| The research on extremum seeking control problems, where the operation of a dynamical system is to be regulated to maximize or minimize an unknown performance criterion, is of both theoretical and practical values. The application scope of extremum seeking include renewable energy, automotive control, and many other industrial optimization problems.;This work focuses on model-based extremum seeking control, and develops control design to integrate system control and optimization without time-scale separation. It aims to achieve faster convergence as well as better robustness for general nonlinear systems. Practical issues in implementation, including model uncertainties, disturbances, actuator limitations are considered. Three different controller structures are proposed based on specific system structures and model accuracy. The convergence conditions are established through rigorous mathematical analysis.;The first extremum seeking approach utilizes integral sliding mode and focuses on dynamical systems with fast dynamics. In particular, it is designed for systems with relative degree one. Integral sliding mode is employed to estimate the derivative of the performance function and provide feedback to the extremum seeking controller, so that fast convergence towards optimum is achieved. For systems with relative degrees greater than one, a sliding mode based extremum seeking algorithm incorporating a coordinated stabilizing control component is proposed. In the situation of limited actuator efforts, the stabilizing component helps to enforce the existence condition of sliding mode when the performance measurement is outside a vicinity of the optimum. Model uncertainties and disturbances in real-world applications are also considered. A prototype controller structure is presented with corresponding convergence conditions for robust extremum seeking. The proposed structure relies on robust gradient estimation and utilizes variable structure control to achieve asymptotic regulation. Finally, an application example in constrained source seeking in the context of communication network optimization is also discussed. Extremum seeking control with sliding mode is utilized for direction finding, and variable structure control is designed to address the constraints on vehicle kinematics and the accessible area. |
