Extremum seeking is a non-model based adaptive control technique that involves online extremization of plant output with respect to its inputs through feedback. This dissertation develops a stability test in SISO format for multiparameter extremum seeking, and derives systematic design guidelines to satisfy the stability test using standard linear SISO control tools. The results herein render possible rates of adaptation as fast as the plant dynamics. The analysis and design results on extremum seeking are generalized to develop slope seeking, a new idea for non-model based control that involves operating a plant at a commanded slope of its reference to output map.; The method is successfully applied to suppression of gas turbine combustor instabilities in a 4MW combustor at United Technologies Research Center. Successful suppression of instabilities is achieved by means of tuning a phase shifting controller by extremum seeking feedback. The result permits running gas turbine power plants at leaner fuel-air ratios, and hence will yield enormous savings of fuel for power plants, besides reducing emissions.; The dissertation also supplies the first comprehensive design procedure with performance guarantees for minimum power demand formation flight. The design procedure involves development of a wake-robust formation autopilot and extremum seeking feedback to supply the set-point to the autopilot. The design uses sensing and actuation already available on aircraft, and should aid in practical implementation of formation flight and consequent fuel savings of upto 50%.; Finally, near optimal compressor operation under slope seeking feedback is presented. The slope seeking feedback keeps the compressor from entering stall under finite pressure disturbances at the operating point. Furthermore, the feedback is shown robust to variation in the compressor operating characteristic, and permits use of low bandwidth low cycling actuation, showing a potential for large-scale industrial application.
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