A Second Order Extremum Seeking Controller with a Nonlinear Gain

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Battista, Angela S.
Extremum Seeking Control
Extremum seeking control is an established model free optimization technique that estimates unknown system parameters and applies a gradient descent. Extremum seeking has proven to be a resourceful tool to effectively deal with systems with complex dynamics, where developing a model offline might be a challenging task. In this thesis, we apply extremum seeking control to two optimization problems. First, we develop a continuous time distributed extremum seeking controller with a nonlinear gain term which adapts to the system dynamics to ensure the controller gain is sufficiently large. The distributed controller has three main parts: 1) consensus, 2) parameter estimation and 3) extremum seeking control law with a nonlinear gain. The consensus algorithm provides each agent with an estimate of the average total cost of the system. From the consensus estimation, each agent performs its own parameter estimation routine to estimate the gradient of the average total cost and a system drift term. Finally, a Proportional-Integral extremum seeking control law is proposed using the gradient information provided by the parameter estimation routine. In the second part of this thesis, we develop an extremum seeking control law for a class of second order nonlinear systems. We propose a control law with a proportional, integral, and derivative term and a nonlinear gain term. We use a nested parameter estimation routine to estimate the gradient of the local cost function and a low power high gain observer to estimate the derivative of the gradient. We show that, under some assumptions, tuning parameters exist such that the system will converge to a region around the optimum.
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