4,869 research outputs found
Parameter Estimation of Sigmoid Superpositions: Dynamical System Approach
Superposition of sigmoid function over a finite time interval is shown to be
equivalent to the linear combination of the solutions of a linearly
parameterized system of logistic differential equations. Due to the linearity
with respect to the parameters of the system, it is possible to design an
effective procedure for parameter adjustment. Stability properties of this
procedure are analyzed. Strategies shown in earlier studies to facilitate
learning such as randomization of a learning sequence and adding specially
designed disturbances during the learning phase are requirements for
guaranteeing convergence in the learning scheme proposed.Comment: 30 pages, 7 figure
Mathematical control of complex systems
Copyright © 2013 ZidongWang et al.This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
Contracting Nonlinear Observers: Convex Optimization and Learning from Data
A new approach to design of nonlinear observers (state estimators) is
proposed. The main idea is to (i) construct a convex set of dynamical systems
which are contracting observers for a particular system, and (ii) optimize over
this set for one which minimizes a bound on state-estimation error on a
simulated noisy data set. We construct convex sets of continuous-time and
discrete-time observers, as well as contracting sampled-data observers for
continuous-time systems. Convex bounds for learning are constructed using
Lagrangian relaxation. The utility of the proposed methods are verified using
numerical simulation.Comment: conference submissio
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
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