Air Combat Maneuvering Tactical Formation 1976 US  Navy Pilot Training Episode II
Channel: LT OneX
Date: 2018-11-25

MODERN air combat is carried out by air-to-air missiles and guns, and an aircraft may be
considered as a weapons platform whose purpose is to bring the armament into a suitable
launch condition (Shaw, 1985). Two main elements affecting the success in air combat are the
performance of air combat arsenal and tactics. From the mathematical point of view, the above
elements can be analyzed by the means of constructive simulation.
Considering air combat optimization problems and games, the emphasis has traditionally
been on the computation of optimal open-loop solutions associated with a specific set of initial
conditions (see, e.g., Betts, 1998). Such solutions provide an insight about characteristics of
optimal flight paths, but cannot however be applied, e.g., in the guidance of an aerial vehicle
because of unpredictable disturbances and inherent uncertainties that tend to deviate the vehicle
from its nominal flight path. The trend has been changing due to the ongoing increase in
computational resources, which enables the utilization of efficient numerical methods in the online
solution of near-optimal feedback controls associated with the current state and time (see,
e.g., Mayne et al., 2000). Contrary to open-loop solutions, feedback solutions can reckon with
ambiguity, which makes them suitable for the guidance purposes.
The thesis at hand introduces new modeling approaches and computational methods for
various aircraft trajectory optimization and one-on-one air combat scenarios. The main emphasis
is on the on-line solution of the constructed models in feedback form. The analyses are carried
out in three dimensions by mainly using point-mass models which generally can describe realistic
vehicles that consider both transitional and rotational motions. Consequently, the introduced
approaches provide the basis for the onboard guidance system of an aerial vehicle or a pilot
advisory system.
For missile avoidance problems between a guided missile and a fighter aircraft, the thesis
develops an on-line aircraft guidance scheme based on receding horizon control (RHC) (García
et al., 1989; Mayne et al., 2000). Compared to related approaches, the scheme can be utilized
with various performance measures exploiting different weaknesses of the missile system, and
the guidance law of the missile can be selected freely. Moreover, the target’s uncertainty about
the guidance law of the missile is taken into account by using a belief model based on Bayesian
reasoning (see, e.g., Ross, 2006). As a result, an adaptive controller for missile avoidance is
obtained.
The thesis also introduces a new approach and its software implementation for the useroriented
solution of realistic near-optimal aircraft trajectories. In the approach, the optimal openloop
trajectory is first solved off-line for a coarse aircraft model, after which the obtained trajectory
is inverse simulated (see, e.g., Hess et al., 1991) on-line with a more delicate aircraft model. The
resulting trajectory is realistic in a sense that it could be flown by a real aircraft, and near-optimal
in a sense that it follows closely the optimal open-loop trajectory computed with the coarse
model. With the current implementation, both aircraft minimum time and missile avoidance problems
can be solved. Contrary to existing trajectory optimization softwares, the implementation of
the approach provides a way to assess the realism of the obtained trajectories.
For one-on-one air combat, the thesis introduces an influence diagram (Howard and Matheson,
1984, 2005, see the latter reference for a reprint) game that models pilots’ maneuvering
decisions in a dogfight. A computational method based on RHC for the near-optimal solution of
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the game model is introduced as well. Overall, the work extends the seminal work carried out
by Virtanen et al. (1999b, 2003, 2004) by elaborating and implementing the earlier ideas in practice.
In addition, a game model providing game optimal support times of air-to-air missiles in a
missile duel is constructed. The support time refers to a period for which the aircraft relays target
information to the missile after the launch. A computational method for the on-line calculation
of approximate game optimal support times associated with a given set of launch conditions is
introduced as well.