A systematic approach to extremum seeking based on parameter estimation

We present a systematic approach for design of extremum seeking (ES) controllers for a class of uncertain plants that are parameterized with unknown parameters. First, we present results for static plants and show how it is possible to combine, under certain general conditions, an arbitrary optimization method with an arbitrary parameter estimation method in order to obtain extremum seeking. Our main results also specify how controller needs to be tuned in order to achieve extremum seeking. Then, we consider dynamic plants and separate our results into the stable plant case and unstable plant case. For each of these cases, we present conditions on general plants, controllers, observers, parameter estimators and optimization algorithms that guarantee semi-global practical convergence to the extremum when controller parameters are tuned appropriately. Our results apply to general nonlinear plants with multiple inputs and multiple parameters.