This article generalizes two recently proposed opinion dynamics models with control. The generalized model consists of a standard model of agents interacting with each other, to which affine control inputs from players are added. The controls, influencing the opinions of agents, are exercised by entities called players, who specify targets, possibly conflicting, for agents. Three game-playing procedures are defined: sequential, parallel, and asynchronous. Each player has knowledge of the current state of all agents, but no other information about the other players. The player controls are designed using one step ahead optimization. This leads to several novel results: easily computable control policies for each player that depend only on the player’s own information and conditions for convergence to the equilibrium as well as formulas for the latter. Comparisons showing advantages over prior Riccati equation-based methods for networks of different sizes are provided. The code to reproduce all examples and simulations is available on the GitHub site. Overall, the main contribution is the one step ahead optimal control (OSAOC) framework for influencing multiagent opinion dynamics in a decentralized game-theoretic setting.

We add a missing hypothesis, inadvertently omitted in [1], to Theorems 1, 2, and 3, namely that the sets of agents (nodes) influenced by players are disjoint. All the experimental results and simulations shown in the article satisfy the disjoint set hypothesis and remain valid, with no changes. The abstract and conclusion are modified to include the words “disjoint set” (of agents).

This paper presents a complete analysis of a new model of market share dynamics under advertising effort, taking into account word-of-mouth (WOM) interactions between satisfied customers, dissatisfied defectors, as well as undecided customers. The populations of satisfied customers and defectors are both modeled as competing predators preying on a population of undecided customers, using Lotka-Volterra-type interaction terms, which have also been used in a related, but different, class of WOM and electronic WOM models. The proposed model describes the dynamics of market share from arbitrary nonnegative initial conditions, up to and including the market in which there are no longer any undecided customers, thereby extending both the classical Vidale-Wolfe model in which the market with no undecided customers is never reached at equilibrium due to the positive decay term, as well as the Lanchester model which only deals with the market with no undecided customers. Another new feature of the proposed model is that, even under constant advertising effort, and fixed values of interaction coefficients, different outcomes can arise, depending on the initial fractions of satisfied customers and defectors. The design of a class of advertising policies that attain a desired market share is also presented, with corresponding numerical simulations.

Though the Extreme Learning Machine (ELM) has become quite popular in recent years, there are no performance guarantees; the resultant networks also tend to be densely connected. The complexity of a learning machine may be measured by the Vapnik-Chervonenkis (VC) dimension, and a small VC dimension leads to good generalization and lower test set errors. The Minimal Complexity Machine (MCM), that has been proposed very recently, shows that it is possible to learn a classifier with minimal VC dimension, leading to sparse representations and good generalization. In this paper, we draw on results from the MCM to propose a hybrid variant of the ELM, termed the Minimal Complexity - Extreme Learning Machine (MC-ELM), in order to realize a robust classifier that minimizes an exact bound on the VC dimension. The MC-ELM solves a linear programming problem for the last layer and offers the advantages of large margin and low VC dimension. In effect, the learning paradigm elucidated in this paper helps us build a classifier which is based on a minimal representation of the training data owing to MCM, and high training speed attributed to ELM. This makes it feasible for use in complex machine learning applications, where these advantages are of significance.

This paper introduces an ACO model and associated algorithm, called Coupled EigenAnt, for the problem of finding the shortest of N paths between a source and a destination node. It is based on the recently introduced EigenAnt algorithm, the novelty being that it allows probabilistic path choice on both the forward and return journeys, as well as the fact that it introduces decay of pheromone deposition following a geometric progression. Equilibrium points of the model are calculated and the local stability of the two path synchronous version analyzed. Simulations illustrate the main features of the algorithm.

This paper presents a Hill-climbing technique applied to a residential energy system control and management, based on battery energy storage connected to power grids. The main focus is to develop an optimal controller that is both easy to implement and capable of minimizing the electricity cost for residential customers. Simulation results corroborate the advantages of the proposed method.

This paper presents a unified way to design neural networks characterized as second-order ordinary differential equations (ODE), the trajectories of which can converge to the global minimum of nonconvex scalar functions. These neural networks, sometimes also called continuous-time algorithms, are interpreted as closed-loop control systems and the state feedback design is based on control Lyapunov functions. The focus is on a new family of continuous-time versions of conjugate gradient method, named controlled conjugate gradient (CCG) nets, that generalize heavy ball with friction (HBF) nets. For nonconvex functions, the goal of these nets is to produce trajectories that start from an arbitrary initial point and can escape from local minima, thereby increasing the chances of converging to the global minimum. Several numerical examples are given, using benchmark problems, showing that this escape and subsequent convergence to the global minimum occurs.

