Maximizing higher derivatives of unknown maps with stochastic extremum seeking
- Resource Type
- Conference
- Authors
- Mills, Greg; Krstic, Miroslav
- Source
- 2016 American Control Conference (ACC) American Control Conference (ACC), 2016. :6097-6102 Jul, 2016
- Subject
- Aerospace
Bioengineering
Communication, Networking and Broadcast Technologies
Components, Circuits, Devices and Systems
Computing and Processing
Engineered Materials, Dielectrics and Plasmas
Engineering Profession
General Topics for Engineers
Power, Energy and Industry Applications
Robotics and Control Systems
Signal Processing and Analysis
Transportation
Heuristic algorithms
Convergence
Stability analysis
Optimization
Demodulation
Markov processes
- Language
- ISSN
- 2378-5861
We present a stochastic generalization to the scalar Newton-based extremum seeking algorithm which through measurements of an unknown map, maximizes the map's higher derivatives. The proposed method perturbs the estimate of the optimal parameter with the sinusoid of Brownian motion about the boundary of a circle. Then by properly demodulating the map output of the randomly perturbed estimate, the extremum seeking algorithm maximizes the nth derivative only through measurements of the map. The Newton-based extremum seeking approach removes the dependence of the convergence rate on the unknown Hessian of the higher derivative, an effort to improve performance over standard gradient-based extremum seeking. 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. We prove local stability of the algorithm for general nonlinear static maps via stochastic averaging theory developed for extremum seeking.