This paper proposes an adaptive slope seeking strategy targeting any reachable operating point-including extremum-on the input/output map of a general dynamic single input single output (SISO) system approximated either by a quadratic Hammerstein, Wiener, or Wiener-Hammerstein model. The proposed control strategy is based on a recursive estimation algorithm which is used to estimate the model parameters, a slope reference generator, and a controller. A new algorithm called auxiliary model-recursive prediction error method (AM-RPEM) is used for the first task, and it is shown that the three model structures are equivalent from an identification point of view. Using the estimated parameters, a slope reference generator is proposed together with a self-governed pole placement controller with integral action, which advantageously replaces the heuristic integrator gain tuning in classical extremum-seeking schemes. Finally, the proposed control strategy is tested in simulation, first with a numerical example and then, using a dynamic model of Isochrysis galbana cultures so as to achieve concurrently extremum-seeking and suboptimal control. Simulation results using a recursive least squares algorithm and the proposed AM-RPEM are discussed.