LP-Generated Control Lyapunov Functions With Application to Multicopter Control

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.