(eng): The presented paper deals with a problem of fuel consumption optimization. Today's automotive industry solves this problem mainly via various conceptual approaches (hybrid and electric vehicles). However, it leads to high initial cost of a vehicle. This paper focuses on fuel economy for conventional vehicles. For this aim, recursive algorithms of adaptive optimal quadratic control under Bayesian methodology are used. A stochastic servo problem, including set-point tracking, is a part of the considered adaptive control design. In this paper, fuel consumption and speed of a driven vehicle are the controlled variables, where the first one is to be optimized and the second one is pushed to track its set-point. This set-point is a recommended road-dependent speed. Experiments with real data measured on a driven vehicle are provided.