Second-order switching time and magnitude optimization for impulsive hybrid systems

This paper presents a method to perform second-order impulsive hybrid system optimization that optimizes a cost functional over mode transition times and impulse magnitudes simultaneously. The derivation of the first-order and second-order derivatives of the cost functional with respect to switching times and impulse magnitudes is presented. An adjoint formulation is utilized to compute the derivatives for a faster convergence at a lower computational cost. An example in robotics illustrates the effectiveness of this optimization technique when measurement noise is present.