Tuomas Raivio

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.

On applied nonlinear and bilevel programming for pursuit-evasion games

Motivated by the benefits of discretization in optimal control problems, we consider the possibility of discretizing pursuit-evasion games. Two approaches are introduced. In the first approach, the solution of the necessary conditions of the continuous-time game is decomposed into ordinary optimal control problems that can be solved using discretization and nonlinear programming techniques. In the second approach, the game is discretized and transformed into a bilevel programming problem, which is solved using a first-order feasible direction method. Although the starting points of the approaches are different, they lead in practice to the same solution algorithm. We demonstrate the usability of the discretization by solving some open-loop representations of feedback solutions for a complex pursuit-evasion game between a realistically modeled aircraft and a missile, with terminal time as the payoff. The solutions are compared with those obtained via an indirect method.

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.

Aircraft trajectory optimization using nonlinear programming

We describe two discretization methods, direct collocation and a scheme based on differential inclusion, that enable the solution of optimal control problems by nonlinear programming. We apply the methods in calculating optimal trajectories for a modern fighter aircraft. Unlike collocation, the differential inclusion scheme converges robustly even in the presence of singular controls.

Capture Set Computation of an Optimally Guided Missile

A game theoretical approach is presented for numerically computing the capture set of an optimally guided medium-rangeair-to-airmissileagainstagiventarget.Realisticpointmassmodelsareusedbecauselonge ighttimes prevent simplie cations such as coplanarity or constant speed target. The capture set is obtained by constructing saddle point trajectories on its boundary, or the barrier, numerically. Instead of solving a game of kind, the trajectories are identie ed by setting up an auxiliary game of degree. The necessary conditions of the auxiliary game are shown to coincide with those of the gameofkind. Thegameof degree issolved from systematically varied initial states with a decomposition method that does not require setting up or solving the necessary conditions. Examples are calculated for a generic e ghter and a missile.

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.

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.

Optimal maneuvering after engine failure

The controls and trajectories of a BAe Hawk after an engine failure are studied using optimization and simulation, with the aim of maximizing the gliding distance into a given direction. The optimization scheme is validated by simulations in a reference case, after which a parametric study concerning widely varying initial heading errors, airspeeds and altitudes is described. To conclude, the feasibility of optimal control in practice is discussed.