Jean Chamberlain Chedjou

GSM RSSI-based positioning using extended Kalman filter for training artificial neural networks

The precise position of the mobile station is critical for the ever increasing number of applications based on location. We introduce a novel positioning technique for positioning a GSM mobile phone in real-time. This technique is based on the GSM mobile phone feature that it can measure the signal strengths from a number of nearby base stations. We use the GSM signal strengths measured in a real environment to train an artificial neural network. The neural network is trained using the second order learning algorithm (extended Kalman filter) because of its superiority in learning speed and mapping accuracy. The mobile position can be determined with good accuracy by providing the current signal strength data to a previously trained neural network. The EKF shows its superiority to back propagation (BP) in both the general feed forward (GFF) and the multilayer perceptron (MLP) neural network architectures. The good accuracy of the calculated position with EKF training in either a GFF or MLP neural network is shown.

Behavior of a Self-Sustained Electromechanical Transducer and Routes to Chaos

This paper studies the dynamics of a self-sustained electromechanical transducer. The stability of fixed points in the linear response is examined. Their local bifurcations are investigated and different types of bifurcation likely to occur are found. Conditions for the occurrence of Hopf bifurcations are derived. Harmonic oscillatory solutions are obtained in both nonresonant and resonant cases. Their stability is analyzed in the resonant case. Various bifurcation diagrams associated to the largest one-dimensional (1-D) numerical Lyapunov exponent are obtained, and it is found that chaos can appear suddenly, through period doubling, period adding, or torus breakdown. The extreme sensitivity of the electromechanical system to both initial conditions and tiny variations of the coupling coefficients is also outlined. The experimental study of the electromechanical system is carried out. An appropriate electronic circuit (analog simulator) is proposed for the investigation of the dynamical behavior of the electromechanical system. Correspondences are established between the coefficients of the electromechanical system model and the components of the electronic circuit. Harmonic oscillatory solutions and phase portraits are obtained experimentally. One of the most important contributions of this work is to provide a set of reliable analytical expressions (formulas) describing the electromechanical system behavior. These formulas are of great importance for design engineers as they can be used to predict the states of the electromechanical systems and respectively to avoid their destruction. The reliability of the analytical formulas is demonstrated by the very good agreement with the results obtained by both the numeric and the experimental analysis.

Comparison of gradient descent method, Kalman filtering and decoupled Kalman in training neural networks used for fingerprint-based positioning

The success of neural network architectures depends heavily on the availability of effective learning algorithms. Radial basis function (RBF) neural networks provide attractive possibilities for solving signal processing and pattern classification problems. Gradient descent training (GD) of RBF networks has proven to be much more effective than more conventional methods. However, gradient descent training can be computationally expensive and its learning speed is very slow. The paper compares (GD) to methods based on either Kalman filtering (KF) or decoupled Kalman filter (DEKF). These new methods prove to be quicker than gradient descent training while still providing good performance at the same level of effectiveness when they are used in fingerprint-based positioning.

A Universal Concept Based on Cellular Neural Networks for Ultrafast and Flexible Solving of Differential Equations

This paper develops and validates a comprehensive and universally applicable computational concept for solving nonlinear differential equations (NDEs) through a neurocomputing concept based on cellular neural networks (CNNs). High-precision, stability, convergence, and lowest-possible memory requirements are ensured by the CNN processor architecture. A significant challenge solved in this paper is that all these cited computing features are ensured in all system-states (regular or chaotic ones) and in all bifurcation conditions that may be experienced by NDEs.One particular quintessence of this paper is to develop and demonstrate a solver concept that shows and ensures that CNN processors (realized either in hardware or in software) are universal solvers of NDE models. The solving logic or algorithm of given NDEs (possible examples are: Duffing, Mathieu, Van der Pol, Jerk, Chua, Rössler, Lorenz, Burgers, and the transport equations) through a CNN processor system is provided by a set of templates that are computed by our comprehensive templates calculation technique that we call nonlinear adaptive optimization. This paper is therefore a significant contribution and represents a cutting-edge real-time computational engineering approach, especially while considering the various scientific and engineering applications of this ultrafast, energy-and-memory-efficient, and high-precise NDE solver concept. For illustration purposes, three NDE models are demonstratively solved, and related CNN templates are derived and used: the periodically excited Duffing equation, the Mathieu equation, and the transport equation.

