The Observer Error Linearization Problem via Dynamic Compensation

Abstract

International audienceLinearization by output injection has played a key role in the observer design for nonlinear control systems for almost three decades. In this paper, following some recent works, ge- ometric necessary and sufficient conditions are derived for the existence of a dynamic compensator solving the problem under regular output transformation. An algorithm which computes a compensator of minimal order is given

Fixed-time observer with simple gains for uncertain systems

“…tems up to input-output injections and uniformly observable systems. In the rst case, methods for turning systems into a linear system up to input-output injection through dieomorphism can be found in [23,24,11], and through immersion in [6,21]. In the second case of uniformly observable systems, due to the nonlinearity structure of the obtained system, authors use mainly highgain linear corrective term leading to at least a semiglobal exponential convergence of the error (global convergence can be performed when the nonlinearity has a Lipschitz property).…”

Restricted dynamic observer error linearizability

“…Also, by Theorem 2, system (67) is not RDOEL. However, Califano and Moog (2014) showed that system (67) is observer error linearizable via a more general dynamic compensator than the restricted one (5), together with multi-output scheme.…”

“…As we see in Example 4, our conditions cannot be applied for (general) DOEL problem, while the conditions of Califano and Moog (2014) can be. If system is RDOEL, then our solution is different from the one of Califano and Moog (2014), as mentioned in Remark 4.…”

“…As we see in Example 4, our conditions cannot be applied for (general) DOEL problem, while the conditions of Califano and Moog (2014) can be. If system is RDOEL, then our solution is different from the one of Califano and Moog (2014), as mentioned in Remark 4. Our conditions for RDOEL are, as in the Appendix, simply implemented by a MATLAB programming, because the conditions of Theorem 1 contain only the Lie brackets of the vector fields.…”

“…The sufficient problems of RDOEL problem have been investigated by Back et al (2006) and Boutat and Busawon (2011). Very recently, Califano and Moog (2014) have found the necessary and sufficient conditions for system (1) to be DOEL by using the multi-output scheme y a = [w 1 · · · w d y] T in Definition 2.…”