Optimal Ground-to-Air Interception with Time-Varying Acceleration Bounds

Abstract: This paper proposes novel optimal-control-based guidance laws for ground-to-air missiles with time-varying acceleration bounds. In such engagements, as the missile climbs in altitude, its acceleration bound decreases, which may lead to acceleration saturation and significant miss distances if not explicitly accounted for. The proposed guidance laws incorporate hard acceleration command constraints directly into a linear-quadratic optimal-control framework, in contrast to conventional unbounded or softly constrained approaches. Analytically based guidance laws are developed for linear zero-order and first-order strictly proper missile dynamics with arbitrary-order linear target dynamics. Unlike the constant hard-bound case with minimum-phase missile dynamics, time-varying acceleration command bounds permit an initial unsaturated interval in which the proposed guidance laws can anticipate future saturation and reshape the acceleration profile accordingly. This enables earlier maneuvers when the missile possesses greater low-altitude maneuverability, fundamentally altering the structure of the optimal solution. The proposed approach is evaluated in nonlinear simulations and compared with equivalent unbounded and softly constrained optimal guidance laws. The results demonstrate substantially improved interception performance under saturation, reduced tuning requirements compared to softly constrained guidance laws, and enhanced capability in challenging engagement scenarios.