Design and testing of a constrained data-driven iterative reference input tuning algorithm

Optimal behaviour prediction using a primitive-based data-driven model-free iterative learning control approach

“…In [12,18,[27][28][29] it is shown that in order to obtain the quantity T T X for a SISO system, where T is the input-output map (the convolution matrix) of the dynamical system and X is the lifted form of the input signal, it is enough to set the reversed vector rev(X) as an input to the system and record the output as the result Trev(X). Then T T X ¼ revðT revðXÞÞ.…”

“…The first term in (11) correspondsin unified notation-to the gradient of the first terms of J i in (8) with respect to the corresponding optimization variable R While the second term in the sum (11) depends on known quantities at the current iteration, the fist term in (11) depends on the maps T {i,i} . An experimental approach to obtain the first term in (11) is given as follows using a non causal filtering operation [12,18,[27][28][29]. In this regard we define the reverse operation of a vector X 2 R NÀn :…”

“…Therefore, in the MIMO case concerning the corresponding SISO parallel OPs (8), the term T fi;ig TWf1g j is straightforward to obtain by matrix multiplication, at each iteration j of the search algorithm, for each reference input of ith SISO control channel. In order to prevent the operation of each SISO control channel (i.e., control loop) far from the current iteration operating point, a perturbation based approach is used [18]. In addition, the coupling effect between channels is being taken care of as follows.…”

“…The system impulse response is estimated in [15] using input/output measurements from previous iterations and next used in a norm-optimal ILC structure that accounts for actuator limitations by means of linear inequality constraints. Other modelbased approaches for constrained ILC are proposed in [16,17], but they differ from the model-free approach suggested in [18]. A datadriven approach to estimate the Markov matrices from input/ output data using MFAC is given in [19] and integrated in a terminal ILC framework.…”

“…Building upon recent results given in [18], this paper's main contributions with respect to the state-of-the-art are:…”