Heterogeneous Dynamical Systems Research Articles

Asymmetric space-dependent systems: partial stabilization through the addition of noise and exact solutions for the corresponding nonlinear Langevin equations

In many instances, the dynamical richness and complexity observed in natural phenomena can be related to stochastic drives influencing their temporal evolution. For example, random noise allied to spatial asymmetries may induce stabilization of otherwise diverging trajectories in dynamical systems. However, to identify how exactly this takes place in actual processes usually is not a simple task. Here we unveil a few trends leading to dynamical stabilization and diversity of behavior by introducing Gaussian white noise to a class of exactly solvable non-linear deterministic models displaying space-dependent drifts. For the resulting nonlinear Langevin equations, the associated Fokker-Planck equations can be solved through the similarity method or the Fourier transform technique. By comparing the cases with and without noise, we discuss the changes in the systems dynamical characteristics. Simple examples of drift and diffusion coefficients are explicitly analyzed and comparisons with some other models in the literature are made. Our study illustrates the rich phenomenology originated from spatially heterogeneous dynamical systems under the influence of white noise.

Antagonistic interactions can stabilise fixed points in heterogeneous linear dynamical systems

We analyse the stability of large, linear dynamical systems of variables that interact through a fully connected random matrix and have inhomogeneous growth rates. We show that in the absence of correlations between the coupling strengths, a system with interactions is always less stable than a system without interactions. Contrarily to the uncorrelated case, interactions that are antagonistic, i.e., characterised by negative correlations, can stabilise linear dynamical systems. In particular, when the strength of the interactions is not too strong, systems with antagonistic interactions are more stable than systems without interactions. These results are obtained with an exact theory for the spectral properties of fully connected random matrices with diagonal disorder.

Uncertain Multiagent Systems With Distributed Constrained Optimization Missions and Event-Triggered Communications: Application to Resource Allocation

This article deals with solving distributed optimization problems with equality constraints by a class of uncertain nonlinear heterogeneous dynamic multiagent systems. It is assumed that each agent with an uncertain dynamic model has limited information about the main problem and limited access to the information of the state variables of the other agents. A distributed algorithm that guarantees cooperatively solving of the constrained optimization problem by the agents is proposed. Via applying this algorithm, the agents do not need to continuously broadcast their data. It is shown that the proposed algorithm can be useful in solving resource allocation problems.

NetworkDynamics.jl-Composing and simulating complex networks in Julia.

NetworkDynamics.jl is an easy-to-use and computationally efficient package for simulating heterogeneous dynamical systems on complex networks, written in Julia, a high-level, high-performance, dynamic programming language. By combining state-of-the-art solver algorithms from DifferentialEquations.jl with efficient data structures, NetworkDynamics.jl achieves top performance while supporting advanced features such as events, algebraic constraints, time delays, noise terms, and automatic differentiation.

Язык моделирования гетерогенных динамических систем LISMA_HDS

Heterogeneous dynamic systems (HDS) simultaneously describe processes of different physical nature. Systems of this kind are typical for numerous applications. HDSs are characterized by the following features. They are often multimode or hybrid systems. In general, their modes are defined as initial value problems (Cauchy problems) for implicit differential-algebraic systems of equations. Due to the presence of heterogeneous dynamic components or processes evolving in both time and space, the dimension of the complete system of equations may be pretty high. In some cases, the system of equations has an internal structure, for instance, the differential-algebraic system of equations approximating a partial differential equation by the method of lines. An original huge system of equations can then be algorithmically rewritten in a compact form. Moreover, heterogeneous hybrid dynamical systems can generate events of qualitatively different types. Therefore one has to use different numerical event detection algorithms. Nowadays, HDSs are modeled and simulated in computer environments. The modeling languages widely used by engineers do not allow them to fully specify all the properties of the systems of this class. For instance, they do not include event typing constructs. That is why a declarative general-purpose modeling language named LISMA_HDS has been developed for the computer-aided modeling and ISMA simulation environment. The language takes into account all of the characteristic features of HDSs. It includes constructs for plain or algorithmic declaration of model constants, initial value problems for explicit differential-algebraic systems of equations, and initial guesses for variables. It also allows researchers to define explicit time events, modes and transitions between them upon the occurrence of events of different types, to use macros and implement event control. LISMA_HDS is defined by a generative grammar in an extended Backus-Naur form and semantic constraints. It is proved that the grammar belongs to the LL(2) subclass of context-free grammars.

