Integral Quadratic Constraints and Safety Certificates for Uncertainty Characterization and Control Safety-Aware Filtering of Proximity Operations Between Satellites

Abstract

Techniques in robust optimization and formal verification methods are used (1) to examine the stability and robust performance of a satellite controller that considers six-dimensional, uncertain state, and often unmodeled dynamics during rendezvous and proximity operations, and (2) to explore the synthesis of control Lyapunov/barrier functions (CLFs/CBFs) using neural networks and stochastic gradient descent to provide safety-aware filtering for the fuel-optimal control policies. A linear quadratic regulator controller for a servicer satellite (Servicer) is analyzed via the dissipativity inequality principle and quadratic constraints. This method allows the capture of unmodeled dynamics to reduce system uncertainty of proximity operations among the Servicer, client satellite (Client), and unsafe regions (e.g., obstacle). The same controller is implemented with a finite time horizon (i.e., model predictive controller) to filter out unsafe control output during an autonomous inspection of a Client. This framework mitigates the collision risk based on integral quadratic constraints (IQCs) worst bounds recommendation, miss distance, Mahalanobis distance, and Probability of Collision (Pc) metrics. Innovative deterministic reachability methods based on integral quadratic constraints and neural Lyapunov functions are compared and connected. The novel contributions of this work focus on formulating mathematical safety guarantees, modeling controller output, and reducing uncertainty on system performance when designing fuel-optimal and safe maneuvers of Servicer around the Client while avoiding unsafe regions in LEO.