Thesis - Leigh Moody.pdf - Bad Request - Cranfield University

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Chapter 7 / Missile Trajectory Optimisation
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Chapter 7
TRAJECTORY OPTIMISATION
The impetus in missile guidance is to find globally optimum solutions to
guidance problems involving complex cost functions using off-line methods
such as simulated annealing, or shooting techniques. Although their
implementation is relatively simple they require large flight data tables
tuned for a nominal missile. Using these tables the guidance commands
(trajectory) are updated at regular intervals taking account of the current
state estimates. It is difficult to introduce new in-flight constraints into this
process without revising the flight tables.
The aforementioned optimisation techniques are unsuitable for on-line
optimisation and a return to simpler constrained optimisation techniques is
proposed. The work builds on that of Vorley [V.4] – on gradients in function
space, and Moody [M.12] – their use for on-line optimisation. §7 starts by
describing the process of continually re-optimising a fixed number of
controls for the fire solutions, the launch criteria, and in-flight use of
controls by the autopilot.
An optimiser state space is selected, the time evolution of the missile and
target dynamics defined, together with their variation with respect to the
state space and controls. The cost function is built-up of commonly used
elements, each activated by a switch that can also acts as a constant scaling
normalising their effect on gradient computations.
The TPBVP is defined and reduced to the lesser problem of minimisation of
an Hamiltonian function. The missile controls are related to the optimiser
state space as required by Pontryagin theory. Discrete formulation of these
continuous optimisation equations for a fixed number of controls is based on
Euler integration for real-time operation. Search directions and univariate
search techniques to reduce the cost without having to bracket the nearest
minima are reviewed.
Gradient techniques have proven to be surprisingly robust given a good
initial track, here an augmented PN trajectory. The TPBVP solution must
also be robust to changes in the smoothed boundary conditions provided by
the state observer. The simulation monitors the processing time taken and
limits the optimisation process as the controls are required by the autopilot.
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