Global inverse optimal controller with guaranteed convergence rate for input-affine nonlinear systems

Dilated homogeneous systems are local canonical forms of nonlinear control systems. In this paper, we propose a global inverse optimal controller with guaranteed convergence rate by implementing the local homogeneity. First, we clearly describe assumptions, and then design a global inverse optimal controller achieving local homogeneity for input-affine local-homogeneous nonlinear systems by using local-homogeneous control Lyapunov functions. The proposed controller guarantees convergence rate thanks to the local homogeneity. Finally, we discuss what systems it is available for, and confirm the effectiveness of the proposed controller by computer simulation.