| Tracking a varying maximum or minimum of a performance (output, cost) function is called extremum seeking control. The motivation for the research on extremum seeking control arises from its practical interest, since even small improvements in performance can lead to large savings in raw material and energy consumption. For example, maximize the yield of bioreactors, minimize the power demand in formation control, maximize the traction between the wheel and the road to stop the vehicle faster, or even get a better tuning of the PID coefficients. The main purpose of this dissertation is to study the perturbation-based extremum seeking control, numerical optimization-based extremum seeking control, and their applications. We first introduce a new idea to extend the applicability of perturbation-based extremum seeking control to moderately unstable systems. Then, we propose a novel numerical optimization-based extremum seeking control based on optimization algorithm and state regulation, starting from simple linear time invariant, system and extending to a class of feedback linearizable nonlinear systems. We also analyze the robustness of two main optimization algorithms: line search methods and trust region methods. Further design flexibility is achieved via the robustness analysis of the optimization algorithms and the output tracking framework. Robust and adaptive design of numerical optimization-based extremum seeking control are then pursued, where nonlinear damping and nonlinear adaptive control are used to deal with input disturbances and unmodeled plant dynamics.; On the application aspects, we perform a comparative study of antilock braking system design via different extremum seeking control schemes. Another interesting and promising application studied here is the autonomous vehicle source seeking problem. We especially study the perturbation-based extremumn seeking control to the design of autonomous vehicle source seeking, where the stability analysis is conducted for different models of autonomous vehicle. Finally, we make further progress on the swarm seeking problem, where source seeking, formation control, collision avoidance and obstacle avoidance of a group of autonomous vehicles are achieved via extremum seeking control and potential fields. |