Set-theoretical approach to finding the range of possible values of the size of a group of objects in a situation of multiple indistinguishability

In situations where it is not possible to timely use new methods for assessing hazardous objects, traditional methods of risk assessment can be supplemented with new methods based on possible assessments of objective primary information. Evaluation of the destructive capacity and consequences of the use of high-risk systems becomes increasingly important as their structural and functional complexity grows.Despite the existence of the considered works on certain aspects, the known approaches to the consideration of the problem of indistinguishability of influencing factors are characterized by limited functionality. These capabilities do not fully provide the required level of reliability when making management decisions. In view of this, the problem of predicting equipment failure caused by an unfavourable coincidence of circumstances due to the indistinguishability of the initial data is one of the urgent tasks of risk management. Its solution is of significant theoretical and practical interest for many complex heterogeneous dynamical systems. The paper deals with a problem from the field of probabilistic modeling. The relevance of the performed research lies in the fact that the existing methods for predicting equipment failure in systems of potentially hazardous objects do not take into account the causes of accidents that occurred due to unfavourable circumstances.The aim of the work is to develop a method for the set-theoretic modeling of the occurrence of problems with equipment due to an unfavourable coincidence of circumstances, which provides a range of possible values for the size of a group with a given composite very dangerous sign. To achieve this goal, the following tasks are solved:– finding the range of possible values of the number of groups of objects modeled by the intersection of indistinguishable sets and finding the range of possible values of the number of groups of objects modeled by the union and the difference of indistinguishable sets;– finding possible values of the number of groups of objects modeled by an arbitrary composite property and generalization of the problem, features of the set-theoretic apparatus of its solution.In the course of the study, it was found that a set of objects with a compound very dangerous feature of an arbitrary type can be associated with a set representing the union of intersections (intersection of unions) of sets of objects with simple features and their complements. Moreover, the operations of intersection, union, and complement constitute a complete set of operations for the most common version of Boolean algebra of sets.

Accelerating the convergence of AFETI partitioned analysis of heterogeneous structural dynamical systems

Variationally based algorithms for the partitioned solution of structural mechanics problems are presented. Two key features of the present algorithms are the judicious application of the d’Alembert-Lagrange principal equations and the use of dominant substructural deformation modes. The paper includes three developments:1. Variational derivation of AFETI parallel solution methods.2. One-level and two-level AFETI implicit transient analysis algorithms with coarse problem included in the projector and based on free floating rigid body modes.3. A new AFETI implicit transient solution algorithm derived by constraining the interface equilibrium equations with the floating and dominant deformational modes.In addition to variational derivations of solution algorithms, the present paper is strived to offer new physical and/or numerical insight as each of variational derivational steps is succinctly explained. Performance evaluations of the algorithms described herein are presented.

Cultural-Dialogic Interdeterminist Metaperspective for Mental Health and Well-Being

The static, fragmentary nature of the existing approaches to the mental health and wellbeing problems, which cannot grasp the dynamic, nonlinear, and heterogeneous nature of changes in the external natural and social environment, is stated. Author's attempt to extend the problem of this problem field vision horizons offers cultural-dialogic interdeterminist metatheory of psychological knowledge integration. Based on the determinist and indeterminist directions of scientific thought analysis is proved the epistemological heuristic potential of the cultural-dialogic interdeterminist approach. For this task solution was introduced epistemological construct “cultural-dialogic interdeterminism” allowed to analyze phenomenology in the context of quality, acquired by the whole and not reducible to the simple sum of its constituent parts. It articulated the necessity of mental health and wellbeing phenomenology multidimensional consideration in the spaces of hetero qualitative natures, psychic spheres and behavioral determinants in their cultural conditionality and qualitative specificity. This phenomenology is viewed from the heterogeneous dynamic systems approach standpoint. Theoretical and empirical explanations and evidence of cultural-dialogical interdeterminist metatheoretical approach innovativeness for the analyzed phenomenology understanding deepening is presented.

Multivariable Fractional Order PI Autotuning Method for Heterogeneous Dynamic Systems

In this paper the application of robust Fractional Order Proportional-Integral (FO-PI) autotuning control strategy is presented and applied to heterogeneous dynamic systems using decentralized control. The automatic tuning of controller gains is based on a single sine test, with user-defined robustness margins guaranteed. Its performance is compared against two other fractional order controllers based on PI gain-crossover autotuning method and Internal Model Control (IMC). The closed loop control simulations applied on the heterogeneous dynamic systems indicate that the proposed method performs properly.

Достоверность и точность решения систем ОДУ в среде моделирования разнородных динамических систем ПА10 (PA10)

Достоверность и точность решения систем ОДУ в среде моделирования разнородных динамических систем ПА10 (PA10)

Fault Detection and Isolation in Linear Heterogeneous Multi-Agent Networks

Detection and isolation of faulty behaviours in multi-agent dynamical networks under cooperative control laws is of paramount importance to secure that the network operation is not jeopardized by the failing of one or more of its nodes. The paper investigates under which conditions the fault detectability and isolability (FDI) properties of the individual agent are improved because of the information sharing with other agents in the network. Relying on the parity space method and focusing the analysis on linear heterogeneous dynamical systems two main contributions are achieved: (i) the sharing of information through the cooperative control law does not improve the FDI properties of the individual agents; (ii) the presence of relative measurements among the agents results in improved fault detection and isolation capabilities the multi-agent system under the assumption of a strongly connected network.

