The paper describes a multistage influence diagram game for modeling the maneuvering decisions of pilots in one-on-one air combat. It graphically describes the elements of the decision process, contains a model for the dynamics of the aircraft, and takes into account the pilots' preferences under conditions of uncertainty. The pilots' game optimal control sequences with respect to their preference models are obtained by solving the influence diagram game with a moving horizon control approach. In this approach, the time horizon of the original game is truncated, and a feedback Nash equilibrium of the dynamic game lasting only a limited planning horizon is determined and implemented at each decision stage. To demonstrate the influence diagram game and its aspects, examples with a realistic three-dimensional point mass aircraft model are computed and analyzed. The presented game model offers a novel way to analyze optimal air combat maneuvering and to develop an automated decision making system for selecting combat maneuvers in air combat simulators.

This paper introduces a receding horizon control scheme for obtaining near-optimal controls in a feedback form for an aircraft trying to avoid a closing air-to-air missile. The vehicles are modeled as point masses. Rotation kinematics of the aircraft are taken into account by limiting the pitch and roll rates as well as the angular accelerations of the angle of attack and the bank angle. The missile uses proportional navigation and it has a boostsustain propulsion system. In the proposed scheme, the optimal controls of the aircraft over a short planning horizon are solved online by the direct shooting method at each decision instant. Thereafter, the state of the system is updated by using only the first controls in the sequence, and the process is repeated. The performance measure defining the objective of the aircraft can be chosen freely. In this paper, six performance measures consisting of the capture time, closing velocity, miss distance, gimbal angle, tracking rate, and control effort of the missile are considered. The quality of the receding horizon solutions computed by the scheme is validated by comparing them to the off-line computed optimal open-loop solutions.

This paper formulates a support time game arising in one-on-one air combat with medium range air-to-air missiles. The game model provides game optimal support times of the missiles that can receive target information from the launching aircraft for selectable support times. The payoffs of the game are formulated as a weighted sum of the probabilities of hit to the adversary and own survival. Under suitable simplifying assumptions, a Nash equilibrium of the game can be computed by an iterative search involving a series of optimal control problems. For practical situations, an approximate real time computation scheme is introduced. The constructed model and the scheme are illustrated by numerical examples.

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A new approach towards the automated solution of realistic near-optimal aircraft trajectories is introduced and implemented in a software named Ace. In the approach, the optimal open-loop trajectory for a three degreeof-freedom aircraft model is first solved by using direct multiple shooting. Then, the obtained trajectory is inverse simulated with a more sophisticated five degree-of-freedom performance model by using an integration inverse method based on Newton's iteration. The trajectories are evaluated visually and by analyzing errors between the trajectories. If the errors remain within a suitable application-specific tolerance, the inverse simulated trajectory can be considered a realistic near-optimal trajectory that could be flown by a real aircraft. Otherwise, the parameters affecting the optimization and inverse simulation are altered and the computations are repeated. The example implementation of the approach, the Ace software, contains a graphical user interface that provides a user-oriented way for analyzing aircraft minimum time and missile avoidance problems. In the software, the computation of the optimal and inverse simulated trajectories is fully automated. The approach is demonstrated with numerical examples by using Ace.