Approaches to Optimizing Fuel Consumption in Cars

One of the most important problems which the automotive industry faces is that of reducing fuel consumption, in view of the increasing cost of energy and the need to save oil for more sophisticated uses, while keeping pollutants emissions as low as possible, in view of the resulting health and environmental problems. Reduction of fuel consumption can be obtained working on different features of the car, including type of engine, aerodynamical design, used materials and optimal operations of the engine. In this work we shall be concerned with the last approach, which can result in a 5-20% saving on fuel, depending on which parameters are optimized. Mathematically, the problem can be formulated as follows: let s(t) be the value of a vector of state parameters (typically speed and power) at time t; then one has to choose optimal values of control parameters u(t), typically spark advance angle, air-fuel ratio and possibly transmission ratio, in such a way that the total fuel consumption on a certain cycle (EPA or European cycle) be minimized subject to constraints, of legal type, on the total amount of certain emitted pollutants (typically co, NO_x HC) during the cycle and of course to drivebility constraints. The resulting problem is formally an optimal control problem, which is in practice discretized and thus reduced to a mathematical programming problem, of the nonlinear type and of moderately large dimensions (the number of independent variables is in practice about fifty, with about twice that number of constraints).