Distributed Optimal Output Feedback Control of Heterogeneous Multi-agent Systems under a Directed Graph

In this paper, we consider distributed optimal feedback control design problem for a network of heterogeneous systems. The agents are coupled through their linear quadratic cost function and their interaction (communication) topology is given by a strongly connected directed graph. The goal is to design a distributed optimal feedback control which minimizes the total cost function in a distributed manner by only relying on the neighboring information of each agent. Moreover, the design of the optimal feedback control gain is also performed in a distributed manner by only relying on the neighboring information of each agent. To this end, firstly the necessary conditions are derived for the noninferior solution to the overall performance index. Then, by utilizing the idea of finite-time consensus algorithm, it is shown that the optimal feedback gain can also be computed in a distributed manner by the agents. Finally, we demonstrate the effectiveness of the proposed control law via a simulation on a group of heterogeneous dynamical systems.

Hybrid time Bayesian networks

Capturing heterogeneous dynamic systems in a probabilistic model is a challenging problem. A single time granularity, such as employed by dynamic Bayesian networks, provides insufficient flexibility to capture the dynamics of many real-world processes. The alternative is to assume that time is continuous, giving rise to continuous time Bayesian networks. Here the problem is that the level of temporal detail is too precise to match available probabilistic knowledge. In this paper, we present a novel class of models, called hybrid time Bayesian networks, which combine discrete-time and continuous-time Bayesian networks. The new formalism allows us to more naturally model dynamic systems with regular and irregularly changing variables. We also present a mechanism to construct discrete-time versions of hybrid models and an EM-based algorithm to learn the parameters of the resulting BNs. Its usefulness is illustrated by means of a real-world medical problem.

Hierarchical Decentralized Controller Synthesis for Heterogeneous Multi-Agent Dynamical Systems by LQR

This paper is concerned with systematic ways of designing hierarchical decentralized controllers for heterogeneous multi-agent dynamical systems. Given a bunch of independent agents or subsystems with a class of information networks, the aim of the paper is to propose a systematic design procedure for hierarchical decentralized controllers, where each subsystem cooperatively interacts with each other as well as controls it locally to achieve both the local and global goals in some senses. It is shown that employing the LQR (Linear Quadratic Regulator) method with properly chosen weighting matrices in the performance index, both the local and global objectives can be achieved by the desired hierarchical decentralized structure which fits the given information network. The effectiveness of the proposed design method is confirmed through an illustrative example and its application to a velocity consensus problem in vehicle platoons.

Modularized design for cooperative control and plug-and-play operation of networked heterogeneous systems

In this paper, a cooperative control analysis and design method is investigated for heterogeneous dynamical systems that may be of arbitrary relative degree or nonminimum-phase or both. To achieve consensus or cooperative stability, a negative value of input-feedforward passivity index is used to accommodate and analyze such systems, and the magnitude of the index value is also used as the impact coefficient to quantify the impacts of heterogeneous dynamics of these systems on their networked operations. Physical-system-level designs are explicitly carried out to make individual linear and nonlinear systems (which are either feedback linearizable or nonminimum phase of certain form) become passivity-short and to embed one pure integrator into their input–output dynamics. The network-level distributed control can simply be chosen without any knowledge of the heterogeneous dynamics but with only information of an upper bound on their impact coefficients. It is shown, using the impact equivalence principle, that these controls separately designed but implemented together always ensure either local or global consensus and that a global non-trivial consensus emerges if and only if the information network has at least one globally reachable node or is varying but cumulatively connected. The proposed methodology of fully modularized designs unravels complexity of analyzing and designing cyber–physical systems and enables their plug-and-play into networked operations.

Computational capabilities of random automata networks for reservoir computing

This paper underscores the conjecture that intrinsic computation is maximal in systems at the "edge of chaos". We study the relationship between dynamics and computational capability in random Boolean networks (RBN) for reservoir computing (RC). RC is a computational paradigm in which a trained readout layer interprets the dynamics of an excitable component (called the reservoir) that is perturbed by external input. The reservoir is often implemented as a homogeneous recurrent neural network, but there has been little investigation into the properties of reservoirs that are discrete and heterogeneous. Random Boolean networks are generic and heterogeneous dynamical systems and here we use them as the reservoir. A RBN is typically a closed system; to use it as a reservoir we extend it with an input layer. As a consequence of perturbation, the RBN does not necessarily fall into an attractor. Computational capability in RC arises from a tradeoff between separability and fading memory of inputs. We find the balance of these properties predictive of classification power and optimal at critical connectivity. These results are relevant to the construction of devices which exploit the intrinsic dynamics of complex heterogeneous systems, such as biomolecular substrates.

