An efficient method for solution of the linear hybrid optimal control problem

Considering some resent results on the extension of the necessary conditions for optimality of a solution of a hybrid dynamical system, the case of linear hybrid systems is investigated in this work. A numerically efficient method is proposed for solving the linear hybrid optimal control problem with a finite horizon quadratic cost functional. The proposed method requires less computational effort compared to other applicable numerical algorithms. Efficiency of this method is shown via a case study in which a hopping robot is required to reach a given height in a given number of hops.