Abstract
The paper studies a novel adaptive identifier proposed in IFAC World Congress 2020 for nonlinear time-delay systems composed of linear, Lipschitz and non-Lipschitz components. To begin with, an identifier is designed for uncertain systems with a priori known delay values, and then it is generalized for systems with unknown delay values. The algorithm ensures the asymptotic parameter estimation and state observation by using gradient algorithms. The unknown delays and plant parameters are estimated by using a special equivalent extension of the plant equation. The algorithms stability is presented by solvability of linear matrix inequalities. Simulation results are invoked to support the developed identifier design and to illustrate the efficiency of the proposed synthesis procedure.
Highlights
Since the mid-1980s, the definition of synchronization has been used as the coincidence of the coordinates of subsystem state vectors [Fujisaka and Yamada (1983)]
The investigation focuses on adaptive/on-line identification of unknown time-invariant plant parameters
In the paper we study a novel adaptive identifier proposed in [Furtat and Orlov (2020)] for nonlinear systems composed of linear part, Lipschitz and non-Lipschitz nonlinearities
Summary
Since the mid-1980s, the definition of synchronization has been used as the coincidence of the coordinates of subsystem state vectors [Fujisaka and Yamada (1983)]. In [Nakagiri and Yamamoto(1995); Verduyn(2001)] the identification of time-delay systems demonstrated complexity of the problem, the identifiability of a delay system was shown to place a restrictive condition on the structure of the system This condition was defined through the characteristic matrix of the functional differential equation of the plant whereas no indication was given on how to attain this condition using some accessible inputs. The present investigation continues that of [Furtat and Orlov (2020)] to collect both theoretical and numerical studies yielding a model-synchronization-based approach to identification of parameters of nonlinear systems with unknown time delays. The identifiability of the system parameters and delays can be enforced by applying to the system a sufficiently nonsmooth signal that persistently excites the system These signals are constructively introduced by imposing the state of the system and the system input to have different smoothness properties [Orlov et al(2003)]. In what follows, such an identification algorithm is developed for the nonlinear time-delay system in question
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