Convexification in energy optimization of a hybrid electric propulsion system for aerial vehicles

This paper concerns the energy management of a hybrid electric propulsion system for aerial vehicles, using convex optimization. The main contribution of this paper is the proposal of a new convexification, which simplifies the formation of the convexified problem, and the proof of equality between the original problem and the convexified problem. The primary energy management is formulated from first principles and using experimental data. The convexity of the original problem is clarified via investigating the approximation to the experimental data. Then, change of variables and equality relaxation are implemented to convexify the concave constraints. The introduced variable-battery internal energy, is proposed to convexify the battery model. The relaxation of a non-affine equality yields to new convex inequality constraints. Numerical examples and forward simulations were carried out to validate the convexified problem. The first test case verifies that the convex relaxation does not sacrifice the optimality of the solution nor does the variable change lose the original bounds. Also, the optimal control from convex optimization is demonstrated to be robust to a disturbance in power demand. Comparison with the benchmark optimization-dynamic programming, shows that convex optimization achieves a minimal objective value with less fluctuation of the optimal control value. Most significant is that the convexification reduces the optimization computation time to a level compatible with implementation in practical application.