Mauro Di Marco

Sonar-Based Wall-Following Control of Mobile Robots

In this paper, the wall-following problem for low-velocity mobile robots, equipped with incremental encoders and one sonar sensor, is considered. A robust observer-based controller, which takes into account explicit constraints on the orientation of the sonar sensor with respect to the wall and the velocity of the wheels, is designed. The feedback controller provides convergence and fulfillment of the constraints, once an estimate of the position of the mobile robot, is available. Such an estimate is given by an Extended Kalman Filter (EKF), which is designed via a sensor fusion approach merging the velocity signals from the encoders and the distance measurements from the sonar. Some experimental tests are reported to discuss the robustness of the control scheme.

Necessary and sufficient condition for multistability of neural networks evolving on a closed hypercube.

The paper considers nonsmooth neural networks described by a class of differential inclusions termed differential variational inequalities (DVIs). The DVIs include the relevant class of neural networks, introduced by Li, Michel and Porod, described by linear systems evolving in a closed hypercube of R(n). The main result in the paper is a necessary and sufficient condition for multistability of DVIs with nonsymmetric and cooperative (nonnegative) interconnections between neurons. The condition is easily checkable and provides a sharp bound between DVIs that can store multiple patterns, as asymptotically stable equilibria, and those for which this is not possible. Numerical examples and simulations are presented to confirm and illustrate the theoretic findings.

COMPLEX DYNAMICS IN NEARLY SYMMETRIC THREE-CELL CELLULAR NEURAL NETWORKS

The paper introduces a class of third-order nonsymmetric Cellular Neural Networks (CNNs), and shows through computer simulations that they undergo a cascade of period doubling bifurcations which leads to the birth of a large-size complex attractor. A major point is that these bifurcations and complex dynamics happen in a small neighborhood of a particular CNN with a symmetric interconnection matrix.

Discontinuous Neural Networks for Finite-Time Solution of Time-Dependent Linear Equations

This paper considers a class of nonsmooth neural networks with discontinuous hard-limiter (signum) neuron activations for solving time-dependent (TD) systems of algebraic linear equations (ALEs). The networks are defined by the subdifferential with respect to the state variables of an energy function given by the L1 norm of the error between the state and the TD-ALE solution. It is shown that when the penalty parameter exceeds a quantitatively estimated threshold the networks are able to reach in finite time, and exactly track thereafter, the target solution of the TD-ALE. Furthermore, this paper discusses the tightness of the estimated threshold and also points out key differences in the role played by this threshold with respect to networks for solving time-invariant ALEs. It is also shown that these convergence results are robust with respect to small perturbations of the neuron interconnection matrices. The dynamics of the proposed networks are rigorously studied by using tools from nonsmooth analysis, the concept of subdifferential of convex functions, and that of solutions in the sense of Filippov of dynamical systems with discontinuous nonlinearities.

Robustness of convergence in finite time for linear programming neural networks

A recent work has introduced a class of neural networks for solving linear programming problems, where all trajectories converge toward the global optimal solution in finite time. In this paper, it is shown that global convergence in finite time is robust with respect to tolerances in the electronic implementation, and an estimate of the allowed perturbations preserving convergence is obtained. Copyright

HARMONIC BALANCE APPROACH TO PREDICT PERIOD-DOUBLING BIFURCATIONS IN NEARLY SYMMETRIC CNNs

This paper further investigates a basic issue that has received attention in the recent literature, namely, the robustness of complete stability of standard Cellular Neural Networks (CNNs) with respect to small perturbations of the nominal symmetric interconnections. More specifically, a class of third-order CNNs with a nominal symmetric interconnection matrix is considered, and the Harmonic Balance (HB) method is exploited for addressing the possible existence of period-doubling bifurcations, and complex dynamics, for small perturbations of the nominal interconnections. The main result is that there are indeed parameter sets close to symmetry for which period-doubling bifurcations are predicted by the HB method. Moreover, the predictions are found to be reliable and accurate by means of computer simulations.

