detection in cooperative interception, a cooperative-detection approach is proposed based on mixed-logic dynamic optimization. Combiningthe characteristics of terminal guidance system, relative kinematics model is formulatedbetween the target and the flight vehicle. The definitions of level-of-interest and age areintroduced, on this basis, age-correction model is formulated considering the informationexchange among vehicles. Based on the idea of mixed-logic dynamic optimization, theoptimization problem on processing frequency of target information is solved. A robotexperiment is implemented for verifying the feasibility of the proposed method.
Thirdly, aiming at target assignment in cooperative interception, a finite-time-norm-based target-assignment approach is proposed. Combining the characteristics of targetassignment in cooperative interception, the constraints and assignment principle are pro-posed. We point out the main factors of energy cost are handover error and target maneu- ver, the index function is constructed in a finite-time norm pattern which represents theenergy cost of the flight vehicle. Based on the performance criterion of finite-time norm,the solving methods of the finite-time-norm-based target-assignment problem is proposed.According to the result of target assignment, cooperative guidance in the many-to-manyinterception is decomposed into one-to-one, one-to-many and many-to-one guidance sce-narios.
Fourthly, aiming at cooperative guidance-law design in cooperative interception, aone-to-many guidance law based on finite-time H∞control and a many-to-one guidancelaw based on finite-time consensus are proposed. The models for both one-to-many andmany-to-one guidance are formulated. The one-to-many principle is given based on finite-time quadratic optimal control, on this basis, a one-to-many guidance law is proposedbased on finite-time H∞control. Besides, considering the constraints of control input,a many-to-one guidance law is design based on finite-time consensus, furthermore theconnection condition of network is analyzed which guarantee the salvo.
At last, a control and guidance design for cooperative interception using multipleflight vehicles against a hypersonic target is carried out. Combining the motion charac-teristics of hypersonic target, the condition of cooperative interception is set up. On thisbasis, aiming at the problems of cooperative detection, target assignment and cooperativeguidance in the terminal guidance of cooperative interception, corresponding optimizationand guidance-law design are implemented. The efectiveness of the proposed methods isverified through the simulation result.
首先，针对协同拦截问题是有限时间问题这一特点，对有限时间系统理论进行了研究。介绍了延拓Lp空间内系统性能的输入－输出信号度量及有限时间H∞控制方法；针对离散事件系统，给出了基于混合逻辑动态的有限时间二次型优化方法；另外，给出了多智能体网络的描述方法及一些重要性质，在此基础上，提出了输入约束下的有限时间一致性设计方法。
其次，针对多飞行器协同拦截过程中的协同探测问题，提出了基于混合逻辑动态优化的协同探测方法。结合末制导问题的特点，建立了目标－飞行器相对运动模型；引入目标兴趣值及目标年龄的概念，并在此基础上建立了考虑多飞行器信息交换的目标年龄修正模型；基于混合逻辑动态优化的思想，解决了协同探测中目标信息处理频率的优化问题；通过地面机器人实验对协同探测方法进行了验证。
再次，针对多飞行器协同拦截过程中的目标分配问题，提出了基于有限时间范数的目标分配方法。结合协同拦截中目标分配问题的特点，给出了目标分配的约束条件及目标分配准则；指出了中末交班误差及目标机动是导致飞行器能量消耗的主要因素，构造了反映能量需求的有限时间范数指标函数，并提出了基于有限时间范数的目标分配方法；给出了有限时间范数性能准则，在此基础上，给出了基于有限时间范数的目标分配问题求解方法。根据目标分配优化结果，多对多协同拦截中的协同制导问题被分解为一对一、一对多及多对一制导问题。
然后，针对多飞行器协同拦截过程中的协同制导律设计问题，提出了基于有限时间H∞控制理论的一对多制导方法及基于有限时间一致性的多对一制导方法。建立了一对多及多对一制导的数学模型。基于有限时间二次型最优控制，给出了一对多兼顾准则，并在此基础上，基于有限时间H∞控制理论设计了一对多制导律；此外，考虑飞行器控制输入受约束的情况下，基于有限时间一致性方法设计了多对一协同制导律，并分析了保证同时拦截的多飞行器网络连通条件。
最后，对多飞行器协同拦截高超声速目标的过程进行了制导控制设计。结合高超声速飞行器的运动特性，设定了多飞行器协同拦截的条件。在此基础上，针对协同拦截高超声速目标末制导过程中的协同探测、目标分配及协同制导问题进行了优化和制导律设计；仿真结果验证了本文提出协同拦截方法的有效性。
