Kai Virtanen

Modeling Air Combat by a Moving Horizon Influence Diagram Game

Thepaperdescribesamultistageinfluencediagramgameformodelingthemaneuveringdecisionsofpilotsinoneon-one air combat. The game 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, exampleswithapointmassaircraftmodelarecomputedandanalyzed.Thegamemodelpresentedinthepaperoffers a new way to analyze optimal air combat maneuvering and to develop an automated decision making system for selecting combat maneuvers in air combat simulators.

Modeling Pilot's Sequential Maneuvering Decisions by a Multistage Influence Diagram

The paper presents an approach toward the off-line computation of preference optimal flight paths against given air combat maneuvers. The approach consists of a multistage influence diagram modeling the pilot’s sequential maneuvering decisions and a solution procedure that utilizes nonlinear programming. The influence diagram graphically describes the elements of the decision process, contains a point-mass model for the dynamics of an aircraft, and takes into account the decision maker’s preferences under conditions of uncertainty. Optimal trajectories with respect to the given preference model are obtained by converting the multistage influence diagram into a discrete-time dynamic optimization problem that is solved with nonlinear programming. The initial estimate for the decision variables of the problem is generated by solving a set of myopic single stage influence diagrams that anticipate the future state of the aircraft only a short planning horizon ahead. The presented solution procedure is illustrated by a numerical example.

Near-Optimal Missile Avoidance Trajectories via Receding Horizon Control

The 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 utilizes proportional navigation and it has a boost-sustain propulsion system. In the proposed scheme, the optimal controls of the aircraft over a short planning horizon are solved on-line 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.

Improving Maintenance Decision Making in the Finnish Air Force Through Simulation

We used discrete-event simulation to model the maintenance of fighter aircraft and improve maintenance-related decision making within the Finnish Air Force. We implemented the simulation model as a stand-alone tool that maintenance designers could use independently. The model has helped the designers to study the impact of maintenance resources, policies, and operating conditions on aircraft availability. It has also enabled the Finnish Air Force to advance the operational capability of its aircraft fleet. We designed the model to simulate both normal and conflict operating conditions. The main challenge of the project was the scarcity and confidentiality of data about the fighter aircraft, their maintenance, and various operational scenarios, especially during conflict situations.

Decision Theoretical Approach to Pilot Simulation

We simulate and analyze pilot decision making in one-on-one air combat by using an ine uence diagram. Unlike most of the existing approaches, an ine uence diagram graphically describes the factors of a decision process and explicitly handles the decision maker’ s preferences under conditions of uncertainty. In the pilot decision model, the possible combat situations related to each maneuver alternative are associated with a probability and a utility. Ine uence diagram analysis produces a probability distribution of the overall utility that represents the successfulness of a maneuver and gives information to make rational maneuvering decisions. Sensitivity analysis determines the impacts of different factors on the outcome of the maneuvering decision. The effects of sensor information that will reduce the uncertainty of the model are evaluated with Bayesian reasoning. The model can be utilized in the analysis of a single decision situation or as an automated decision-making system that selects combat maneuvers in air combat simulators.

Automated Generation of Realistic Near-Optimal Aircraft Trajectories

A new approach toward the automated solution of realistic near-optimal aircraft trajectories is introduced and implemented in a software package named Ace. In the approach, the optimal open-loop trajectory for a three-degree-of-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 Newtons 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 to be 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 to analyze 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.

Simulation Metamodeling with Dynamic Bayesian Networks

This paper presents a novel approach to simulation metamodeling using dynamic Bayesian networks (DBNs) in the context of discrete event simulation. A DBN is a probabilistic model that represents the joint distribution of a sequence of random variables and enables the efficient calculation of their marginal and conditional distributions. In this paper, the construction of a DBN based on simulation data and its utilization in simulation analyses are presented. The DBN metamodel allows the study of the time evolution of simulation by tracking the probability distribution of the simulation state over the duration of the simulation. This feature is unprecedented among existing simulation metamodels. The DBN metamodel also enables effective what-if analysis which reveals the conditional evolution of the simulation. In such an analysis, the simulation state at a given time is fixed and the probability distributions representing the state at other time instants are updated. Simulation parameters can be included in the DBN metamodel as external random variables. Then, the DBN offers a way to study the effects of parameter values and their uncertainty on the evolution of the simulation. The accuracy of the analyses allowed by DBNs is studied by constructing appropriate confidence intervals. These analyses could be conducted based on raw simulation data but the use of DBNs reduces the duration of repetitive analyses and is expedited by available Bayesian network software. The construction and analysis capabilities of DBN metamodels are illustrated with two example simulation studies.

Game-Theoretic Validation and Analysis of Air Combat Simulation Models

This paper presents a new game-theoretic approach toward the validation of discrete-event air combat (AC) simulation models and simulation-based optimization. In this approach, statistical techniques are applied for estimating games based on data produced by a simulation model. The estimation procedure is presented in cases involving games with both discrete and continuous decision variables. The validity of the simulation model is assessed by comparing the properties of the estimated games to actual practices in AC. These games are also applied for simulation-based optimization in a two-sided setting in which the action of the opponent is taken into account. In optimization, the estimated games enable the study of effectiveness of AC tactics as well as aircraft, weapons, and avionics configurations. The game-theoretic approach enhances existing methods for the validation of discrete-event simulation models and techniques for simulation-based optimization by incorporating the inherent game setting of AC into the analysis. It also provides a novel game-theoretic perspective to simulation metamodeling which is used to facilitate simulation analysis. The utilization of the game-theoretic approach is illustrated by analyzing simulation data obtained with an existing AC simulation model.

Game Optimal Support Time of a Medium Range Air-to-Air Missile

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 aweighted sumof 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.

Analyzing air combat simulation results with dynamic Bayesian networks

In this paper, air combat simulation data is reconstructed into a dynamic Bayesian network. It gives a compact probabilistic model that describes the progress of air combat and allows efficient computing for study of different courses of the combat. This capability is used in what-if type analysis that investigates the effect of different air combat situations on the air combat evolution and outcome. The utilization of the dynamic Bayesian network is illustrated by analyzing simulation results produced with a discrete event air combat simulation model called X-Brawler.