An important issue arising in system identification is to solve the identifiability of a parametric system in a given experiment. This issue originates from numerous engineering applications where identification has to be performed in control processes, especially with feedback inherent (Astrom & Wittemnark, 1971; Forssell & Ljung, 1999; Grewal, Bekey, & Payne, 1974; Gustavsson, Ljung, & Soderstrom, 1977; Li & Chen, 2016; Mejaria, Pigab, & Bemporada, 2018; Van den Hof & Schrama, 1995). Unlike identification operating in open loop, a prominent feature of closed-loop identification is that there is no data design level in parameter estimation, once a feedback law is chosen. It is now well understood that if experiments are allowed to be intended for identification, identifiability is a property of parametrization (Gevers, Bazanella, Coutinho, & Dasgupta, 2016). Otherwise, inputs are probably not able to serve as good excitation signals. So, identifiability in a given experiment hinges on parametrization and experiments both (Nomma & Moog, 2016).
This paper studies the identification of discrete-time nonlinear parameterized control systems in given experiments. A necessary and sufficient condition of the closed-loop identifiability is established for the stable experiments and an algorithm is proposed to estimate the parameter. The estimates are shown to be strongly consistent with the convergence rate explicitly computed under some simple algebraic condition.
- Automotica, 131 (2021)
- Chanying Li (Institute of Systems Science, AMSS, Chinese Academy of Sciences)