As the environment of air-combat is getting more and more complicated and theperformance of weapons is getting more and more improved, cooperative battle usingmultiple flight vehicles is becoming the main mode in the complex air-combat. In orderto expand defense area and improve defense power, lots of countries lay the defense tac-tics with cooperative interception using multiple flight vehicles. Most of existing worksignore the external relevance between top-level strategy and low-level design. In prac-tice, we have to synthesize relevance of all parts so that the requirement of cooperativebattle can be satisfied. Therefore, it’s necessary to sum up the subproblems under thisbackground and adopt efective methods to guarantee the integral performance of cooper-ative interception, considering the relevance among subproblems. Under the backgroundof cooperative interception, this dissertation mainly works on some guidance and controlproblems. The main contributions are summarized as follows.
First, aiming at the finite-time characteristic of cooperative interception, we studiedfinite-time system theory. An extended Lpspace and input-output signal measure of sys-tem performance are introduced. Finite-time H∞control is introduced. For discrete-eventsystem, finite-time quadratic optimizations are proposed based on mixed-logic dynamic.Besides, the description and characteristic of multi-agent network are introduced basedon which finite-time consensus is proposed under input constraints.
Second, aiming at cooperative detection in cooperative interception, a cooperative-detection approach is proposed based on mixed-logic dynamic optimization. Combiningthe characteristics of terminal guidance system, relative kinematics model is formulatedbetween the target and the flight vehicle. The definitions of level-of-interest and age areintroduced, on this basis, age-correction model is formulated considering the informationexchange among vehicles. Based on the idea of mixed-logic dynamic optimization, theoptimization problem on processing frequency of target information is solved. A robotexperiment is implemented for verifying the feasibility of the proposed method.
Thirdly, aiming at target assignment in cooperative interception, a finite-time-norm-based target-assignment approach is proposed. Combining the characteristics of targetassignment in cooperative interception, the constraints and assignment principle are pro-posed. We point out the main factors of energy cost are handover error and target maneu- ver, the index function is constructed in a finite-time norm pattern which represents theenergy cost of the flight vehicle. Based on the performance criterion of finite-time norm,the solving methods of the finite-time-norm-based target-assignment problem is proposed.According to the result of target assignment, cooperative guidance in the many-to-manyinterception is decomposed into one-to-one, one-to-many and many-to-one guidance sce-narios.
Fourthly, aiming at cooperative guidance-law design in cooperative interception, aone-to-many guidance law based on finite-time H∞control and a many-to-one guidancelaw based on finite-time consensus are proposed. The models for both one-to-many andmany-to-one guidance are formulated. The one-to-many principle is given based on finite-time quadratic optimal control, on this basis, a one-to-many guidance law is proposedbased on finite-time H∞control. Besides, considering the constraints of control input,a many-to-one guidance law is design based on finite-time consensus, furthermore theconnection condition of network is analyzed which guarantee the salvo.
At last, a control and guidance design for cooperative interception using multipleflight vehicles against a hypersonic target is carried out. Combining the motion charac-teristics of hypersonic target, the condition of cooperative interception is set up. On thisbasis, aiming at the problems of cooperative detection, target assignment and cooperativeguidance in the terminal guidance of cooperative interception, corresponding optimizationand guidance-law design are implemented. The efectiveness of the proposed methods isverified through the simulation result.
引文
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