A Framework for Extremum Seeking Control of Systems With Parameter Uncertainties

Traditionally, the design of extremum seeking algorithm treats the system as essentially a black-box, which for many applications means disregarding known information about the model structure. In contrast to this approach, there have been recent examples where a known plant structure with uncertain parameters has been used in the online optimization of plant operation. However, the results for these approaches have been restricted to specific classes of plants and optimization algorithms. This paper seeks to provide general results and a framework for the design of extremum seekers applied to systems with parameter uncertainties. General conditions for an optimization method and a parameter estimator are presented so that their combination guarantees convergence of the extremum seeker for both static and dynamic plants. Tuning guidelines for the closed loop scheme are also presented. The generality and flexibility of the proposed framework is demonstrated through a number of parameter estimators and optimization algorithms that can be combined to obtain extremum seeking. Examples of anti-lock braking and model reference adaptive control are used to illustrate the effectiveness of the proposed framework.