Approximate Dynamic Programming Applied to Parallel Hybrid Powertrains

The extra degree of freedom offered in hybrid electric vehicles have inspired manyresearchers to formulate and solve optimal control problems of various kinds. This paper presentsan Approximate Dynamic Programming scheme that efficiently solves the optimal power splitbetween 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. Thescheme combines two ideas to reduce the computational time of the iterations performed inthe dynamic programming. First, the value function is approximated using piecewise linearfunctions on a sparse grid. Secondly, by using model approximation the iterations performed inthe dynamic programming are reduced to solving scalar quadratic problems. In the simulationsthe approximation scheme is able to find a good approximation of the optimal control trajectory