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

Chapter 1 / Introduction
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simpler optimal guidance solutions in the 80s. It is the Linear Quadratic
Regulator (LQR) problem, and its solution via the Ricatti equation, that
forms the link with the “open-loop” trajectory optimisation. The LQR is a
Bolza Two-Point-Boundary-Value-Problem (TPBVP) constrained to linear
systems and a quadratic Performance Index (PI), thereby limiting its
potential.
Basic and augmented forms of PN are provided, highlighting their
sensitivity to parasitic errors and the relationship between the kinematic
gain and time-to-go estimates. Similarly, CLOS feed-forward and stability
acceleration demands are derived incorporating weave tuning by Vorley [V.3] ,
and compensation for straight flying targets introduced by Lee [L.4] . These
conventional guidance laws provide an insight into the closed form
optimisation and the cost functions used in their derivation, information that
can be exploited in open-loop formulations. They are used for missile
model proving since their underlying principles are relatively simple
compared with open-loop equivalents, and to create a performance baseline
to compared with on-line trajectory optimisation; the province of §9.
1.3.5 Chapter 7 : Trajectory Optimisation
Increasing coverage, rear hemisphere engagements, higher impact speeds
and controlled approach angles avoiding jamming regions to improve kill
probability against agile targets requires sophisticated trajectory
optimisation. Such optimisation irrefutably improves performance
dependent on the PI used compared with conventional missile guidance in
respect of,
• Increased impact speed for given range
• Increased coverage for a given impact speed
• Increased warhead lethality by approaching the target at an optimal aspect
• Reduce impact time for close-range high speed engagements
• Compensate for model mismatches and abnormal missile performance
• Increased resistance to target electronic counter-measures
• Avoidance of exclusion zones
• Maintenance of up-link communications
• Maintain sensor tracking-lock within pointing and beam-width limitations
• Promote a smooth transition of from mid-coarse to terminal guidance
• Improve state observability
Off-line optimisation often involves approximations over a range of
engagement scenarios that are detrimental to those few cases actually
encountered. Indeed LQR solutions, if they exist, tend to over-control with
emphasis on the terminal conditions, Archer [A.1] . Posing closed loop
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