Advanced Guidance Algorithms

Classic PNG and APNG were initially based on intu­ition. Modern or advanced guidance algorithms exploit op­timal control theory, i. e. optimizing a performance mea­sure subject to dynamic constraints. Even simple opti­mal control formulations of a missile-target engagement (e. g., quadratic acceleration measures) lead to a nonlinear two-point boundary value problem requiring creative so­lution techniques, e. g., approximate solutions to the asso­ciated Hamilton-Jacobi-Bellman equation—a formidable nonlinear partial differential equation (23). Such a formu­lation remains somewhat intractable given today’s comput­ing power, even for command guidance implementations that can exploit powerful remotely situated computers. As a result, researchers have sought alternative approaches to design advanced (near-optimal) guidance laws. In Ref­erence 20, the authors present a PNG-like control law that optimizes square-integral acceleration subject to zero miss distance in the presence of a one pole guidance-control – seeker system.

Even for advanced guidance algorithms (e. g., optimal guidance methods), the effects of guidance and control sys­tem parasitics must be carefully evaluated to ensure nom­inal performance and robustness (20). Advanced (optimal)

In contrast with PNG, this expression shows that the re­sulting APNG acceleration requirements decrease with time rather than increase. From the expression, it fol­lows that increasing N increases the initial acceleration requirement but also reduces the time required for the acceleration requirements to decrease to negligible lev­els. For N — 4, the maximum acceleration requirement

for APNG, acAPNGmax — — Nat, is equal to that for PNG,

-]at. For large N — 5, APNG requires a

acA png(,) — 2 N

N2

N

it can be shown (under the simplifying assumptions given earlier) that

Variants of PNG

Within Reference 20, the authors compare PNG, APNG, and optimal guidance (OG). The zero miss distance (sta­bility) properties of PPNG are discussed within Reference 24. A nonlinear PPNG formulation for maneuvering tar­gets is provided in Reference 27. Closed form expressions for PPNG are presented in Reference 28. A more complex version of PNG that is “quasi-optimal” for large maneu­vers (but requires tgo estimates) is discussed in Reference 29. Two-dimensional miss distance analysis is conducted in Reference 21 for a guidance law that combines PNG and pursuit guidance. Within Reference 30, the authors extend PNG by using an outer LOS rate loop to control the ter­minal geometry of the engagement (e. g., approach angle). Generalized PNG, in which acceleration commands are is­sued normal to the LOS with a bias angle, is addressed in Reference 31. Three-dimensional (3D) generalized PNG is addressed within Reference 32 using a spherical coor­dinate system fixed to the missile to better accommodate the spherical nature of seeker measurements. Analytical solutions are presented without linearization. Generalized guidance schemes are presented in Reference 33, which re­sult in missile acceleration commands rotating the missile perpendicular to a chosen (generalized) direction. When this direction is appropriately selected, standard laws re­sult. Time-energy performance criteria are also examined. Capturability issues for variants of PNG are addressed in Reference 34 and the references therein. Within Reference 35, the authors present a 2-D framework that shows that many developed guidance laws are special cases of a gen­eral law. The 3-D case, using polar coordinates, is consid­ered in Reference 36.

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