Complete stability of feedback CNNs with dynamic memristors and second‐order cells

The paper considers a feedback cellular neural network (CNN) obtained by interconnecting elementary cells with an ideal capacitor and an ideal flux‐controlled memristor. It is supposed that during the analogue computation of the CNN the memristors behave as dynamic elements, so that each dynamic memristor (DM)‐CNN cell is described by a second‐order differential system in the state variables given by the capacitor voltage and the memristor flux. The proposed networks are called DM‐CNNs, that is CNNs using a dynamic (D) memristor (M). After giving a foundation to the DM‐CNN model, the paper establishes a fundamental result on complete stability, that is convergence of solutions toward equilibrium points, when the DM‐CNN has symmetric interconnections. Because of the presence of dynamic memristors, a DM‐CNN displays peculiar and basically different dynamic properties with respect to standard CNNs. First of all a DM‐CNN computes during the time evolution of the memristor fluxes, instead of the capacitor voltages as for a standard CNN. Furthermore, when a steady state is reached, the memristors keep in memory the result of the computation, that is the limiting values of the fluxes, while all memristor currents and voltages, as well as all currents, voltages, and power in the DM‐CNN vanish. Instead, for standard CNNs, currents, voltages, and power do not drop off when a steady state is reached. Copyright © 2016 John Wiley & Sons, Ltd.     

ANALOGUE COMBINATORICS AND CELLULAR AUTOMATA—KEY ALGORITHMS AND LAY-OUT DESIGN

This paper demonstrates how certain logic and combinatorial tasks can be solved using CNNs. A design method is proposed for solving combinatorial tasks on a CNN. It can be used to simulate cellular automata on a CNN, to prove the self-reproducing capability of the CNNUM and for sorting, histogram calculation, parity analysis and minimum Hamming distance computation. These solutions are especially useful since they can serve as subroutines of more complex CNNUM algorithms. As an important real-life application the lay-out of printed circuit boards is designed with the CNNUM at an extremely high speed.     

External inputs,stable equilibria and complete stability of CNNs

We construct two cellular neural networks (CNNs) of three cells to show that a CNN can have stable equilibria, but is not completely stable and that the complete stability of CNN depends on the choice of external inputs. These phenomena cannot occur for two‐cell CNNs. Copyright © 2003 John Wiley & Sons, Ltd.     

Cellular neural networks with opposite‐sign templates for image thinning

This paper presents image thinning algorithms using cellular neural networks (CNNs) with one‐ or two‐dimensional opposite‐sign templates (OSTs) as well as non‐unity gain output functions. Two four‐layer CNN systems with one‐dimensional (1‐D) OSTs are proposed for image thinning with 4‐ or 8‐connectivity, respectively. A CNN system, which consists of an eight‐layer CNN with two‐dimensional (2‐D) OSTs followed by another four‐layer CNN with 2‐D OSTs, is constructed for image thinning with 8‐connectivity, in which designs of B‐ and I‐templates are simpler than in CNNs with 1‐D OSTs. In the aforementioned designs, parameter values of 1‐D OSTs are chosen to make CNNs operate with thinning‐like property 1 (TL‐1), and those of 2‐D OSTs with 2‐D thinning‐like property (2‐DTL). Simulation studies show that these CNN systems have a good image thinning performance. Copyright © 1999 John Wiley & Sons, Ltd.     

Multi‐template approach to realize central pattern generators for artificial locomotion control

Biologically inspired control of artificial locomotion often makes use of the concept of central pattern generator (CPG), a network of neurons establishing the locomotion pattern within a lattice of neural activity. In this paper a new approach, based on cellular neural networks (CNNs), for the design of CPGs is presented. From a biological point of view this new approach includes an approximated chemical synapse realized and implemented in a CNN structure. This allows to extend the results, previously obtained with a reaction‐diffusion‐CNN (RD‐CNN) for the locomotion control of a hexapod robot, to a more general class of artificial CPGs in which the desired locomotion pattern and the switching among patterns are realized by means of a spatio‐temporal algorithm implemented in the same CNN structure. Copyright © 2002 John Wiley & Sons, Ltd.     

Watermarking on CNN‐UM for image and video authentication

In this paper a new approach to fragile watermarking technique is introduced. This problem is particularly interesting in the field of modern multimedia applications, when image and video authentication are required. The approach exploits the cellular automata suitability to work as pseudorandom pattern generators and extends the related algorithms under the framework of the cellular non‐linear networks (CNNs). The result is a novel way to perform watermarking generation in real time, using the presently available CNN‐universal chip prototypes. In this paper, both the CNN algorithms for fragile watermarking as well as on‐chip experimental results are reported, confirming the suitability of CNNs to successfully act as real‐time watermarking generators. The availability of CNN‐based visual microprocessors allows to have powerful algorithms to watermark in real time images or videos for efficient smart camera applications. Copyright © 2004 John Wiley & Sons, Ltd.     

