Searching for control Lyapunov-Morse functions using genetic programming for global asymptotic stabilization of nonlinear systems

The purpose of this paper is searching for control Lyapunov-Morse functions (CLMF) using genetic programming (GP) for one-input-affine systems on general manifolds. The CLMF is an extended control Lyapunov function (CLF) to have multiple critical points. It is shown that a C ¹ global stabilizer is derived from a CLF for the system. As in the case of CLF, a discontinuous global asymptotic stabilizer is obtained from a CLMF. However, there is no method constructing CLMF systematically. Then, we propose a method of searching for CLMF via GP to design the global asymptotic stabilizer