LP-Generated Control Lyapunov Functions With Application to Multicopter Control

• Published in: IEEE transactions on control systems technology Vol. 32; no. 6; pp. 2090 - 2101
• Main Authors: Do, Huu-Thinh, Blanchini, Franco, Miani, Stefano, Prodan, Ionela
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-11-2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE); Institute of Electrical and Electronics Engineers
• Subjects: Aerospace electronics; Automatic; Basis functions; Computer Science; Constrained control; Engineering Sciences; homogeneous polynomials; Liapunov functions; Linear programming; Linear systems; Lyapunov function; Lyapunov methods; Mathematics; open-loop trajectories; Optimization and Control; Polynomials; Rotary wing aircraft; Systems and Control; Trajectory; Vectors; Constrained control Lyapunov function open loop trajectories linear programming homogeneous polynomials; open loop trajectories; linear programming; Constrained control; homogeneous polynomials; Lyapunov function
• ISSN: 1063-6536; 1558-0865
• DOI: 10.1109/TCST.2024.3396704

In this work, we study a technique of exploiting open-loop-generated trajectories for a constrained control problem, using them to shape suitable nonquadratic control Lyapunov functions (CLFs). These trajectories, generated offline, allow detecting a suitable domain of attraction (DOA) in which a candidate Lyapunov function has a negative derivative. Given suitably constructed basis functions, our working machinery is based on linear programming; hence, the technique can be applied to problems of nontrivial size in terms of the number of basis functions and points in the state space. For linear systems, we seek convex Lyapunov functions, which are homogeneous polynomials. Simulation and experimental results for drone control are given.