Guidance Law Based on Differential Games for High Order Input Constrained Missile and Target

Abstract

The problem of derivation of guidance laws based on the differential games formalism for high order and acceleration constrained missile and target is formulated. The objective used is the minimaximization of the square of the miss and of the energy expenditure of the players. Explicit formula of the guidance law based on differential game formulation for unconstrained arbitrary order minimum or non-minimum phase is derived. For constrained players with this approach numerous cases emerge. For constrained players only implicit formulas of the GL are derivable. Each case has different structure of the implicit formulas. The cases that are treated-classified are created for different player’s transfer functions, i.e. missile or target autopilot transfer functions are minimum or non-minimum phase, respectively. Relatively tractable case is when the missile and the target are both minimum phase (or belong to a wider class of autopilot transfer functions with monotonous ramp response). For the case of constrained missile and target, implicit formula of the guidance law are derived and numerically solved. For minimum phase players one would guess, from results of one sided optimization, that the GL for constrained players would be obtained by limiting the acceleration commands derived as if there were not acceleration limits. It is shown that although this may be considered a practical-pragmatic solution it is strictly suboptimal.