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This study investigates the cooperative time-varying formation guidance (CTFG) problem for leader-following missiles to intercept a maneuvering target with switching communication topologies. Multiple missiles are classified into a leader missile and multiple follower missiles. The leader missile intercepts the maneuvering target under the modified proportional navigation guidance law. The follower missiles are expected to form a predefined time-varying formation and track the trajectory of the leader missile. Multiple missiles intercept the maneuvering target simultaneously and then form a many-to-one engagement. A four-step approach to determine the parameters in the CTFG law is given. The convergence of the approach is discussed. A numerical example for multiple missiles intercepting a maneuvering target subjected to switching communication topologies is presented.

Distributed group cooperative guidance (DGCG) problems for multiple missiles with fixed and switching directed communication topologies are dealt with. In contrast to traditional cooperative guidance utilized to intercept one single target, the group cooperative guidance is applicable to multiple targets. In the group cooperative attack, multi-missile system is classified into multiple subgroups, and each subgroup attacks its respective target. Missiles in the same subgroup are required to reach the target simultaneously, while different subgroups may cooperate successively in terms of the impact time. To realize the group cooperative attack, a two-step guidance strategy is developed. The first step adopts a DGCG law based on local neighboring information for multiple missiles to realize group consensus on range-to-go and leading angle. The second step begins when the group consensus of missiles is achieved. During this step, each missile attacks the target under the proportional navigation guidance law. Derived from feedback linearization and convergence analysis, sufficient conditions for multiple missiles to realize the group cooperative attack with fixed and switching directed communication topologies are proposed, respectively. Finally, numerical examples with two subgroups are given to show the effectiveness of the two-step guidance strategy.

This study investigates cooperative guidance problems for multiple missiles with fixed and switching directed communication topologies. A two-step guidance strategy is proposed to realize the simultaneous attack. In the first step, a distributed cooperative guidance law is designed using local neighboring information for multiple missiles to achieve consensus on range-to-go and leading angle. The second step begins when the consensus of multiple missiles is realized. During the second step, multiple missiles disconnect from each other and hit the target using the proportional navigation guidance law. First, based on the local neighboring communications, a sufficient condition for multiple missiles to realize simultaneous attack with a fixed communication topology is presented, where the topology is only required to have a directed spanning tree. Then, the results are extended to the case of switching communication topologies. Finally, numerical simulations are provided to validate the theoretical results.

Time-varying group formation control problems for second-order multi-agent systems with directed topologies are investigated. Firstly, a time-varying group formation control protocol is constructed using local relative positions and velocities of each agent and its neighbors. Then based on graph theory, nonsingular transformations are applied to the closed-loop multi-agent systems. Sufficient conditions for second-order multi-agent systems to achieve time-varying group formation are further presented together with the time-varying group formation feasibility constraints. Explicit expressions of the subgroup formation reference functions are derived to describe the macroscopic movement of the time-varying subgroup formations. Moreover, by solving an algebraic Riccati equation, an approach to design the time-varying group formation protocol is proposed. Finally, a numerical example with three subgroups is provided to demonstrate the effectiveness of the obtained results. In contrast to the traditional complete formation, where only one formation is realized by the multi-agent system, in the group formation discussed in the current paper, agents are classified into subgroups and each subgroup is required to form a specified time-varying sub-formation via inter-subgroup and intra-subgroup interactions.

Time-varying formation pursuit based cooperative (TFPBC) guidance for multiple missiles to intercept a maneuvering target is investigated. In TFPBC guidance, multiple missiles are not only expected to intercept the target simultaneously but also need to form a desired time-varying formation configuration during the engagement. The motivation for TFPBC guidance is to create a favorable relative geometry for multiple missiles, which may enclose a maneuvering target and then improve the hit performance. Multiple missiles are classified into leader missile and follower missiles. TFPBC guidance law for the leader missile and follower missiles is constructed, respectively. An approach with four steps to determine the parameters in the TFPBC guidance law is given. The convergence of the designed TFPBC guidance law is proved. A numerical example for multiple missiles to intercept a maneuvering target is provided.

Distributed group cooperative guidance (DGCG) problems for multiple missiles with switching directed communication topologies are dealt with. In contrast to traditional cooperative guidance utilized to intercept one single target, the group cooperative guidance is applicable to multiple targets. In the group cooperative attack, multi-missile system are classified into multiple subgroups, and each subgroup attacks its respective target. Missiles in the same subgroup are required to reach the target simultaneously, while different subgroups may cooperate successively in terms of the impact time. To realize the group cooperative attack, a two-step guidance strategy is developed. The first step adopts a DGCG law based on local neighboring information for multiple missiles to realize group consensus on range-to-go and leading angle. The second step begins when the group consensus of missiles is achieved. During this step, each missile attacks the target under the proportional navigation (PN) guidance law. Derived from a feedback linearization approach and convergence analysis, sufficient conditions for multiple missiles to realize the group cooperative attack with switching directed communication topologies are proposed, respectively. Finally, numerical examples are given to show the effectiveness of the two-step guidance strategy.

