Section: Research Program
Estimation is quite easy in the absence of perturbations. It becomes challenging in more realistic situations, faced to measurement noises or other unknown inputs. In our works, as well as in the founding text of Non-A, we have shown how our estimation techniques can successfully get rid of perturbations of the so-called structured type, which means the ones that can be annihilated by some linear differential operator (called the annihilator). ALIEN already defined such operators by integral operators, but using more general convolution operators is an alternative to be analyzed, as well as defining the “best way to kill” perturbations. Open questions are:
OQ1) Does a normal form exist for such annihilators?
OQ2) Or, at least, does there exist an adequate basis representation of the annihilator in some adequate algebra?
OQ3) And lastly, can the annihilator parameters be derived from efficient tuning rules?
The two first questions will directly impact Indicators 1 (time) and 2 (complexity), whereas the last one will impact indicator 3 (robustness).