A method for the approximate synthesis of cellular non‐linear networks—Part 2: Circuit reduction

In this paper, we face the problem of model reduction in piecewise‐linear (PWL) approximations of non‐linear functions. The reduction procedure presented here is based on the PWL approximation method proposed in a companion paper and resorts to a strategy that exploits the orthonormality of basis functions in terms of a proper inner product. Such a procedure can be favourably applied to the synthesis of the resistive parts of cellular non‐linear networks (CNNs) to reduce the complexity of the resulting circuits. As an example, the method is applied to a case study concerning a CNN for image processing. Copyright © 2003 John Wiley & Sons, Ltd.     

Cellular neural network design for solving specific image-processing problems

This paper is concerned with determining simple CNN-paradigm-based circuits for solving specific binary image-processing problems. Single-layer CNN templates for performing specified shape extraction, extraction of shapes which contain a desired feature and modified feature detection are derived using a formulated design strategy. the concept of CNNs composed of modified cells is developed and circuits designed for realizing simultaneous detection of distinct features and for extracting horizontal line midpoints are presented.     

DESIGN AND LEARNING WITH CELLULAR NEURAL NETWORKS

The template coefficients (weights) of a CNN which will give a desired performance, can either be found by design or by learning. ’By design‘ means that the desired function to be performed can be translated into a set of local dynamic rules, while ’by learning‘ is based exclusively on pairs of input and corresponding output signals, the relationship of which may be far too complicated for the explicit formulation of local rules. An overview of design and learning methods applicable to CNNs, which sometimes are not clearly distinguishable, will be given from an engineering point of view.     

Cellular neural networks: Theory and circuit design

Cellular neural networks or CNNs are a novel neural network architecture introduced by Chua and Yang which is very general and flexible, has some important properties desirable for design applications and can be efficiently implemented on custom hardware based on analogue VLSI technology. In this paper an abstract normalized definition of cellular neural networks with arbitrary interconnection topology is given. Instead of stability, the property of convergence is found to be of central importance: large classes of convergent CNNs in practice always asymptotically approach some stable equilibrium where each component of the corresponding output is binary-valued. A highly efficient CMOS-compatible CNN circuit architecture is then presented where a basic cell consists of only two fully differential op amps, two capacitors and several MOSFETs, while a variable interconnection weight is realized with only four MOSFETs. Since all these elements are standard components in the current analogue IC technology and since all network functions are implemented directly on the device level, this architecture promises high cell and interconnection densities and extremely high operating speeds.     

Stability analysis of generalized cellular neural networks

A rather general class of neural networks, called generalized cellular neural networks (CNNs), is introduced. the new model covers most of the known neural network architectures, including cellular neural networks, Hopfield networks and multilayer perceptrons. Several sets of conditions ensuring the input-output stability and global asymptotic stability of generalized CNNs have been obtained. the conditions for the stability of individual cells are checked in the frequency domain, while the stability of the overall network is analysed in terms of the stability of individual cells and the connectivity characteristics. the results on the global asymptotic stability are useful for the design of a generalized CNN such that the orbit of each state converges to a globally asymptotically stable equilibrium point which depends only on the input and not on the initial state. Such a network defines an algebraic map from the space of external inputs to the space of steady state values of the outputs and hence can accomplish cognitive and computational tasks.     

CIRCULANT MATRICES AND THE STABILITY OF A CLASS OF CNNs

In this paper we show that feedback matrices of ring CNNs are block circulants; as special cases, for example, feedback matrices of one-dimensional ring CNNs are circulant matrices. Circulants and their close relations the block circulants possess many pleasant properties which allow one to describe their spectrum completely. After deriving the spectrum of the feedback operator, we discuss conditions for a CNN to be contractive, ensuring global asymptotic stability.     

A SPECTRAL APPROACH TO THE STUDY OF PROPAGATION PHENOMENA IN CNNs

The propagation phenomena occurring in cellular neural networks (CNNs) described by a one-dimensional template are investigated using a spectral technique. The CNN is represented as a scalar Lur'e system to which a suitable extension of the describing function technique is applied for predicting the existence and characteristics of spatiotemporal periodic oscillations. It is shown that such a method yields results that are in good agreement with those observed by time simulation of the system.     

Compact CMOS implementation of a low‐power,current‐mode programmable cellular neural network

We report on the design and characterization of a full‐analog programmable current‐mode cellular neural network (CNN) in CMOS technology. In the proposed CNN, a novel cell‐core topology, which allows for an easy programming of both feedback and control templates over a wide range of values, including all those required for many signal processing tasks, is employed. The CMOS implementation of this network features both low‐power consumption and small‐area occupation, making it suitable for the realization of large cell‐grid sizes. Device level and Monte Carlo simulations of the network proved that the proposed CNN can be successfully adopted for several applications in both grey‐scale and binary image processing tasks. Results from the characterization of a preliminary CNN test‐chip (8×1 array), intended as a simple demonstrator of the proposed circuit technique, are also reported and discussed. Copyright © 2001 John Wiley & Sons, Ltd.     

