Quantized iterative learning control for impulsive differential inclusion systems with data dropouts.

This paper studies the quantized iterative learning control with encoding-decoding mechanism of a class of impulsive differential inclusion systems with random data dropouts. First, the set-valued mappings in the differential inclusion systems are transformed into single-valued mappings by using the Steiner-type selector. Then, a learning algorithm based on the intermittent update principle is designed to address the data asynchronism problem caused by two-sided data dropouts. If the data are successfully transmitted at the actuator and measurement sides, then the control input is effectively updated. Furthermore, a suitable scaling sequence is introduced to ensure the system output to achieve zero-error tracking performance for a desired trajectory. An upper bound of the quantization level is determined such that the quantization error is always bounded. The results show that the quantization method reduces the burden of network communication at the cost of increasing the amount of computation, and the learning algorithm does not require the data dropouts to satisfy a certain probability distribution. Finally, the effectiveness of the learning algorithm is verified by numerical simulations of the switched reluctance motor system.

A New Decomposition of the Graph Laplacian and the Binomial Structure of Mass-Action Systems.

We provide a new decomposition of the Laplacian matrix (for labeled directed graphs with strongly connected components), involving an invertible core matrix, the vector of tree constants, and the incidence matrix of an auxiliary graph, representing an order on the vertices. Depending on the particular order, the core matrix has additional properties. Our results are graph-theoretic/algebraic in nature. As a first application, we further clarify the binomial structure of (weakly reversible) mass-action systems, arising from chemical reaction networks. Second, we extend a classical result by Horn and Jackson on the asymptotic stability of special steady states (complex-balanced equilibria). Here, the new decomposition of the graph Laplacian allows us to consider regions in the positive orthant with given monomial evaluation orders (and corresponding polyhedral cones in logarithmic coordinates). As it turns out, all dynamical systems are asymptotically stable that can be embedded in certain binomial differential inclusions. In particular, this holds for complex-balanced mass-action systems, and hence, we also obtain a polyhedral-geometry proof of the classical result.

Equivalent Formulations of Optimal Control Problems with Maximum Cost and Applications.

We revisit the optimal control problem with maximum cost with the objective to provide different equivalent reformulations suitable to numerical methods. We propose two reformulations in terms of extended Mayer problems with state constraints, and another one in terms of a differential inclusion with upper-semi-continuous right member without state constraint. For the latter we also propose a scheme that approximates from below the optimal value. These approaches are illustrated and discussed in several examples.

Neuronal Population Transitions Across a Quiescent-to-Active Frontier and Bifurcation.

The mechanistic understanding of why neuronal population activity hovers on criticality remains unresolved despite the availability of experimental results. Without a coherent mathematical framework, the presence of power-law scaling is not straightforward to reconcile with findings implying epileptiform activity. Although multiple pictures have been proposed to relate the power-law scaling of avalanche statistics to phase transitions, the existence of a phase boundary in parameter space is until now an assumption. Herein, a framework based on differential inclusions, which departs from approaches constructed from differential equations, is shown to offer an adequate consolidation of evidences apparently connected to criticality and those linked to hyperexcitability. Through this framework, the phase boundary is elucidated in a parameter space spanned by variables representing levels of excitation and inhibition in a neuronal network. The interpretation of neuronal populations based on this approach offers insights on the role of pharmacological and endocrinal signaling in the homeostatic regulation of neuronal population activity.

Smoothing neural network for L0 regularized optimization problem with general convex constraints.

In this paper, we propose a neural network modeled by a differential inclusion to solve a class of discontinuous and nonconvex sparse regression problems with general convex constraints, whose objective function is the sum of a convex but not necessarily differentiable loss function and L0 regularization. We construct a smoothing relaxation function of L0 regularization and propose a neural network to solve the considered problem. We prove that the solution of proposed neural network with any initial point satisfying linear equality constraints is global existent, bounded and reaches the feasible region in finite time and remains there thereafter. Moreover, the solution of proposed neural network is its slow solution and any accumulation point of it is a Clarke stationary point of the brought forward nonconvex smoothing approximation problem. In the box-constrained case, all accumulation points of the solution own a unified lower bound property and have a common support set. Except for a special case, any accumulation point of the solution is a local minimizer of the considered problem. In particular, the proposed neural network has a simple structure than most existing neural networks for solving the locally Lipschitz continuous but nonsmooth nonconvex problems. Finally, we give some numerical experiments to show the efficiency of proposed neural network.