Group cooperative guidance problems for multiple missiles with directed interaction topologies are dealt with, where the multiple missiles are classified into subgroups and each subgroup is required to reach its respective target simultaneously. In contrast to the traditional multi-missile salvo attack, where only one single target is intercepted by the multiple missiles, in the group cooperative attack, there could be more than one target. Firstly, a two-step guidance strategy is constructed to achieve group cooperative attack. In the first step, a distributed cooperative guidance law is adopted for multiple missiles to reach group consensus asymptotically. During the second step, the multiple missiles reach the target independently with proportional navigation guidance law. Then by feedback linearization, the group cooperative guidance problem is transformed into the group consensus problem for second-order system. Considering the realistic situation of neighbor-to-neighbor communication and unidirectional information exchange, a distributed cooperative guidance law is derived. Sufficient condition for multiple missile to realize group cooperative attack is further proposed. It is shown that the guidance law derived can be used to realize the group cooperative attack autonomously and is relatively easier in application. Finally, a numerical example with two missile groups is given to verify the effectiveness of the obtained results.

Time-varying group formation control problems for general linear multi-agent systems with directed topologies are studied, where the agents in the multi-agent system are classified into subgroups and each subgroup is required to form a specified time-varying sub-formation. Different from the traditional complete formation, where only one formation is realized by the multi-agent system, in the group formation, there could be multiple sub-formations. Firstly, a time-varying group formation protocol is constructed by local relative information of each agent and its neighbors. Then nonsingular transformations are applied to the closed-loop multi-agent systems. Sufficient conditions for the multi-agent systems to achieve time-varying group formation are further presented together with the time-varying group formation feasibility constraints. Explicit expressions of the subgroup formation reference functions are derived to describe the macroscopic movement of the time-varying subgroup formations. It is shown that the subgroup formation reference functions are jointly determined by the dynamics, the initial states and formation information of each agent in the same subgroup, and also by the interaction topologies among agents from the same or different subgroups. Moreover, an approach to design the time-varying group formation protocol is proposed by solving an algebraic Riccati equation. Finally, a numerical example with three subgroups is provided to demonstrate the effectiveness of the obtained theoretical results.

Time-varying group formation control problems for second-order multi-agent systems with directed topologies are investigated, where the agents in the multi-agent system are classified into subgroups and each subgroup is required to form a specified time-varying sub-formation. In contrast to the traditional complete formation, where only one formation is realized by the multi-agent system, in the group formation, there could be multiple sub-formations. Firstly, a time-varying group formation protocol is constructed using local relative positions and velocities of each agent and its neighbors. Then based on graph theory, nonsingular transformations are applied to the closed-loop multi-agent systems. Sufficient conditions for second-order multi-agent systems to achieve time-varying group formation are further presented together with the time-varying group formation feasibility constraints. Explicit expressions of the subgroup formation reference functions are derived to describe the macroscopic movement of the time-varying subgroup formations. Moreover, by solving an algebraic Riccati equation, an approach to design the time-varying group formation protocol is proposed. Finally, a numerical example with three subgroups is provided to demonstrate the effectiveness of the obtained results.

Summary Time-varying group formation control problems for general linear multi-agent systems with directed topologies are studied. Different from the traditional complete formation, where only one formation is realized by the multi-agent system, in the group formation, there could be multiple time-varying sub-formations. Firstly, a time-varying group formation protocol is constructed by local neighboring relative information. Then nonsingular transformations are applied to the closed-loop multi-agent systems. Sufficient conditions for the multi-agent systems to achieve time-varying group formation are further presented together with the time-varying group formation feasibility constraints. Explicit expressions of the subgroup formation reference functions are derived to describe the macroscopic movement of the time-varying subgroup formations. Moreover, an approach to design the time-varying group formation protocol is proposed by solving an algebraic Riccati equation. Finally, a numerical example with three subgroups is provided to demonstrate the effectiveness of the obtained theoretical results. Copyright © 2016 John Wiley & Sons, Ltd.

Aiming at intercepting a hypersonic weapon in a hypersonic pursuit-evasion game, this paper presents a fractional calculus guidance algorithm based on a nonlinear proportional and differential guidance law. First, under the premise of without increasing the complexity degree of the guidance system against a hypersonic manoeuvering target, the principle that the differential signal of the line-of-sight rate is more sensitive to the target manoeuver than the line-of-sight rate is employed as the guidelines to design the guidance law. A nonlinear proportional and differential guidance law (NPDG) is designed by using the differential derivative of the line-of-sight rate from a nonlinear tracking differentiator. By using the differential definition of fractional calculus, on the basis of the NPDG, a fractional calculus guidance law (FCG) is proposed. According to relative motions between the interceptor and target, the guidance system stability condition with the FCG is given and quantitative values are also proposed for the parameters of the FCG. Under different target manoeuver conditions and noisy conditions, the interception accuracy and robustness of these two guidance laws are analysed. Numerical experimental results demonstrate that the proposed guidance algorithms effectively reduce the miss distance against target manoeuvers. Compared with the NPDG, a stronger robustness of the FCG is shown under noisy condition.

After generating reference trajectory in the process of reentry guidance for reusable launch vehicle, if the designed bank angle curve is too close to the constraint boundary, there is a great possibility for the obtained reference trajectory to exceed the reentry corridor boundary. This paper proposed a margin searching method, to reduce the likelihood of generating a reference trajectory which exceeds the reentry corridor boundary and to improve the design success rate.