291 research outputs found
Adaptive observers for biophysical neuronal circuits
This paper presents adaptive observers for online state and parameter
estimation of a class of nonlinear systems motivated by biophysical models of
neuronal circuits. We first present a linear-in-the-parameters design that
solves a classical recursive least-squares problem. Then, building on this
simple design, we present an augmented adaptive observer for models with a
nonlinearly parameterized internal dynamics, the parameters of which we
interpret as structured uncertainty. We present a convergence and robustness
analysis based on contraction theory, and illustrate the potential of the
approach in neurophysiological applications by means of numerical simulations.Comment: 16 pages. The Julia code used in this paper can be found in
https://github.com/thiagoburghi/online-learnin
Adaptive Observers and Parameter Estimation for a Class of Systems Nonlinear in the Parameters
We consider the problem of asymptotic reconstruction of the state and
parameter values in systems of ordinary differential equations. A solution to
this problem is proposed for a class of systems of which the unknowns are
allowed to be nonlinearly parameterized functions of state and time.
Reconstruction of state and parameter values is based on the concepts of weakly
attracting sets and non-uniform convergence and is subjected to persistency of
excitation conditions. In absence of nonlinear parametrization the resulting
observers reduce to standard estimation schemes. In this respect, the proposed
method constitutes a generalization of the conventional canonical adaptive
observer design.Comment: Preliminary version is presented at the 17-th IFAC World Congress,
6-11 Seoul, 200
Adaptive observers for nonlinearly parameterized systems subjected to parametric constraints
We consider the problem of adaptive observer design in the settings when the
system is allowed to be nonlinear in the parameters, and furthermore they are
to satisfy additional feasibility constraints. A solution to the problem is
proposed that is based on the idea of universal observers and non-uniform
small-gain theorem. The procedure is illustrated with an example.Comment: 19th IFAC World Congress on Automatic Control, 10869-10874, South
Africa, Cape Town, 24th-29th August, 201
Adaptive Observer for Nonlinearly Parameterised Hammerstein System with Sensor Delay – Applied to Ship Emissions Reduction
Taking offspring in a problem of ship emission reduction by exhaust gas recirculation control for large diesel engines, an underlying generic estimation challenge is formulated as a problem of joint state and parameter estimation for a class of multiple-input single-output Hammerstein systems with first order dynamics, sensor delay and a bounded time-varying parameter in the nonlinear part. The paper suggests a novel scheme for this estimation problem that guarantees exponential convergence to an interval that depends on the sensitivity of the system. The system is allowed to be nonlinear parameterized and time dependent, which are characteristics of the industrial problem we study. The approach requires the input nonlinearity to be a sector nonlinearity in the time-varying parameter. Salient features of the approach include simplicity of design and implementation. The efficacy of the adaptive observer is shown on simulated cases, on tests with a large diesel engine on test bed and on tests with a container vessel
Observers for canonic models of neural oscillators
We consider the problem of state and parameter estimation for a wide class of
nonlinear oscillators. Observable variables are limited to a few components of
state vector and an input signal. The problem of state and parameter
reconstruction is viewed within the classical framework of observer design.
This framework offers computationally-efficient solutions to the problem of
state and parameter reconstruction of a system of nonlinear differential
equations, provided that these equations are in the so-called adaptive observer
canonic form. We show that despite typical neural oscillators being locally
observable they are not in the adaptive canonic observer form. Furthermore, we
show that no parameter-independent diffeomorphism exists such that the original
equations of these models can be transformed into the adaptive canonic observer
form. We demonstrate, however, that for the class of Hindmarsh-Rose and
FitzHugh-Nagumo models, parameter-dependent coordinate transformations can be
used to render these systems into the adaptive observer canonical form. This
allows reconstruction, at least partially and up to a (bi)linear
transformation, of unknown state and parameter values with exponential rate of
convergence. In order to avoid the problem of only partial reconstruction and
to deal with more general nonlinear models in which the unknown parameters
enter the system nonlinearly, we present a new method for state and parameter
reconstruction for these systems. The method combines advantages of standard
Lyapunov-based design with more flexible design and analysis techniques based
on the non-uniform small-gain theorems. Effectiveness of the method is
illustrated with simple numerical examples
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