A parameter estimation approach to state observation of nonlinear systems

Abstract

A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial conditions. The class of systems for which the method is applicable is identified via two assumptions related to the transformability of the system into a suitable cascaded form and our ability to estimate the unknown parameters. The first condition involves the solvability of a partial differential equation while the second one requires some persistency of excitation-like conditions. The proposed observer is shown to be applicable to position estimation of a class of electromechanical systems, for the reconstruction of the state of power converters and for speed observation of a class of mechanical systems.

Relaxing the conditions for parameter estimation-based observers of nonlinear systems via signal injection

“…To apply the signal injection technique it is necessary to develop a slight variation of the main result of [22], where the full state-instead of part of it as done in [22]-is observed. For the sake of completeness we give also the proof of this result.…”

“…Lemma 1. Consider the closed-loop system (22) and its averaged behaviour (23). For all initial conditions (…”

“…It is worth pointing out that in [6] the estimator is designed for the virtual output of ideal system (18), that is, ignoring the perturbation term ∆(χ, t) in (A.2). This estimate is clearly not useful for observer design, therefore, we propose to design the estimator for the practically realisable system (22). This result is contained in the proposition below whose proof is given in Appendix B.…”

“…Proposition 3. Suppose Assumption 1 holds and consider the dynamics of the system (22). Define the estimator of the virtual output y v aŝ…”

“…In [22] a novel class of observers for nonlinear control systems, called parameter estimation-based observers (PEBOs), was proposed. The distinguishing feature of PEBOs is that it formulates the observer design problem as a parameter estimation problem.…”