Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  generalize the Newton-based extremum seeking algorithm, which, through measurements of an unknown map, maximizes the map's higher derivatives. Specifically,  propose a method for choosing the demodulation signals of a sinusoidally perturbed estimate, such that the extremum seeking algorithm maximizes the n th derivative only through measurements of the map. The Newton-based extremum seeking approach removes the dependence of the average convergence rate on the unknown Hessian of the higher derivative. This dependence is present in standard gradient-based extremum seeking while the average convergence rate of our parameter estimates is user-assignable. Our design stems from the existing multivariable Newton-based extremum seeking algorithm where a differential Riccati equation estimates the inverse Hessian of the function to be maximized. Algebraically computing a direct estimate of the inverse Hessian is susceptible to singularity, where-as employing the Riccati filter removes that potential.  prove local stability of the algorithm for general nonlinear maps via averaging theory.
['Greg Mills', 'Miroslav Krstic']
I am writing a research paper on a idea Maximizing higher derivatives of unknown maps with extremum seeking
[{"from": "human", "value": "I am writing a research paper on a idea Maximizing higher derivatives of unknown maps with extremum seeking"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  generalize the Newton-based extremum seeking algorithm, which, through measurements of an unknown map, maximizes the map's higher derivatives. Specifically,  propose a method for choosing the demodulation signals of a sinusoidally perturbed estimate, such that the extremum seeking algorithm maximizes the n th derivative only through measurements of the map. The Newton-based extremum seeking approach removes the dependence of the average convergence rate on the unknown Hessian of the higher derivative. This dependence is present in standard gradient-based extremum seeking while the average convergence rate of our parameter estimates is user-assignable. Our design stems from the existing multivariable Newton-based extremum seeking algorithm where a differential Riccati equation estimates the inverse Hessian of the function to be maximized. Algebraically computing a direct estimate of the inverse Hessian is susceptible to singularity, where-as employing the Riccati filter removes that potential.  prove local stability of the algorithm for general nonlinear maps via averaging theory."}]