On solvability of the impulsive Cauchy problem for integro-differential inclusions with non-densely defined operators.

We prove the existence of at least one integrated solution to an impulsive Cauchy problem for an integro-differential inclusion in a Banach space with a non-densely defined operator. Since we look for integrated solution we do not need to assume that A is a Hille Yosida operator. We exploit a technique based on the measure of weak non-compactness which allows us to avoid any hypotheses of compactness both on the semigroup generated by the linear part and on the nonlinear term. As the main tool in the proof of our existence result, we are using the Glicksberg-Ky Fan theorem on a fixed point for a multivalued map on a compact convex subset of a locally convex topological vector space. This article is part of the theme issue 'Topological degree and fixed point theories in differential and difference equations'.

Stabilization of non-smooth variable order switched nonlinear systems.

The paper discusses the issue of global asymptotic stabilization for non-smooth variable order nonlinear switched systems with partial unstable modes. The existence and uniqueness of solution for the considered system is firstly verified by utilizing Gronwall-Bellman inequality and the inductive method. Then, a slow switching strategy is performed for the stable modes and the unstable modes are handled by a fast switching mechanism. Under the framework of Filippov differential inclusion, sufficient stabilization criteria are derived by applying the mode-dependent average dwell time and dwell time schemes. Finally, some objects in real life are introduced and a numerical simulation is offered to show the validity of the obtained results.

Periodicity and finite-time periodic synchronization of discontinuous complex-valued neural networks.

This paper discusses the issue of periodicity and finite-time periodic synchronization of discontinuous complex-valued neural networks (CVNNs). Based on a modified version of Kakutani's fixed point theorem, general conditions are obtained to guarantee the periodicity of discontinuous CVNNs. Next, several criteria for finite-time periodic synchronization (FTPS) are given by using a new proposed finite-time convergence theorem. Different from the traditional convergence lemma, the estimated upper bound of the derivative of the Lyapunov function (LF) is allowed to be indefinite or even positive. In order to achieve FTPS, novel discontinuous control algorithms, including state-feedback control algorithm and generalized pinning control algorithm, are designed. In the generalized pinning control algorithm, a guideline is proposed to select neurons to pin the designed controller. Finally, two simulations are given to substantiate the main results.

Plant coexistence mediated by adaptive foraging preferences of exploiters or mutualists.

Coexistence of plants depends on their competition for common resources and indirect interactions mediated by shared exploiters or mutualists. These interactions are driven either by changes in animal abundance (density-mediated interactions, e.g., apparent competition), or by changes in animal preferences for plants (behaviorally-mediated interactions). This article studies effects of behaviorally-mediated interactions on two plant population dynamics and animal preference dynamics when animal densities are fixed. Animals can be either adaptive exploiters or adaptive mutualists (e.g., herbivores or pollinators) that maximize their fitness. Analysis of the model shows that adaptive animal preferences for plants can lead to multiple outcomes of plant coexistence with different levels of specialization or generalism for the mediator animal species. In particular, exploiter generalism promotes plant coexistence even when inter-specific competition is too strong to make plant coexistence possible without exploiters, and mutualist specialization promotes plant coexistence at alternative stable states when plant inter-specific competition is weak. Introducing a new concept of generalized isoclines allows us to fully analyze the model with respect to the strength of competitive interactions between plants (weak or strong), and the type of interaction between plants and animals (exploitation or mutualism).

Fixed-time synchronization of coupled memristor-based neural networks with time-varying delays.

This paper investigates the fixed-time synchronization of Memristor-based neural networks with time-delayed and coupled. In view of the retarded differential inclusions theory, drive-response concept, the authors give some sufficient conditions to ensure the fixed-time synchronization issue of Memristor-based neural networks. Two novel state-feedback controllers and adaptive controller are designed such that the system can realize fixed-time complete synchronization by means of inequality technique and non-smooth analysis theory. It is worth to point out that, without desiring values of the initial conditions or under the linear growth condition of the controller, the settling time of fixed-time synchronization is estimated. Finally, an example is given to further illustrate the benefits of the proposed switched control approach.

