I am interested in the application of derivative-free methods, in particular pattern search algorithms, to the identification of nonlinear systems. I have found many application papers that use this kind of methods to identify the parameters of the plant, but I have not found too much information about the advantages of using those algorithms with respect to gradient-based methods. Obviously the results will depend on your model structure, but is there any paper comparing both alternatives in general?
Dear Edgar,
I suggest you to see links and attached files in topic.
-Direct filter tuning and optimization in multivariable identification ...
ieeexplore.ieee.org/abstract/document/7039659/ -
-System Identification (SYSID '03): A Proceedings Volume from the ...
https://books.google.dz/books?isbn=0080437095
-Simulation optimization: A review of algorithms and applications
https://arxiv.org/pdf/1706.08591
-Identification of Dynamic Systems: An Introduction with Applications
https://books.google.dz/books?isbn=3540788794
Best regards
Please find attached two my works devoted to Posynomial and Signomial fitting. They are wrotte in Spanish Lenguage, so will be easy to read by you. In my researchgate profile you can find other works that could be also useful
Best wishes
En una primera lectura me pareció que usted necesitaba hallar modelos para identificar relaciones complejas. Si lo que le interesa es una visión sistémica para identificar procesos de toma de decisiones, incluyendo la composición de modelos, le recomiendo mi libro "Sistemas de Ingeniería" o la monografía "Análisis y Síntesis de Sistemas de Ingeniería", las que usted puede encontrar en mi perfil de researchgate.
Maybe you can consider the recursive least squares algorithm (RLS) which allows for (real-time) dynamical application of least squares (LS) regression to a time series of time-stamped continuously acquired data points. As with LS, there may be several correlation equations with the corresponding set of dependent (observed) variables. RLS is the recursive application of LS, so that each new data point is taken in account to modify (correct) a previous estimate of the parameters from some linear (or linearized) correlation thought to model the observed system. For RLS with forgetting factor (RLS-FF), acquired data is weighted according to its age, with increased weight given to the most recent data. This is often convenient for adaptive control and/or real-time optimization purposes. A particularly clear introduction to RLS/RLS-FF is found at: Karl J. Åström, Björn Wittenmark, "Computer-Controlled Systems: Theory and Design", Prentice-Hall, 3rd ed., 1997.
Application example ― While investigating adaptive control and energetic optimization of aerobic fermenters, I have applied the RLS-FF algorithm to estimate the parameters from the KLa correlation, used to predict the O2 gas-liquid mass-transfer. Estimates were improved by imposing sinusoidal disturbance to air flow and agitation speed (manipulated variables). The power dissipated by agitation was accessed by a torque meter (pilot plant). The proposed (adaptive) control algorithm compared favourably with PID. Simulations assessed the effect of numerically generated white Gaussian noise (2-sigma truncated) and of first order delay. This investigation was reported at (MSc Thesis):
Thesis Controlo do Oxigénio Dissolvido em Fermentadores para Minimi...
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