On the universe of stable cellular neural networks

A cellular neural network (CNN) is a novel analogue circuit architecture with many desirable features. This paper extends previous stability results of CNNs to include classes of strictly sign-symmetric and acyclic templates. We show that most of the 3×3 strictly sign-symmetric templates are stable almost everywhere, with the unknown templates reduced to three classes. We also introduce template graphs and CNN graphs and utilize them to obtain results concerning stability and irreducibility of CNN templates.     

Robot vision with cellular neural networks: a practical implementation of new algorithms

Cellular neural networks (CNNs) are well suited for image processing due to the possibility of a parallel computation. In this paper, we present two algorithms for tracking and obstacle avoidance using CNNs. Furthermore, we show the implementation of an autonomous robot guided using only real‐time visual feedback; the image processing is performed entirely by a CNN system embedded in a digital signal processor (DSP). We successfully tested the two algorithms on this robot. Copyright © 2006 John Wiley & Sons, Ltd.     

Preliminary results from an analog implementation of first‐order TDCNN dynamics

This work falls into the category of linear cellular neural network (CNN) implementations. We detail the first investigative attempt on the CMOS analog VLSI implementation of a recently proposed network formalism, which introduces time‐derivative ‘diffusion’ between CNN cells for nonseparable spatiotemporal filtering applications—the temporal‐derivative CNNs (TDCNNs). The reported circuit consists of an array of Gm‐C filters arranged in a regular pattern across space. We show that the state–space coupling between the Gm‐C‐based array elements realizes stable and linear first‐order (temporal) TDCNN dynamics. The implementation is based on linearized operational transconductance amplifiers and Class‐AB current mirrors. Measured results from the investigative prototype chip that confirms the stability and linearity of the realized TDCNN are provided. The prototype chip has been built in the AMS 0.35 µm CMOS technology and occupies a total area of 12.6 mm sq, while consuming 1.2 µW per processing cell. Copyright © 2010 John Wiley & Sons, Ltd.     

A study on WTA cellular neural networks

This paper addresses a number of basic issues concerning the dynamics of a class of winner‐take‐all cellular neural networks (WTA CNNs) proposed by Seiler and Nossek. The main result is an analytical estimate for the settling time, which shows from a theoretical point of view that such CNNs are well suited for on‐line applications requiring a large number of units, fast processing speed and a relatively high resolution. Other results are the determination of the largest parameter set that guarantee a correct WTA functionality for all initial conditions and the solution of a conjecture made by Seiler and Nossek. These results are proved by means of a new Lyapunov function to analyse the global dynamical behaviour of the WTA CNNs. Copyright © 2001 John Wiley & Sons, Ltd.     

Guiding a mobile robot with cellular neural networks

We show how cellular neural networks (CNNs) are capable of providing the necessary signal processing needed for visual navigation of an autonomous mobile robot. In this way, even complex feature detection and object recognition can be obtained in real time by analogue hardware, making fully autonomous real‐time operation feasible. An autonomous robot was first simulated and then implemented by simulating the CNN with a DSP. The robot is capable of navigating in a maze following lines painted on the floor. Images are processed entirely by a CNN‐based algorithm, and navigation is controlled by a fuzzy‐rule‐based algorithm. Copyright © 2002 John Wiley & Sons, Ltd.     

Cellular neural networks based on resonant tunnelling diodes

Resonant tunnelling diodes (RTDs) have intriguing properties which make them a primary nanoelectronic device for both analogue and digital applications. We propose two different types of RTD‐based cells for the cellular neural network (CNN) which exhibit superior performance in terms of complexity, functionality, or processing speed compared to standard cells. In the first cell model, the resistor of the standard cell is replaced by an RTD, which results in a more compact and versatile cell which requires neither self‐feedback nor a non‐linear output function, and allows three stable equilibrium points. If a resonant tunnelling transistor (RTT) is used instead of the RTD, the dynamics can be controlled through its gate voltage as an additional network parameter. In a majority of CNN applications, bistable cells are sufficient. Utilizing RTD‐based bistable logic elements to store the state of the cell, switching occurs almost instantaneously as virtually no charge transfer is necessary, and it is possible to implement non‐linear connections in a straightforward manner. Hence, it turns out that RTD‐based CNNs are tailor‐made for the implementation of extremely fast bipolar operations and non‐linear templates. The ideas presented in this paper may also be beneficially applied to other types of circuits and systems such as A/D converters or sigma‐delta modulators. Copyright © 2001 John Wiley & Sons, Ltd.