Finite Horizon Robustness with Applications to Missile Engagements

Abstract

This dissertation advances theoretical and computational tools for robustness analysis and synthesis on a finite time horizon. A motivation for this work is the reliable assessment of missile interceptor system performance, which will also enable the robust design of such systems. Typical performance metrics are infinite-horizon in nature, centered on stability, and rely on frequency-domain concepts, such as gain/phase margins. Such metrics can be inadequate for systems operating on finite-time horizons, as in many launch scenarios. Instead, this thesis focuses on time-domain metrics, e.g., bounds on the system's state at the final time of the horizon, while considering the impact of disturbances, model uncertainty/variability, and initial conditions. The proposed approach is to numerically linearize the dynamics along the trajectory to obtain a Linear Time-Varying (LTV) system. The analysis or synthesis is then performed on a linearized system that captures the dynamics up to the first-order perturbations around the nominal trajectory. This sacrifices some accuracy over the original nonlinear model but enables the use of linear system tools. The proposed worst-case LTV analysis also provides specific bad disturbances and uncertain parameters that can be further studied in high-fidelity nonlinear simulation.