This paper presents a unified approach to the design of neural networks that aim to minimize scalar nonconvex functions that have continuous first- and second-order derivatives and a unique global minimum. The approach is based on interpreting the function as a controlled object, namely one that has an output (the function value) that has to be driven to its smallest value by suitable manipulation of its inputs: this is achieved by the use of the control Liapunov function (CLF) technique, well known in systems and control theory. This approach leads naturally to the design of second-order differential equations which are the mathematical models of the corresponding implementations as neural networks. Preliminary numerical simulations indicate that, on a small suite of benchmark test problems, a continuous version of the well known conjugate gradient algorithm, designed by the proposed CLF method, has better performance than its competitors, such as the heavy ball with friction method or the more recent dynamic inertial Newton-like method.

The problem of restoring images degraded by linear position invariant distortions and noise is solved by means of a L1-norm regularization, which is equivalent to determining a L1-norm solution of an overdetermined system of linear equations, which results from a data-fitting term plus a regularization term that are both in L1norm. This system is solved by means of a gradient-based neural network with a discontinuous activation function, which is ensured to converge to a L1-norm solution of the corresponding system of linear equations.

This paper presents the implementation of two neural networks for SVM training in parallel computers. The results obtained are compared with two well known packages for SVM training and the parallel implementation shows that the neural network approach can be as accurate as the traditional packages and, since the proposed gradient-based neural networks can be easily parallelized, the proposed approach is scalable and the training times can be considerably reduced.

The standard conjugate gradient (CG) method uses orthogonality of the residues to simplify the formulas for the parameters necessary for convergence. In adaptive filtering, the sample-by-sample update of the correlation matrix and the cross-correlation vector causes a loss of the residue orthogonality in a modified online algorithm, which, in turn, results in loss of convergence and an increase of the filter quadratic mean error. This letter extends a recently proposed control Liapunov function analysis of the CG method viewed as a dynamic system in the standard feedback configuration to the case of adaptive filtering.

A gradient system with discontinuous righthand side that solves an underdetermined system of linear equations in the L/sub 1/ norm is presented. An upper bound estimate for finite time convergence to a solution set of the system of linear equations is shown by means of the Persidskii form of the gradient system and the corresponding nonsmooth diagonal type Lyapunov function. This class of systems can be interpreted as a recurrent neural network and an application devoted to solving least squares support vector machines (LS-SVM) is used as an example.

This paper implements support vector machines (SVM) for the discrimination of nonseparable classes using gradient systems with discontinuous righthand sides. The gradient systems are obtained from an exact penalty method applied to the constrained quadratic optimization problems. Global convergence to the solution of the corresponding constrained problems is shown to be independent of the penalty parameters and of the regularization parameter of the SVM.

A k-winners-take-all (KWTA) problem is formulated as a linear programming (LP) problem with bounded variables. The solution set of the LP problem determines the winners. The LP problem is converted into an unconstrained optimization problem with two exact penalty functions, that is solved by using a gradient descent method implemented as a neural network. Theoretical results ensuring the convergence to the correct solution are provided.

It is shown that the assumption of D-stability of the interconnection matrix, together with the standard assumptions on the activation functions, guarantee the existence of a unique equilibrium under a synchronous mode of operation as well as a class of asynchronous modes. For the synchronous mode, these assumptions are also shown to imply local asymptotic stability of the equilibrium. For the asynchronous mode of operation, two results are derived. First, it is shown that symmetry and stability of the interconnection matrix guarantee local asymptotic stability of the equilibrium under a class of asynchronous modes-this is referred to as local absolute asymptotic stability. Second, it is shown that, under the standard assumptions, if the nonnegative matrix whose elements are the absolute values of the corresponding elements of the interconnection matrix is stable, then the equilibrium is globally absolutely asymptotically stable under a class of asynchronous modes. The results obtained are discussed from the points of view of their applications, robustness, and their relationship to earlier results.

This paper formalizes a general technique to combine different methods in the solution of large systems of nonlinear equations using parallel asynchronous implementations on distributed-memory multiprocessor systems. Such combinations of methods, referred to as team algorithms, are evaluated as a way of obtaining desirable properties of different methods and a sufficient condition for their convergence is derived. The load flow problem of electrical power networks is presented as an example problem that, under certain conditions, has the characteristics to make a team algorithm an appealing choice for its solution. Experimental results of an implementation on an Intel iPSC/860 Hypercube are reported, showing that considerable speedup and robustness can be obtained using team algorithms.

This paper investigates a continuous-valued discrete-time analog of the well-known continuous-valued continuous-time Hopfield neural network model, first proposed by Takeda and Goodman (1986). It is shown that the assumption of D-stability of the interconnection matrix, together with the standard assumptions on the activation functions, guarantee the existence of a unique equilibrium under a synchronous mode of operation as well as a class of asynchronous modes. Conditions for local and global asymptotic stability are also derived, for both synchronous and asynchronous modes of operation. The results obtained are discussed both from the points of view of applications and robustness.