Cooperative Differential Games Strategies for Active Aircraft Protection from a Homing Missile
01 May 2011-Journal of Guidance Control and Dynamics (American Institute of Aeronautics and Astronautics (AIAA))-Vol. 34, Iss: 3, pp 761-773
TL;DR: In this paper, a linear quadratic differential game formulation for arbitrary-order linear players' dynamics in the continuous and discrete domains is derived for a team composed of two agents, where the target aircraft performs evasive maneuvers and launches a defending missile to intercept the homing missile.
Abstract: Cooperative pursuit―evasion strategies are derived for a team composed of two agents. The specific problem of interest is that of protecting a target aircraft from a homing missile. The target aircraft performs evasive maneuvers and launches a defending missile to intercept the homing missile. The problem is analyzed using a linear quadratic differential game formulation for arbitrary-order linear players' dynamics in the continuous and discrete domains. Perfect information is assumed. The analytic continuous and numeric discrete solutions are presented for zero-lag adversaries' dynamics. The solution of the game provides 1) the optimal cooperative evasion strategy for the target aircraft, 2) the optimal cooperative pursuit strategy for the defending missile, and 3) the optimal strategy of the homing missile for pursuing the target aircraft and for evading the defender missile. The obtained guidance laws are dependent on the zero-effort miss distances of two pursuer―evader pairs: homing missile with target aircraft and defender missile with homing missile. Conditions for the existence of a saddle-point solution are derived and the navigation gains are analyzed for various limiting cases. Nonlinear two-dimensional simulation results are used to validate the theoretical analysis. The advantages of cooperation are shown. Compared with a conventional one-on-one guidance law, cooperation significantly reduces the maneuverability requirements from the defending missile.
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TL;DR: It is shown how the target can lure in the attacker, allowing its defender to intercept the attacking missile even in scenarios in which the defender's maneuverability is at a disadvantage compared with the attacking ballistic missile.
Abstract: Optimal-control-based cooperative evasion and pursuit strategies are derived for an aircraft and its defending missile. The aircraft-defending missile team cooperates in actively protecting the aircraft from a homing missile. The cooperative strategies are derived assuming that the incoming homing missile is using a known linear guidance law. Linearized kinematics, arbitrary-order linear adversaries' dynamics, and perfect information are also assumed. Specific limiting cases are analyzed in which the attacking missile uses proportional navigation, augmented proportional navigation, or optimal guidance. The optimal one-on-one, noncooperative, aircraft evasion strategies from a missile using such guidance laws are also derived. For adversaries with first-order dynamics it is shown that depending on the initial conditions, and in contrast to the optimal one-on-one evasion strategy, the optimal cooperative target maneuver is either constant or arbitrary. These types of maneuvers are also the optimal ones for the defender missile. Simulation results confirm the usefulness and advantages of cooperation. Specifically, it is shown how the target can lure in the attacker, allowing its defender to intercept the attacking missile even in scenarios in which the defender's maneuverability is at a disadvantage compared with the attacking missile.
185 citations
Cites methods from "Cooperative Differential Games Stra..."
...In a recent paper [19] an analytical solution to the LQDG problem was obtained....
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TL;DR: In this paper, the authors defined the following components of an evasive maneuver component normal to the target-missile line of sight: amp, ad, am, target, defender, and missile lateral accelerations, respectively at max, ad max, am max, max, and am max = target, defenders, and missiles maximum lateral acceleration.
Abstract: = missile evasive maneuver normal to defendermissile line of sight amp = missile evasive maneuver component normal to target-missile line of sight at, ad, am = target, defender, and missile lateral accelerations, respectively at max, ad max, am max = target, defender, and missile maximum lateral accelerations, respectively atplos, adplos, amplos = target, defender, and missile accelerations normal to the line of sight, respectively Rd, Rm, Rdm = target-defender, target-missile, and defendermissile closing ranges, respectively tf = defender-missile interception time vt, vd, vm = target, defender, and missile speeds, respectively vtlos, vdlos, vmlos = target, defender, and missile speeds along the line of sight, respectively vtplos, vdplos, vmplos
127 citations
Cites methods from "Cooperative Differential Games Stra..."
...[11] obtained an analytical solution to the linearquadratic differential game and studied the conditions for the existence of a saddlepoint solution....
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TL;DR: The methods provided are used to determine dominance and solve the game, and a novel, multiplayer pursuit-evasion game is presented that features three players on two teams and can be used to model rescue scenarios and biological behaviors.
