  In this contribution, we introduce an efficient method for solving the
optimal control problem for an unconstrained nonlinear switched system with an
arbitrary cost function. We assume that the sequence of the switching modes are
given but the switching time in between consecutive modes remains to be
optimized. The proposed method uses a two-stage approach as introduced by Xu
and Antsaklis (2004) where the original optimal control problem is transcribed
into an equivalent problem parametrized by the switching times and the optimal
control policy is obtained based on the solution of a two-point boundary value
differential equation. The main contribution of this paper is to use a
Sequential Linear Quadratic approach to synthesize the optimal controller
instead of solving a boundary value problem. The proposed method is numerically
more efficient and scales very well to the high dimensional problems. In order
to evaluate its performance, we use two numerical examples as benchmarks to
compare against the baseline algorithm. In the third numerical example, we
apply the proposed algorithm to the Center of Mass control problem in a
quadruped robot locomotion task.