Bifurcation analysis and synchronisation issues in a three-echelon supply chain

In todays global marketplace, supply chains are dynamic and volatile. This dynamic and volatile nature produces various types of uncertainties along the supply chain, for example, demand uncertainty, supply uncertainty, delivery uncertainty and forecasting uncertainty. These uncertainties make supply chains complex and nonlinear systems as they propagate both upstream and downstream. This work investigates the dynamic behaviour of a three-echelon supply chain. Modelling of this structure is carried out to display its nonlinear dynamic behaviour. It is shown that the dynamics (stability) of the supply chain are very sensitive to external uncertainties. Specifically, a supply chain subjected to these uncertainties can exhibit strange and undesired states such as saturation and chaos. An adaptive algorithm for the automatic cancellation of these strange dynamics due to uncertainties is developed by re-adjusting the internal parameters of the supply chain to achieve its synchronisation. A bifurcation analysis is carried out. This analysis is essential and useful for strategic decision-makers as it allows both the visualisation and control of the states/dynamics of the entire supply chain. The internal parameters of the supply chain are used as control parameters, and various remarkable states are discovered towards the achievement of synchronisation.

Cellular Neural Networks-Based Genetic Algorithm for Optimizing the Behavior of an Unstructured Robot

A new learning algorithm for advanced robot locomotion is presented in this paper. This method involves both Cellular Neural Networks (CNN) technology and an evolutionary process based on genetic algorithm (GA) for a learning process. Learning is formulated as an optimization problem. CNN Templates are derived by GA after an optimization process. Through these templates the CNN computation platform generates a specific wave leading to the best motion of a walker robot. It is demonstrated that due to the new method presented in this paper an irregular and even a disjointed walker robot can successfully move with the highest performance.

Dynamics of a Quasiperiodically Forced Rayleigh Oscillator

This paper studies the dynamics of a self-excited oscillator with two external periodic forces. Both the nonresonant and resonant states of the oscillator are considered. The hysteresis boundaries are derived in terms of the system’s parameters. The stability conditions of periodic oscillations are derived. Routes to chaos are investigated both from direct numerical simulation and from analog simulation of the model describing the forced oscillator. One of the most important contributions of this work is to provide a set of reliable analytical expressions (formulas) describing the system’s behavior. These are of great importance to design engineers. The reliability of the analytical formulas is demonstrated by a very good agreement with the results obtained by both the numeric and the experimental analysis.

New computational modeling for solving higher order ODE based on FPGA

In this paper we propose a method for solving complex higher order ordinary differential equations (ODE) based on an emulation of the analog computing paradigm on digital hardware platforms. In this case, we mimic real analog system elements by digital discretized models. Due to the flexibility and reconfigurability of FPGA and also the possibility of system behavioral modeling through hardware description languages (HDL), we are able to create all fundamental elements that are necessary to both simulating complex systems and the modeling of any ordinary differential equations (ODE) or a system simulation based on ODEs. We therefore propose a novel methodology of solving systems and higher order ODEs. This technique is similar to the analog computing but with the key difference that we possess more flexibility and are able to control at will the precision level wanted/needed. Further features are values scaling of both the results and internal variables.

CNN‐based ultrafast solver of stiff ODEs and PDEs for enabling realtime Computational Engineering

Purpose – This paper seeks to develop, propose and validate, through a series of presentable examples, a comprehensive high‐precision and ultra‐fast computing concept for solving stiff ordinary differential equations (ODEs) and partial differential equations (PDEs) with cellular neural networks (CNN).Design/methodology/approach – The core of the concept developed in this paper is a straight‐forward scheme that we call “nonlinear adaptive optimization (NAOP)”, which is used for a precise template calculation for solving any (stiff) nonlinear ODEs through CNN processors.Findings – One of the key contributions of this work (this is a real breakthrough) is to demonstrate the possibility of mapping/transforming different types of nonlinearities displayed by various classical and well‐known oscillators (e.g. van der Pol‐, Rayleigh‐, Duffing‐, Rossler‐, Lorenz‐, and Jerk‐ oscillators, just to name a few) unto first‐order CNN elementary cells, and thereby enabling the easy derivation of corresponding CNN‐template...

Use of CNN processors for ultra-fast solution ODE's and PDE's: A renaissance of the analog computer

Setting analog cellular computers based on cellular neural networks systems (CNNs) to change the way analog signals are processed is a revolutionary idea and a proof as well of the high importance devoted to the analog computing methods. This paper provides basics of the methods based on the CNNs paradigm that can be exploited for analog computing of very complex systems which are modelled by ODEs and/or PDEs (an implementation on chip using CNN technology is possible even an emulation in FPGA). A proof of concept of the computing approach developed in this paper is validated by solving some complex ODEs and/or PDEs models and by comparing the results obtained with those available in the literature (benchmarking). The computation based CNNs paradigm is advantageous as it provides accurate and ultra-fast solutions of very complex ODEs and PDEs.