Authors:
Murat Arcak,
Petar V. Kokotović,
Volume: 1, Page 778 Paper number 1484
Abstract:
This paper analyzes the robustness of a nonlinear observer design
recently introduced by the authors. For uncertainties in the nonlinearities,
bounds are given within which the observer error gradually increases
with an increase in the uncertainty. For dynamic modeling errors,
a robust output-feedback design is developed using ISS small-gain
tools. A jet engine compressor example is used to illustrate the design.
Authors:
Jaime Moreno,
Alejandro Vargas,
Volume: 1, Page 784 Paper number 1962
Abstract:
A methodology for the design of continuous practical observers for
nonlinear uniformly observable systems is presented. The system is
first transformed into observability normal form, using the observability
map semi-diffeomorphism. Since this normal form may have a non-Lipschitz
continuous right hand side, a so called (epsilon)-approximate high-gain
observer is designed for it, constituting the dynamic part of the observer.
The inverse of the transformation is used as the static part. Convergence
of the observer's state trajectory to a ball around the true state
trajectory is guaranteed, with the radius of the ball as small as desired.
Authors:
Jaime Moreno,
Volume: 1, Page 790 Paper number 1964
Abstract:
The existence conditions for unknown input observers for LTI systems
are well known and several methods for its design have been proposed
in the literature. However, for nonlinear systems only sufficient conditions
are known for certain classes of systems. In this paper sufficient
conditions under which the construction of an state unknown input observer
for nonlinear systems are derived. Furthermore, this conditions are
also shown to be necessary, under some additional conditions. A method
to design full order and reduced order unknown input observers is proposed,
and its convergence is analyzed. Although in this paper the study is
restricted to SISO systems, most of the results can be carried on to
MIMO systems. These results are important in the design of Fault Detection
and Isolation Filters, robust nonlinear observers, and decentralized
control.
Authors:
Michel Zasadzinski,
Eric Magarotto,
Mohamed Darouach,
Volume: 1, Page 796 Paper number 2028
Abstract:
In this paper, a method to design a reduced order unknown input observer
for bounded control inputs singular bilinear system with bilinear measurements
and subjected unknown disturbances is investigated. The design of this
unknown input is divided into two parts. The first one consists in
solving some algebraic constraints to obtain an observation error which
is decoupled from the unknown disturbances. In the second part, an
LMI is solved to ensure the exponential stability of the reconstruction
error for all admissible control inputs and unmeasurable disturbances.
Authors:
Alain Rapaport,
Abdelmalek Maloum,
Volume: 1, Page 802 Paper number 1329
Abstract:
For nonlinear systems in R^n which admit an observability index m strictly
larger than n, we show that under the existence of an injective immersion
onto a manifold of R^m, one can build an exponential observer. The
main point concerns the determination of a Lipschitz extension to R^m
of the dynamics, which is defined only on a manifold of dimension n.
We propose some constructive tools and illustrate their utility on
a simple biological model.
Authors:
Hassan Hammouri,
Nicolas Marchand,
Volume: 1, Page 804 Paper number 2081
Abstract:
Under some observability assumptions (uniform observability), a high
gain observer for a class of implicit dynamical systems is given in
this paper. Numerically, the computation of trajectories of such implicit
systems usually necessitates the use of an optimization algorithm together
with an ODE numerical method. This complicates the synthesis of an
observer. The observer design proposed here leads to a classical dynamical
system defined on some R^N, with N >= n, n being the dimension of the
state space of the implicit system.
Authors:
Hyungbo Shim,
Jin Heon Seo,
Volume: 1, Page 809 Paper number 1101
Abstract:
We propose a novel recursive design scheme of state observer for lower
triangular nonlinear systems. The design begins from the bottom dynamics
and propagates to upper dynamics recalling the backstepping scheme
for nonlinear control. The proposed class of systems is fairly general
since it includes non-uniformly observable or detectable multi-output
systems. The error convergence to zero is proved assuming the boundedness
of input a posteriori, which is preferable whereas most results in
the literature assume the boundedness a priori. A global observer is
proposed with the global Lipschitz condition of the system. However,
this condition is removed via the Lipschitz extension technique when
the semi-global observer is of interest.
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