Bounding Transient Instability in Sensor Data Injected Nonlinear Stochastic Flight Dynamics

2026-04-22

AI Summary

This study addresses the challenge of transient instability induced by finite-time disturbances in nonlinear stochastic flight dynamics, where conventional asymptotic or mean-square stability criteria fail to ensure short-term safety. The work presents the first extension of logarithmic norms to nonlinear Itô stochastic systems, establishing a finite-time transient stability analysis framework based on matrix measures of Lipschitz nonlinear mappings. By leveraging Itô calculus, it derives explicit bounds on the growth of state mean and variance, elucidating the fundamental distinction between expected-value stability and sample-path stability. Furthermore, it introduces a trade-off mechanism between estimation consistency and transient robustness under data injection. Experiments on lunar lander–like telemetry data demonstrate that trajectories with identical mean behavior can exhibit markedly different transient responses, with mission failure strongly correlated to cumulative transient instability during critical short intervals, thereby offering a novel finite-time probabilistic stability metric for autonomous systems.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation
• Multiagent Systems: Multiagent Systems under Uncertainty

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

Transient instability in nonlinear stochastic dynamical systems is a fundamental limitation in safety-critical aerospace applications, particularly during powered descent and landing where failure is driven by finite-time excursions rather than asymptotic divergence. Classical notions of mean-square or asymptotic stability are therefore insufficient for certification and design. This paper develops a logarithmic-norm-based framework for finite-time transient stability analysis of nonlinear Ito stochastic differential equations. The approach extends matrix measures to nonlinear mappings in a Lipschitz sense, enabling efficient characterization of instantaneous perturbation growth without local linearization. Using Ito calculus, bounds on the mean and variance of transient growth are derived, providing conditions for non-positive finite-time mean growth and probabilistic bounds on instability events. The analysis highlights a key distinction between mean and sample-path behavior, showing that stability in expectation does not guarantee pathwise finite-time safety, and that almost-sure transient stability cannot generally be ensured under stochastic diffusion. The framework is extended to data-constrained stochastic dynamics in navigation and estimation, revealing a trade-off between estimation consistency and transient robustness due to continuous data injection. Demonstrations with flight-like lunar lander telemetry show that similar mean trajectories can exhibit significantly different transient stability behaviour, and that mission failure correlates with accumulation of transient instability over short critical intervals. These results motivate probabilistic finite-time stability metrics for safety-critical autonomous systems.

Problem

• transient instability
• nonlinear stochastic dynamics
• finite-time stability
• sensor data injection
• flight dynamics

Innovation

• logarithmic norm
• finite-time stability
• nonlinear stochastic dynamics
• Ito calculus
• transient instability