Dynamics of economic growth: Uncertainty treatment using differential inclusions.

The article is focused on applications of the differential inclusions to the models of economic growth, rather than the model building. The models are taken from the known literature, and some modifications are introduced to reflect an additional inertia. The aim is to treat the uncertainty in the model parameters by using differential inclusions instead of the stochastic approach. The reachable sets for the models are shown, to assess the possible ranges of the outcome with given parameters uncertainty. The approach may be interpreted as a generalization to the system dynamics methodology, providing attainable sets instead of single model trajectory and simple sensitivity analysis. A comparison with Powersim risk analysis is provided. The models of Solow and Swan, Mankiw, Bhattacharya, Romer and Weil are used. A brief review of the models is given, and several examples of simple simulations, differential inclusion applications and optimization are presented.

Neural network for nonsmooth pseudoconvex optimization with general convex constraints.

In this paper, a one-layer recurrent neural network is proposed for solving a class of nonsmooth, pseudoconvex optimization problems with general convex constraints. Based on the smoothing method, we construct a new regularization function, which does not depend on any information of the feasible region. Thanks to the special structure of the regularization function, we prove the global existence, uniqueness and "slow solution" character of the state of the proposed neural network. Moreover, the state solution of the proposed network is proved to be convergent to the feasible region in finite time and to the optimal solution set of the related optimization problem subsequently. In particular, the convergence of the state to an exact optimal solution is also considered in this paper. Numerical examples with simulation results are given to show the efficiency and good characteristics of the proposed network. In addition, some preliminary theoretical analysis and application of the proposed network for a wider class of dynamic portfolio optimization are included.

Generalized stability for discontinuous complex-valued Hopfield neural networks via differential inclusions.

Some dynamical behaviours of discontinuous complex-valued Hopfield neural networks are discussed in this paper. First, we introduce a method to construct the complex-valued set-valued mapping and define some basic definitions for discontinuous complex-valued differential equations. In addition, Leray-Schauder alternative theorem is used to analyse the equilibrium existence of the networks. Lastly, we present the dynamical behaviours, including global stability and convergence in measure for discontinuous complex-valued neural networks (CVNNs) via differential inclusions. The main contribution of this paper is that we extend previous studies on continuous CVNNs to discontinuous ones. Several simulations are given to substantiate the correction of the proposed results.

Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity.

We consider a partial differential inclusion problem which models stress-free martensitic inclusions in an austenitic matrix, based on the standard geometrically nonlinear elasticity theory. We show that for specific parameter choices there exist piecewise affine continuous solutions for the square-to-oblique and the hexagonal-to-oblique phase transitions. This suggests that for specific crystallographic parameters the hysteresis of the phase transformation will be particularly small.

A non-penalty recurrent neural network for solving a class of constrained optimization problems.

In this paper, we explain a methodology to analyze convergence of some differential inclusion-based neural networks for solving nonsmooth optimization problems. For a general differential inclusion, we show that if its right hand-side set valued map satisfies some conditions, then solution trajectory of the differential inclusion converges to optimal solution set of its corresponding in optimization problem. Based on the obtained methodology, we introduce a new recurrent neural network for solving nonsmooth optimization problems. Objective function does not need to be convex on R(n) nor does the new neural network model require any penalty parameter. We compare our new method with some penalty-based and non-penalty based models. Moreover for differentiable cases, we implement circuit diagram of the new neural network.

Periodicity and global exponential stability of generalized Cohen-Grossberg neural networks with discontinuous activations and mixed delays.

In this paper, we investigate the periodic dynamical behaviors for a class of general Cohen-Grossberg neural networks with discontinuous right-hand sides, time-varying and distributed delays. By means of retarded differential inclusions theory and the fixed point theorem of multi-valued maps, the existence of periodic solutions for the neural networks is obtained. After that, we derive some sufficient conditions for the global exponential stability and convergence of the neural networks, in terms of nonsmooth analysis theory with generalized Lyapunov approach. Without assuming the boundedness (or the growth condition) and monotonicity of the discontinuous neuron activation functions, our results will also be valid. Moreover, our results extend previous works not only on discrete time-varying and distributed delayed neural networks with continuous or even Lipschitz continuous activations, but also on discrete time-varying and distributed delayed neural networks with discontinuous activations. We give some numerical examples to show the applicability and effectiveness of our main results.