117 citations
TL;DR: In this article, optimal control-based cooperative guidance laws for intercepting a high-value target (such as a ballistic missile) by a team of cooperating interceptors arriving from different directions are presented.
Abstract: Optimal control-based cooperative guidance laws, which enforce at intercept a relative geometry in between a group of missiles and a single maneuvering target, are presented. An example scenario of interest is that of intercepting a high-value target (such as a ballistic missile) by a team of cooperating interceptors arriving from different directions. The problem is posed in the linear quadratic framework, and closed-form analytic solutions are obtained for any team size with any linear missile dynamics. The performance of the cooperative guidance laws is investigated using a nonlinear two-dimensional simulation of the missiles’ lateral dynamics and relative kinematics. It is shown that cooperatively imposing a relative intercept angle between the missiles provides substantially better results than when each missile independently enforces, using a one-on-one strategy, a preselected intercept angle that satisfies the relative intercept requirement. It is also shown that the missiles’ acceleration requirem...
110 citations
TL;DR: It is shown that the performance of the target and the defender is highly dependent on the cooperation scheme, as well as the notion of Pareto fronts.
Abstract: Aircraft protection from a missile employing a known linear guidance strategy is considered The aircraft protects itself by using a cooperating defensive missile Depending on the available cooperation scheme, three different cooperative linear quadratic guidance strategies are derived and investigated for arbitrary-order linear-adversaries dynamics: 1) two-way cooperation, where the target–defender team employs its optimal cooperative strategy, 2) one-way cooperation, realized by the defender employing a classical one-on-one guidance law while the target helps by luring in the missile, and 3) one-way cooperation, realized by the target employing an arbitrary evasive strategy while the defender attempts to reach the predicted interception point The performance of the three different cooperative strategies is compared and analyzed via simulation using the notion of Pareto fronts It is shown that the performance of the target and the defender is highly dependent on the cooperation scheme As expected, th
99 citations
References
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Book•
01 Jan 1990
TL;DR: In this paper, a three-loop Autopilot is used to provide tactical and strategic guidance for a single-antenna MIMO-BMG system using MATLAB units.
Abstract: Numerical Techniques Fundamentals of Tactical Missile Guidance Method of Adjoints and the Homing Loop Noise Analysis Convariance Analysis and the Homing Loop Proportional Navigation and Miss Distance Digital Fading Memory Noise Filters in the Homing Loop Advanced Guidance Laws Kalman Filters and the Homing Loop Other Forms of Tactical Guidance Tactical Zones Strategic Considerations Boosters Lambert Guidance Strategic Intercepts Miscellaneous Topics Ballistic Target Properties Extended Kalman Filtering and Ballistic Coefficient Estimation Ballistic Target Challenges Multiple Targets Weaving Targets Representing Missile Airframe with Transfer Functions Introduction to Flight Control Design Three-Loop Autopilot. Appendices: Tactical and Strategic Missile Guidance Software Converting Programmes to C Converting Programmes to MATLAB Units.
1,536 citations
TL;DR: In this article, conditions for capture and for optimality are derived for a class of optimal pursuit-evasion problems, and results are used to demonstrate that the well-known proportional navigation law is actually an optimal intercept strategy.
Abstract: In this paper it is shown that variational techniques can be applied to solve differential games. Conditions for capture and for optimality are derived for a class of optimal pursuit-evasion problems. Results are used to demonstrate that the well-known proportional navigation law is actually an optimal intercept strategy.
495 citations
TL;DR: In this article, a linear closed loop guidance law was proposed to compensate for the acceleration and time varying navigation gain in short-range intercept trajectories, which is applicable to short range air-to-ground and airto-air interception.
Abstract: Introduction "IVTISSILE dynamic time lags, guidance command satura1? JL tion, and target acceleration are major factors contributing to excessive terminal miss distances resulting from shortrange intercept trajectories. The objective of this Technical Note is to describe a linear closed loop guidance law which compensates for these factors. Optimal control theory is utilized where the missile dynamics, represented as a single time lag, and target acceleration are defined in the constraint equations. A quadratic performance index is employed which implicitly effects a "soft" limit on the acceleration command. A zero terminal miss distance is the only boundary constraint imposed on the problem. The final form of the guidance law which includes a time varying navigation gain represents an extension of the guidance laws discussed by Bryson, Garber, and Abzug and is applicable to short range air-to-ground and air-to-air interception.
217 citations