Convergence and Multistability of Nonsymmetric Cellular Neural Networks With Memristors

Recent work has considered a class of cellular neural networks (CNNs) where each cell contains an ideal capacitor and an ideal flux-controlled memristor. One main feature is that during the analog computation the memristor is assumed to be a dynamic element, hence each cell is second-order with state variables given by the capacitor voltage and the memristor flux. Such CNNs, named dynamic memristor (DM)-CNNs, were proved to be convergent when a symmetry condition for the cell interconnections is satisfied. The goal of this paper is to investigate convergence and multistability of DM-CNNs in the general case of nonsymmetric interconnections. The main result is that convergence holds when there are (possibly) nonsymmetric, non-negative interconnections between cells and an irreducibility assumption is satisfied. This result appears to be similar to the classic convergence result for standard (S)-CNNs with positive cell-linking templates. Yet, due to the presence of DMs, a DM-CNN displays some basically different and peculiar dynamical properties with respect to S-CNNs. One key difference is that the DM-CNN processing is based on the time evolution of memristor fluxes instead of capacitor voltages as it happens for S-CNNs. Moreover, when a steady state is reached, all voltages and currents, and hence power consumption of a DM-CNN vanish. This notwithstanding the memristors are able to store in a nonvolatile way the result of the processing. Voltages, currents and power instead do not vanish when an S-CNN reaches a steady state.

Physically Unclonable Functions Derived From Cellular Neural Networks

We propose the design of Physically Unclonable Functions (PUFs) exploiting the nonlinear behavior of Cellular Neural Networks (CNNs). Our work derives from some theoretical results achieved within the theory of CNNs, adapted to a simpler case. The theoretical analysis discussed in this work has a general validity, whereas the presented basic hardware solution (i.e., the PUF electronic implementation) has to be understood as a reference demonstrating circuit to be further optimized and developed for a profitable use of the proposed approach. Theoretical results have been validated experimentally.

Convergent Dynamics of Nonreciprocal Differential Variational Inequalities Modeling Neural Networks

The paper addresses convergence of solutions for a class of differential inclusions termed differential variational inequalities (DVIs). Each DVI describes the dynamics of a neural network (NN) evolving in a closed hypercube of \BBR n and defined by a continuously differentiable, cooperative and (possibly) nonreciprocal vector field f. The main result in the paper is that under a new condition on f, which is called strong Kamke-Müller (SKM) condition, the solution semiflow generated by the DVI is strongly order preserving (SOP) and hence it satisfies a Limit Set Dichotomy and enjoys generic convergence properties. A characterization of the SKM condition is given in terms of the interconnection properties of the Jacobian matrix of f. In the case where f is an affine, or a linear, vector field the considered DVIs include two relevant classes of NNs, namely, the linear systems operating on a closed hypercube, also known as linear systems in saturated mode (LSSMs), and the full-range (FR) model of cellular neural networks (CNNs). By applying the results to LSSMs it is obtained that any cooperative LSSM with a (possibly) nonsymmetric and fully interconnected matrix is generically convergent. Analogous results hold for FRCNNs. All the obtained convergence results hold in the general case where the DVIs, and the LSSMs and FRCNNs, possess multiple equilibrium points.

Łojasiewicz inequality and exponential convergence of the full-range model of CNNs

This paper considers the Full-range (FR) model of Cellular Neural Networks (CNNs) in the case where the signal range is delimited by an ideal hard-limiter nonlinearity with two vertical segments in the i−v characteristic. A Łojasiewicz inequality around any equilibrium point, for a FRCNN with a symmetric interconnection matrix, is proved. It is also shown that the Łojasiewicz exponent is equal to **image**. The main consequence is that any forward solution of a symmetric FRCNN has finite length and is exponentially convergent toward an equilibrium point, even in degenerate situations where the FRCNN possesses non-isolated equilibrium points. The obtained results are shown to improve the previous results in literature on convergence or almost convergence of symmetric FRCNNs. Copyright