A Quadratic Programming Approach to Flight Envelope Protection Using Control Barrier Functions

TL;DR

The paper addresses flight envelope protection by replacing traditional reference clipping with a quadratic-programming safety filter grounded in Control Barrier Functions (CBFs), guaranteeing forward invariance of a safe envelope for aerospace systems. It leverages High-Order Control Barrier Functions (HOCBFs) to handle the second-order (and higher) dynamics of angle-of-attack, integrating the safety filter as a real-time constraint on the commanded input via a QP that minimizes deviation from a performance-oriented command. The approach is demonstrated on a nonlinear missile pitch dynamics model, deriving upper and lower angle-of-attack bounds from stall and structural constraints, and employing a CLF backup to enhance robustness against disturbances and parametric uncertainties. Numerical results show the CBF-based FEP maintains safety with less conservatism than classical RC/MBCF schemes and remains compatible with existing control architectures, with future work targeting actuator dynamics and experimental validation.$

Abstract

Ensuring the safe operation of aerospace systems within their prescribed flight envelope is a fundamental requirement for modern flight control systems. Flight envelope protection prevents violations of aerodynamic, structural, and performance constraints, mitigating risks such as stall, excessive loads, and loss of control. Conventional FEP approaches, such as reference clipping via saturation functions and model-based command filtering, impose constraints at the reference input level but often fail to account for closed-loop system dynamics, potentially leading to constraint violations during transients. This paper introduces a new approach to the flight envelope protection problem by employing a quadratic programming-based safety filter using control barrier functions to dynamically enforce flight envelope constraints while preserving control performance. Unlike traditional reference filtering methods, the control barrier function-based safety filter actively ensures strict forward invariance of the safe flight envelope set, integrating seamlessly with existing control architectures. The proposed framework is implemented in a nonlinear missile flight control system and evaluated in a simulated environment. The results demonstrate its ability to prevent constraint violations while minimizing conservatism, offering a robust alternative to existing flight envelope protection methodologies.

Figures (12)

• Figure 1: Illustration of two trajectories within $\chi$ but not within the safe set $S$ in dash-dotted red and one trajectory within the safe set $S$ in dashed black, together with its barrier function $h(x(t))$ in solid blue.
• Figure 2: Sketch of external forces and moments acting on an axially symmetric missile.
• Figure 3: Example of a V-n diagram illustrating the relationship between load factors and airspeed, with limits defined by stall and structural loads.
• Figure 4: Block diagram of the integrated control architecture with a FEP safety filter.
• Figure 5: Cascaded inversion-based controller for longitudinal missile dynamics.

Theorems & Definitions (13)

• Definition 1
• Remark 1
• Definition 2
• Definition 3
• Definition 4
• Theorem 1
• Definition 5
• Definition 6
• Definition 7
• Definition 8