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A comparison of two FEM-based methods for the solution of the nonlinear output regulation problem

Branislav Rehák, Sergej Čelikovský, Javier Ruiz, Jorge Orozco-Mora (2009)

Kybernetika

The regulator equation is the fundamental equation whose solution must be found in order to solve the output regulation problem. It is a system of first-order partial differential equations (PDE) combined with an algebraic equation. The classical approach to its solution is to use the Taylor series with undetermined coefficients. In this contribution, another path is followed: the equation is solved using the finite-element method which is, nevertheless, suitable to solve PDE part only. This paper...

A discussion on the Hölder and robust finite-time partial stabilizability of Brockett’s integrator∗

Chaker Jammazi (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We consider chained systems that model various systems of mechanical or biological origin. It is known according to Brockett that this class of systems, which are controllable, is not stabilizable by continuous stationary feedback (i.e. independent of time). Various approaches have been proposed to remedy this problem, especially instationary or discontinuous feedbacks. Here, we look at another stabilization strategy (by continuous stationary or...

A discussion on the Hölder and robust finite-time partial stabilizability of Brockett’s integrator∗

Chaker Jammazi (2012)

ESAIM: Control, Optimisation and Calculus of Variations

We consider chained systems that model various systems of mechanical or biological origin. It is known according to Brockett that this class of systems, which are controllable, is not stabilizable by continuous stationary feedback (i.e. independent of time). Various approaches have been proposed to remedy this problem, especially instationary or discontinuous feedbacks. Here, we look at another stabilization strategy (by continuous stationary or...

A family of model predictive control algorithms with artificial neural networks

Maciej Ławryńczuk (2007)

International Journal of Applied Mathematics and Computer Science

This paper details nonlinear Model-based Predictive Control (MPC) algorithms for MIMO processes modelled by means of neural networks of a feedforward structure. Two general MPC techniques are considered: the one with Nonlinear Optimisation (MPC-NO) and the one with Nonlinear Prediction and Linearisation (MPC-NPL). In the first case a nonlinear optimisation problem is solved in real time on-line. In order to reduce the computational burden, in the second case a neural model of the process is used...

A geometric solution to the dynamic disturbance decoupling for discrete-time nonlinear systems

Eduardo Aranda-Bricaire, Ülle Kotta (2004)

Kybernetika

The notion of controlled invariance under quasi-static state feedback for discrete-time nonlinear systems has been recently introduced and shown to provide a geometric solution to the dynamic disturbance decoupling problem (DDDP). However, the proof relies heavily on the inversion (structure) algorithm. This paper presents an intrinsic, algorithm-independent, proof of the solvability conditions to the DDDP.

A Hamiltonian approach to fault isolation in a planar vertical take-off and landing aircraft model

Luis H. Rodriguez-Alfaro, Efrain Alcorta-Garcia, David Lara, Gerardo Romero (2015)

International Journal of Applied Mathematics and Computer Science

The problem of fault detection and isolation in a class of nonlinear systems having a Hamiltonian representation is considered. In particular, a model of a planar vertical take-off and landing aircraft with sensor and actuator faults is studied. A Hamiltonian representation is derived from an Euler-Lagrange representation of the system model considered. In this form, nonlinear decoupling is applied in order to obtain subsystems with (as much as possible) specific fault sensitivity properties. The...

A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis

Roman Cherniha, Joanna Stachowska-Piętka, Jacek Waniewski (2014)

International Journal of Applied Mathematics and Computer Science

A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a threecomponent nonlinear system of two-dimensional partial differential equations for fluid, glucose and albumin transport with the relevant boundary and initial conditions. Our aim is to model ultrafiltration of water combined with inflow of glucose to the tissue and removal of albumin from the body during dialysis, by finding the spatial distributions of glucose and albumin concentrations...

A new approach to generalized chaos synchronization based on the stability of the error system

Zhi Liang Zhu, Shuping Li, Hai Yu (2008)

Kybernetika

With a chaotic system being divided into linear and nonlinear parts, a new approach is presented to realize generalized chaos synchronization by using feedback control and parameter commutation. Based on a linear transformation, the problem of generalized synchronization (GS) is transformed into the stability problem of the synchronous error system, and an existence condition for GS is derived. Furthermore, the performance of GS can be improved according to the configuration of the GS velocity....

A new LMI-based robust finite-time sliding mode control strategy for a class of uncertain nonlinear systems

Saleh Mobayen, Fairouz Tchier (2015)

Kybernetika

This paper presents a novel sliding mode controller for a class of uncertain nonlinear systems. Based on Lyapunov stability theorem and linear matrix inequality technique, a sufficient condition is derived to guarantee the global asymptotical stability of the error dynamics and a linear sliding surface is existed depending on state errors. A new reaching control law is designed to satisfy the presence of the sliding mode around the linear surface in the finite time, and its parameters are obtained...

A nonlinear dynamic inversion-based neurocontroller for unmanned combat aerial vehicles during aerial refuelling

Jimoh Olarewaju Pedro, Aarti Panday, Laurent Dala (2013)

International Journal of Applied Mathematics and Computer Science

The paper presents the development of modelling and control strategies for a six-degree-of-freedom, unmanned combat aerial vehicle with the inclusion of the centre of gravity position travel during the straight-leg part of an in-flight refuelling manoeuvre. The centre of gravity position travel is found to have a parabolic variation with an increasing mass of aircraft. A nonlinear dynamic inversion-based neurocontroller is designed for the process under investigation. Three radial basis function...

A reduction principle for global stabilization of nonlinear systems

Rachid Outbib, Gauthier Sallet (1998)

Kybernetika

The goal of this paper is to propose new sufficient conditions for dynamic stabilization of nonlinear systems. More precisely, we present a reduction principle for the stabilization of systems that are obtained by adding integrators. This represents a generalization of the well-known lemma on integrators (see for instance [BYIS] or [Tsi1]).

A separation principle for the stabilization of a class of time delay nonlinear systems

Amel Benabdallah (2015)

Kybernetika

In this paper, we establish a separation principle for a class of time-delay nonlinear systems satisfying some relaxed triangular-type condition. Under delay independent conditions, we propose a nonlinear time-delay observer to estimate the system states, a state feedback controller and we prove that the observer-based controller stabilizes the system.

A simple scheme for semi-recursive identification of Hammerstein system nonlinearity by Haar wavelets

Przemysław Śliwiński, Zygmunt Hasiewicz, Paweł Wachel (2013)

International Journal of Applied Mathematics and Computer Science

A simple semi-recursive routine for nonlinearity recovery in Hammerstein systems is proposed. The identification scheme is based on the Haar wavelet kernel and possesses a simple and compact form. The convergence of the algorithm is established and the asymptotic rate of convergence (independent of the input density smoothness) is shown for piecewiseLipschitz nonlinearities. The numerical stability of the algorithm is verified. Simulation experiments for a small and moderate number of input-output...

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