Nonlinear observers for locally uniformly observable systems (original) (raw)

Global Observer Design for Bounded Multi-Output Nonlinear Systems

Under the boundedness and observability conditions, we present a globally convergent observer for a class of multi-output nonlinear systems which covers the blocktriangular observer forms studied previously in the literature. The result presented in this short note incorporates and generalizes the earlier work on the observer design for singleoutput observable systems.

Generalised observers for a class of non-linear systems

International Journal of …, 2007

A general class of MIMO nonlinear systems with unknown inputs is considered with a view to observer synthesis. The particularity of this class of systems lies in the fact that the expression of the outputs depends on the unknown inputs. Different situations are considered and in each case a nonlinear observer, synthesized under appropriate hypotheses, is proposed to jointly estimate all state variables together with the unknown inputs. Simulation results are given in order to highlight the performances of the proposed observers.

An algebraic framework for the design of nonlinear observers with unknown inputs

2007 46th IEEE Conference on Decision and Control, 2007

The observability properties of nonlinear systems with unknown inputs are characterized via differentially algebraic techniques. State variables and unknown inputs are estimated thanks to a new algebraic numerical differentiator. It is shown through an academic example and a concrete casestudy that the proposed scheme can be applied to systems that fail to fulfill some usual structural assumptions.

State observers for nonlinear systems with smooth/bounded input

1999

summary:It is known that for affine nonlinear systems the drift-observability property (i. e. observability for zero input) is not sufficient to guarantee the existence of an asymptotic observer for any input. Many authors studied structural conditions that ensure uniform observability of nonlinear systems (i. e. observability for any input). Conditions are available that define classes of systems that are uniformly observable. This work considers the problem of state observation with exponential error rate for smooth nonlinear systems that meet or not conditions of uniform observability. In previous works the authors showed that drift-observability together with a smallness condition on the input is sufficient to ensure existence of an exponential observer. Here it is shown that drift- observability implies a kind of local uniform observability, that is observability for sufficiently small and smooth input. For locally uniformly observable systems two observers are presented: an ex...

Order extension of nonlinear systems for observer design under reduced observability

Proceedings of the 15th IFAC World Congress, 2002, 2002

Nonlinear unforced systems of order n with reduced observability properties are considered. This reduction concerns the fact that the r-observability map is injective only for r > n. An immersion into a higher order system containing the original system coordinates is proposed, such that estimation of the original states of the system is simplified. Approximate or event-based observers are proposed when some properties are lost for the extension, e.g. smoothness or continuity. Observer design is illustrated by examples and a simplified model of an aerobic bioreactor.

Local observer design for nonlinear systems

Mathematical and Computer Modelling, 2002

This paper is a geometric study of the local observer design for nonlinear systems. First, we obtain necessary and sufficient conditions for local exponential observers for Lyaupnov stable nonlinear systems. We also show that the definition of local exponential observers can be considerably weakened for neutrally stable nonlinear systems. As an application of our local observer design, we consider a class of nonlinear systems with an input generator (ecosystem) and show that for this class of nonlinear systems, under some stability assumptions, the existence of local exponential observers in the presence of inputs implies and is implied by the existence of local exponential observers in the absence of inputs.

On the observer design of multi output systems in discrete-time

Proceedings of the 16th IFAC World Congress, 2005, 2005

The paper deals with the equivalence under coordinates change, of a discrete-time nonlinear multi output system to observer canonical forms. Necessary and sufficient conditions for local equivalence to these forms are given.

Observer Design for a Class of Uniformly Observable MIMO Nonlinear Systems with Coupled Structure

Proceedings of the 17th IFAC World Congress, 2008, 2008

A high gain observer is synthesized from a canonical form that characterizes the class of uniformly observable systems. Two main contributions are to be emphasized: the first is related to the considered structure of the canonical form which does not assume a complete triangular structure. That is, each block may contain nonlinearities which depend on the whole state. The second main contribution lies in the simplicity of the observer gain synthesis since the expression of this gain is given and its calibration is reduced to the choice of a single design parameter. Moreover, this involves a design function that has to satisfy a mild condition which is given. Different expressions of such a function are proposed. Of particular interest, it is shown that high gain observers and sliding mode like observers can be derived by considering particular expressions of the design function. An example with simulation results is given for illustration purposes.

Single Output Dependent Observability Normal Form

SIAM journal on control and optimization, 2007

1. Introduction. Since Luenberger's work [9], the design of an observer for observable linear systems with linear outputs has been a well-known concept. In order to use the same observer for nonlinear systems, the so-called observability linearization problem for nonlinear systems was born. ...