Novel iterative formulation of Correlation-Based Tuning

Stable Iterative Correlation-based Tuning algorithm for servo systems

“…(that is usually the 2-norm of the tracking error) such that to make the output error between the designed and achieved closed-loop CSs uncorrelated with the reference input. Some recent aspects concerning CbT are reported in [13]- [19]. The inclusion of a sufficient CS stability condition in CbT algorithms is discussed in [13].…”

“…Application and implementation issues of CbT are discussed in [17], [18]. An 1FT-based formulation of CbT is suggested in [19] to minimize the c.f. expressed as the squared sum of the cross-correlation function between the output error (i.e., the difference between the controlled output and the reference model output) and the reference input; the iterative estimation of the gradient of the c.f.…”

“…As shown in [13]- [19], the optimization problem can be solved either using a single experiment or iteratively in terms of the following parameter update law:…”

“…where u (p, t) is the control signal produced by the controller with the transfer function C (p, q -I), vet) is the stochastic noise-type disturbance input, and the transfer function of the process p(q-I) is expressed as ratio of two polynomials [19] .…”

“…The calculation of est{ �� (p i )} using experiments conducted with the real-world CS in a model-free manner is suggested in [19] by means of 1FT in the framework of the Robbins-Monro procedure. The expectation of the estimated gradient is assumed to equal the true estimated gradient:…”