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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

When the neuron interconnection matrix is symmetric, the standard Cellular Neural Networks (CNN's) introduced by Chua and Yang [1988a] are known to be completely stable, that is, each trajectory converges towards some stationary state. In this paper it is shown that the interconnection symmetry, though ensuring complete stability, is not in the general case sufficient to guarantee that complete stability is robust with respect to sufficiently small perturbations of the interconnections. To this end, a class of third-order CNN's with competitive (inhibitory) interconnections between distinct neurons is introduced. The analysis of the dynamical behavior shows that such a class contains nonsymmetric CNN's exhibiting persistent oscillations, even if the interconnection matrix is arbitrarily close to some symmetric matrix. This result is of obvious relevance in view of CNN's implementation, since perfect interconnection symmetry in unattainable in hardware (e.g. VLSI) realizations. More insight on the behavior of the CNN's here introduced is gained by discussing the analogies with the dynamics of the May and Leonard model of the voting paradox, a special Volterra-Lotka model of three competing species. Finally, it is shown that the results in this paper can also be viewed as an extension of previous results by Zou and Nossek for a two-cell CNN with opposite-sign interconnections between distinct neurons. Such an extension has a significant interpretation in the framework of a general theorem by Smale for competitive dynamical systems. *

SUMMARYThe 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.

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This paper considers a class of nonsymmetric cooperative neural networks (NNs) where the neurons are fully interconnected and the neuron activations are modeled by piecewise linear (PL) functions. The solution semiflow generated by cooperative PLNNs is monotone but, due to the horizontal segments in the neuron activations, is not eventually strongly monotone (ESM). The main result in this paper is that it is possible to prove a peculiar form of the LIMIT SET DICHOTOMY for this class of cooperative PLNNs. Such a form is slightly weaker than the standard form valid for ESM semiflows, but this notwithstanding it permits to establish a result on convergence analogous to that valid for ESM semiflows. Namely, for almost every choice of the initial conditions, each solution of a fully interconnected cooperative PLNN converges toward an equilibrium point, depending on the initial conditions, as + . From a methodological viewpoint, this paper extends some basic techniques and tools valid for ESM semiflows, in order that they can be applied to the monotone semiflows generated by the considered class of cooperative PLNNs.Index Terms-Convergence, cooperative neural networks, dynamical systems, limit set dichotomy, monotone and eventually strongly monotone semiflows.

The paper analyzes some fundamental properties of the solution semiflow of nonsymmetric cooperative standard (S) cellular neural networks (CNNs) with a typical three-segment piecewise-linear (pwl) neuron activation. Two relevant subclasses of SCNNs, corresponding to one-dimensional circular SCNNs with two-sided or single-sided positive interconnections between nearest neighboring neurons only, are considered. For these subclasses it is shown that the associated solution semiflow satisfies the fundamental properties of the CONVERGENCE CRITERION, the NONORDERING OF LIMIT SETS and the LIMIT SET DICHOTOMY, and that this is true although the semiflow is not eventually strongly monotone. As a consequence such CNNs are almost convergent, i.e., almost all solutions converge toward an equilibrium point as time tends to infinity. To the authors' knowledge the paper is the first rigorous investigation on the geometry of limit sets and convergence properties of cooperative SCNNs with a pwl neuron activation. All available convergence results in the literature indeed concern a modified cooperative CNN model where the original pwl activation of the SCNN model is replaced by a continuously differentiable strictly increasing sigmoid function. The main results in the paper are established by conducting a deep analysis of the properties of the omega-limit sets of the solution semiflow defined by the considered subclasses of SCNNs. In doing so the paper exploits and extends some mathematical tools for monotone systems in order that they can be applied to pwl vector fields that govern the dynamics of SCNNs. By using some transformations and referring to specific examples it is also shown that the treatment in the paper can be extended to other subclasses of SCNNs.