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

Chapter 1 / Introduction
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guidance problems with explicit solutions becomes ever more difficult as
the complexity of the constraints imposed increases, solutions existing only
for the most basic cases. As a result problems are often over-simplified:
reduced missile dynamics, no measurement noise, etc., hence their solutions
are of limited value.
Recently Shooting and Simulated Annealing techniques have emerged to
deal TPBVP involving more sophisticated PI however, their implementation
is by necessity simple and therefore restrictive. Such guidance laws are
often tuned for a limited number of scenarios and require state observer data
to select the appropriate parameter maps for the prevailing conditions, maps
requiring large storage capacities.
An alternative strategy is proposed in §7, in which gradient projection
methods are used to solve the TPBVP on-line. These techniques, discarded
for off-line optimisation in favour of more advanced methods, converge
surprisingly rapidly from a reasonable initial trajectory to a near optimal
solution, and remain robust, Moody [M.12] . An optimal control set is
maintained subject to PI change reflecting current conditions and priorities
using range dependant weighting functions. For example, weights
favouring pre-launch state observability and approach angle that change
gradually after launch to miss distance and energy consumption mitigating
the dominance of the terminal constraints reported by Speyer [S.9] .
Yang [Y.9] observed that guidance laws in literature avoid real-time solutions
in a varied threat environment. Moreover, in attempting to optimise timeto-go
and impact speed, he stated that on-line solutions were impractical due
to numerical instability. The stability of the boundary conditions provided
by the state observation is crucial for convergence. Not only must the
optimiser be relatively insensitive to noisy boundary conditions it must also
be robust for a wide range of target engagements, from constant velocity
crossing targets to weaving targets and extreme avoidance manoeuvres.
§7 starts by describing the gradual use of optimised controls in the missile
autopilot whilst the remainder are re-optimised commensurate with the
processing time available. The missile model dynamic constraints are
defined, and the generation of lateral acceleration demands from the
controls established. The TPBVP is formulated using incidence controls,
dynamic initial conditions, variable impact time, and a PI requiring
inequality constraints and penalty functions. Pontryagin theory is used to
reduce the problem to a univariate optimisation of the Hamiltonian created
by adjoining dynamic constraints to the cost function. Techniques for
selecting the best search direction and step-length are reviewed that includes
Wolfe’s step-length conditions.
The chapter ends with a description of the trajectory optimisation
“simulator”. This alternative guidance law is embedded inside the missile
simulator together with the conventional alternatives provided. The concept
of using the simulation host processor clock to limit the amount of re-
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