Caminhos bifurcantes na educação inclusiva: inclusões e rebeldias silenciosas na educação pública / Rupturing paths in inclusive education: inclusions and silent rebellions in the public education

Este artigo apresenta parte das reflexões efetuadas na pesquisa de mestrado "Políticas inclusivas no chão da escola: usinagens e rebeldias no front-dabatalha" realizada em duas escolas de um município situado na região norte do estado do Espírito Santo. Por meio de conversações buscou-se cartografar os processos de inclusão gestados nas práticas educacionais. Nosso temário geral foi a Educação Inclusiva, campo de intervenção usualmente associado à idéia de inclusão de pessoas com Necessidades Educacionais Especiais (NEE) no ensino regular. Abordamos o tema utilizando especialmente os instrumentos analíticos oferecidos por Michael Hardt e Toni Negri, e Michel Foucault acerca das práticas sociais, dos processos de inclusão e do biopoder. A pesquisa realizada apontou que os modos instituídos que tecem a Educação produzem o chamado fracasso escolar, invisibilizando recusas e inventividades. Apontou ainda, que modos de educar podem revolucionar processos de inclusão diferencial compondo alianças que fortaleçam essas vidas marginais.

This article presents some reflections made on the masters degree research known as "Políticas inclusivas no chão da escola: usinagens e rebeldias no front-da-batalha" (Inclusive policy on the school floor: machining and rebellion at the battlefront). This research took place in two schools from a city at the north region of the state of "Espírito Santo" in Brazil. The inclusion processes managed by the educational system were mapped through reasoning. The main theme considered in the research was the Inclusive Education. This intervention field is usually associated to people with special educational needs who study at regular schools. The themes were approached following Michael Hardt, Toni Negri and Michel Foucault ideas regarding social practices, inclusion processes and biopower. The research showed that the school failure is produced by the established Educational ways. It also showed that the way people educate can revolutionize the differential inclusion processes, making alliances which strengthen these marginal lives.

Caminhos bifurcantes na educação inclusiva: inclusões e rebeldias silenciosas na educação pública / Rupturing paths in inclusive education: inclusions and silent rebellions in the public education

Este artigo apresenta parte das reflexões efetuadas na pesquisa de mestrado "Políticas inclusivas no chão da escola: usinagens e rebeldias no front-dabatalha" realizada em duas escolas de um município situado na região norte do estado do Espírito Santo. Por meio de conversações buscou-se cartografar os processos de inclusão gestados nas práticas educacionais. Nosso temário geral foi a Educação Inclusiva, campo de intervenção usualmente associado à idéia de inclusão de pessoas com Necessidades Educacionais Especiais (NEE) no ensino regular. Abordamos o tema utilizando especialmente os instrumentos analíticos oferecidos por Michael Hardt e Toni Negri, e Michel Foucault acerca das práticas sociais, dos processos de inclusão e do biopoder. A pesquisa realizada apontou que os modos instituídos que tecem a Educação produzem o chamado fracasso escolar, invisibilizando recusas e inventividades. Apontou ainda, que modos de educar podem revolucionar processos de inclusão diferencial compondo alianças que fortaleçam essas vidas "marginais".(AU)

This article presents some reflections made on the masters degree research known as "Políticas inclusivas no chão da escola: usinagens e rebeldias no front-da-batalha" (Inclusive policy on the school floor: machining and rebellion at the battlefront). This research took place in two schools from a city at the north region of the state of "Espírito Santo" in Brazil. The inclusion processes managed by the educational system were mapped through reasoning. The main theme considered in the research was the Inclusive Education. This intervention field is usually associated to people with special educational needs who study at regular schools. The themes were approached following Michael Hardt, Toni Negri and Michel Foucault ideas regarding social practices, inclusion processes and biopower. The research showed that the school failure is produced by the established Educational ways. It also showed that the way people educate can revolutionize the differential inclusion processes, making alliances which strengthen these marginal lives.(AU)