Second order transition-time optimization for switched dynamical systems

This paper presents a method for calculating the first and second derivatives of the cost function with respect to switching times for nonlinear autonomous systems. We focus on the fixed switching-mode sequences and emphasize the importance of the second-order method because it exhibits faster convergence rate compares with the first-order switching time optimization. The second-order derivatives can be derived directly by differentiating the first-order derivative again. Numerical example illustrates the efficacy of the proposed method.