Aircraft Stability and Safety: Practical Applications of Control Lyapunov and Barrier Functions

Ensuring stability and safety is an indispensable priority in the aerospace industry, even though the persistent loss of control remains a major cause of fatal accidents. Hence, the necessity of flight envelope protection algorithms arises to prevent an aircraft from deviating from a safe and reliable flight regime. Within this context, the designs of control Lyapunov functions and control barrier functions are discussed to address the stability and safety issues of an aircraft. The stability of the aircraft during agile and abrupt maneuvers is guaranteed through the use of a control Lyapunov function, while safety is maintained by the flight envelope protection algorithm designed with control barrier functions specific to the angular rates, angle of attack, and load factor. The mathematical derivations of the control Lyapunov function and control barrier functions are presented. The efficacy of the proposed structure is demonstrated through simulations under various circumstances using a 6-degree-of-freedom nonlinear flight dynamics model, and consequently, the promising features of the control Lyapunov function and control barrier function in mitigating the loss of control are discussed.