Approximate Dynamic Programming Applied to Parallel Hybrid Powertrains

The extra degree of freedom offered in hybrid electric vehicles have inspired many researchers to formulate and solve optimal control problems of various kinds. This paper presents an Approximate Dynamic Programming scheme that efficiently solves the optimal power split between the internal combustion engine and the electric machine in parallel hybrid powertrains. Gear switches and switches between hybrid and pure electric mode are formally treated. The scheme combines two ideas to reduce the computational time of the iterations performed in the dynamic programming. First, the value function is approximated using piecewise linear functions on a sparse grid. Secondly, by using model approximation the iterations performed in the dynamic programming are reduced to solving scalar quadratic problems. In the simulations the approximation scheme is able to find a good approximation of the optimal control trajectory.