A pilgr-(image) to Second Life

The article illustrates an alternative topology by taking advantage of the possibilities for new forms of perception in the realm of online virtual worlds. It is based on the outcomes of the ‘Noetic Grace’ project that was held in Linden Lab’s Second Life™ (SL) platform as a part of Yoshikaze project, supported form Humlab, Umeå University. During three months of virtual residency in Yoshikaze studio, the author experimented with different kinds of spatiotemporal awareness formed from the notions of virtuality as expressed during the times of late antiquity. Saint John of Damascus (c. 676–749) was speaking about ‘virtual vision’ when he referred to the concept of ‘noetic grace’. Such an approach raises some fundamental questions about whether virtual worlds can have the potential to alter visual mechanisms in the whole spectrum of imagery; both in its creation as well as in its vision. Technologies of computing can be considered as the most outstanding practice of Descartes’ theories. However even if Cartesian resonance can be regarded as an abstract Logos and as such it is clearly distinguished from the class of the world, its principal effect to western thought was that of its dualism as a deterministic organization. Hence, Euclidian plane with a chosen Cartesian system, the so-called Cartesian plane, became the standard spatial environment. In the dual process model of thinking the forward and backward reasoning can be used to express Euclidian transformations in which the points are detached. Their interaction exists solely to define themselves in relation to the other, rather than to embed themselves in an aggregate space. Nevertheless, scientific progress has demonstrated a source that spurts many kinds of phenomena that are by far distinct from those of a systematic space. Anisotropic and heterogeneous topologies, magnetic flux, non-linear, dynamic systems and emergence are some of the findings that can alter the whole spectrum of human awareness. Consequently, in order to create a being-to-be into virtual worlds, one has to overcome the notion of single-self objectiveness and its systematic space and act as a potential entity released from any references that may set barriers to a formation of a different perception and imagery.

Novel generalized- [formula omitted] methods for interfield parallel integration of heterogeneous structural dynamic systems

A novel partitioned algorithm able to solve ODEs arising from transient structural dynamics is presented. The spatial domain is partitioned into a set of disconnected subdomains owing to computational or physical considerations, and continuity conditions of velocity at the interface are modelled using a dual Schur formulation, where Lagrange multipliers represent reaction forces. Interface equations along with subdomain equations lead to a system of DAEs for which an interfield parallel procedure is developed. The algorithm solves interface Lagrange multipliers, which are subsequently used to advance the solution in subdomains. The proposed coupling algorithm that enables arbitrary Generalized- α schemes to be coupled with different time steps in each subdomain is an extension of a method originally proposed by Pegon and Magonette. Thus, subcycling permitting to deal also with stiff and nonstiff subsystems is allowed. In detail, the paper presents the convergence analysis of the novel interfield parallel scheme for linear single- and two-degrees-of-freedom systems because a multi-degrees-of-freedom system is too difficult for a mathematical treatment. However, the insight gained from the analysis of these coupled problems and the consequent conclusions are confirmed by means of numerical experiments on a four-degrees-of-freedom system.

Passivity Analysis and Passification of Discrete-Time Hybrid Systems

For discrete-time hybrid systems in piecewise affine or piece-wise polynomial (PWP) form, this note proposes sufficient passivity analysis and synthesis criteria based on the computation of piecewise quadratic or PWP storage functions. By exploiting linear matrix inequality techniques and sum of squares decomposition methods, passivity analysis and synthesis of passifying controllers can be carried out through standard semidefinite programming packages, providing a tool particularly important for stability of interconnected heterogeneous dynamical systems.

Scalable robust stability for nonsymmetric heterogeneous networks

Scalable decentralized stability certificates in networks i.e. decentralized stability guarantees for an arbitrary interconnection of heterogeneous dynamical systems, are often based on certain symmetry assumptions in the way the systems are interconnected. Such structure simplifies the mathematical analysis significantly, nevertheless a potential pitfall needs to be addressed: the stability proof might offer no robustness guarantees to deviations from protocol symmetry. This is, for example, the case for Internet congestion control stability results for arbitrary networks i.e. the stability proofs break down with an arbitrarily small deviation from protocol symmetry. We propose in the paper conditions that can guarantee scalable robust stability in a nonsymmetric interconnection setting for a class of networks that includes Internet congestion control models and consensus protocols. The certificates derived are decentralized and scale with the degree of nonsymmetry.