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This paper develops a Lyapunov approach for studying convergence and stability of a class of differential inclusions termed differential variational inequalities (DVIs). The DVIs describe the dynamics of a general system evolving in a compact convex subset of the state space. In particular, they include the dynamics of the full-range (FR) model of cellular neural networks (CNNs), which is characterized by hard-limiter nonlinearities with vertical segments in the i--v characteristic. The approach is based on the following two main tools: 1) a set-valued derivative, which enables to compute the evolution of a Lyapunov function along the solutions of the DVIs without involving integrations, and 2) an extended version of LaSalle's invariance principle, which permits to study the limiting behavior of the solutions with respect to the invariant sets of the DVIs. Then, this paper establishes conditions for convergence (complete stability) of DVIs in the presence of multiple equilibrium points (EPs), global asymptotic stability (GAS), and global exponential stability (GES) of the unique EP. These conditions are applied to investigate convergence, GAS, and GES for FR-CNNs and some extended classes of FR-CNNs. It is shown that, by means of the techniques developed in this paper, the analysis of convergence and stability of FR-CNNs is no more difficult than that of the standard (S)-CNNs. In addition, there are significant cases, such as the symmetric FR-CNNs and the nonsymmetric FR-CNNs with a Lyapunov diagonally stable matrix, where the proof of convergence or global stability is much simpler than that of the S-CNNs. Index Terms--Cellular neural networks (CNNs), convergence, differential variational inequalities (DVIs), full-range (FR) model, LaSalle's invariance principle, set-valued derivative.

The problem of simultaneous localization and map building for a team of cooperating robots moving in an unknown environment is addressed. The robots have to estimate the position of distinguishable static landmarks, and then localize themselves with respect to other robots and landmarks, exploiting distance and angle measurements. A novel set theoretic approach to this problem is presented. The proposed localization algorithm provides position estimates and guaranteed uncertainty regions for all robots and landmarks in the environment. Index Terms--Localization, map building, multirobot systems, set membership, uncertainty.

It is known that additive neural networks with a symmetric interconnection matrix are completely stable, i.e., each trajectory converges toward some equilibrium point. This paper addresses the fundamental question of robustness of complete stability of additive neural networks with respect to small perturbations of the nominal symmetric interconnections. It is shown that in the general case, complete stability is not robust. More precisely, the paper considers a class of neural networks, and gives a necessary and sufficient condition for the existence of Hopf bifurcations (HBs) at the equilibrium point at the origin, arbitrarily close to symmetry. Such HBs originate stable limit cycles and hence cause the loss of complete stability. Furthermore, the paper highlights situations where the HBs are particularly critical, in the sense that the amplitude of the limit cycles is very sensitive to errors due to tolerances in the electronic implementation of the neuron interconnections. It is shown that sensitivity is crucially dependent on the neuron nonlinearity, and it is also significantly influenced by the features of the interconnection matrix and the network dimension. Finally, limitations of the obtained results are discussed and hints for future work are given. Index Terms--Complete stability, Hopf bifurcations, limit cycles, neural networks, robustness.

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. [S0022-0434(00)01101-1]

Summary: The paper studies nonlinear dynamics and bifurcations of a class of memristor oscillatory circuits obtained by replacing the nonlinear resistor of a Chua's oscillator with a flux‐controlled memristor. A recently developed technique, named flux‐charge analysis method, has shown that the state space of such circuits can be decomposed in invariant manifolds, where each manifold is characterized by a different dynamics and different attractors. Goal of the paper is to investigate the use of the harmonic balance method in combination with flux‐charge analysis method in order to study the different kinds of bifurcations generated by changing the circuit parameters on a fixed manifold, changing manifold for a fixed parameter set (bifurcations without parameters), or changing simultaneously circuit parameters and manifolds. The main result is that the harmonic balance method is quite simple to apply in this rich bifurcation context and is effective to detect Hopf and to accurately predict period‐doubling bifurcations of all these different kinds. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]