Order Dynamical Systems Research Articles

Safe Coverage of Compact Domains For Second Order Dynamical Systems

Abstract Autonomous systems operating in close proximity with each other to cover a specified area has many potential applications, but to achieve effective coordination, two key challenges need to be addressed: coordination and safety. For coordination, we propose a locally asymptotically stable distributed coverage controller for compact domains in the plane and homogeneous vehicles modeled with second order dynamics with bounded input forces. This control policy is based on artificial potentials designed to enforce desired vehicle-domain and inter-vehicle separations, and can be applied to arbitrary compact domains including non-convex ones. We prove, using Lyapunov theory, that certain coverage configurations are locally asymptotically stable. For safety, we utilize Hamilton-Jacobi (HJ) reachability theory to guarantee pairwise collision avoidance. Rather than computing numerical solutions of the associated HJ partial differential equation as is typically done, we derive an analytical solution for our second-order vehicle model. This provides an exact, global solution rather than an approximate, local one within some computational domain. In addition to considerably reducing collision count, the collision avoidance controller also reduces oscillatory behaviour of vehicles, helping the system reach steady state faster. We demonstrate our approach in two representative simulations involving a square domain and a non-convex moving domain.

Controlling Chaos for a Fractional-Order Discrete System

In this article two different controllers for the stabilization of a fractional-order discrete system in the left Caputo discrete delta operator sense are given. The first one acts by a fractional proportional pulse control, the second acts by a fractional feedback control. These controllers are applied to fractional-order chaotic discrete dynamical systems to obtain their stability and also we show a comparison with the integer order dynamical systems stability. Some simulations are presented for the fractional logistic map and the fractional Henon map.

Tracking Control for Fractional Order Systems with High Relative Degree Outputs

The fractional order systems represented in commensurate state-space form can exhibit loss of controllability in the error dynamics due to variation in the order of derivative. This poses a challenge while designing tracking control. In this paper we investigate this phenomena, define the concept of relative degree for fractional order systems and also develop new set of identities which simplify the analysis and design of controllers for fractional order dynamical systems.

SEREP Integrated Control of Flexible Structures

Flexible structures are continuum modeled as infinite degrees of freedom. Most of the time finite element models are made with large number of degrees-of-freedom to analyse flexible structures. Continuous monitoring, analysis and control of dynamics of flexible structures need simulation of large degrees of freedom in real time. This is computationally expensive and realtime control fails. This study focuses on the development of a reduced order framework for dynamics of flexible structures and use the reduced order model for controlling the structure. Essentially, in the proposed framework, full order state space obtained from finite element modeling of the flexible structure has been reduced to lower subspace using a reduced order algorithm keeping the dynamical characteristic intact. The transformation matrix for reduction has been calculated using system equivalent reduction expansion process (SEREP). Traditionally, full order dynamical system is being used to find the gain matrix to suppress the uncontrolled dynamics associated with the dynamical system. Here in this methodology, the reduced dimension of state space of the system is used for estimating the gain matrix using optimal linear quadratic regulator (LQR). The gain obtained through the reduced system is subsequently used as a feedback to the attached actuators which produce the required force to control the system. A numerical example of a flexible cantilever beam has been shown to investigate the effectiveness of the algorithm.

Integrable Seventh and Ninth Order Dynamic Systems with Dissipation

We establish the integrability for a class of homogeneous (with respect to a part of variables) dynamic systems of odd (seventh and ninth) order, admitting separation of a system on the tangent bundle of smooth manifolds. Bibliography: 13 titles.

Controllability analysis of nonlinear fractional order differential systems with state delay and non-instantaneous impulsive effects

This manuscript prospects the controllability analysis of non-instantaneous impulsive Volterra type fractional differential systems with state delay. By enroling an appropriate Grammian matrix with the assistance of Laplace transform, the conditions to obtain the necessary and sufficiency for the controllability of non-instantaneous impulsive Volterra-type fractional differential equations are derived using algebraic approach and Cayley-Hamilton theorem. A distinctive approach presents in the manuscript, i have taken non-instantaneous impulses into the fractional order dynamical system with state delay and studied the controllability analysis, since this not exists in the available source of literature. Inclusively, i have provided two illustrative examples with the existence of non-instantaneous impulse into the fractional dynamical system. So this demonstrates the validity and efficacy of our obtained criteria of the main section.

Investigation and robust synthesis of polynomials under perturbations based on the root locus parameter distribution diagram

Investigation of the 4 th order dynamic systems characteristic polynomials behavior in conditions of the interval parametric uncertainties is carried out on the basis of root locus portraits. The roots behavior regularities and corresponding diagrams for the root locus parameter distribution along the asymptotic stability bound are specified for the root locus portraits of the systems. On this basis the stability conditions are derived, graphic-analytical method is worked out for calculating intervals of variation for the polynomial family parameters ensuring its robust stability. The discovered regularities of the system root locus portrait behavior allow to extract hurwitz sub-families from the non-hurwitz families of interval polynomials and to determine whether there exists at least one stable polynomial in the unstable polynomial family.

PSO Based reduced order modelling of autonomous AC microgrid considering state perturbation

Reduced order modelling of complex autonomous microgrid system is crucial to its small signal modelling and stability concerns. To reduce the storage requirements and computational time, the order of such microgrids can be reduced by Model Order Reduction (MOR) techniques. This paper presents an optimal reduction technique, which retains dominant poles of the original system and achieves subsequent error minimization through the Particle Swarm Optimization algorithm (PSO). The 36th order complex microgrid system is reduced to 9th order approximant, which retains the significant dynamics of the original system. The simulation results reflect the superiority of the proposed method as compared to the balanced truncation method in terms of the time and frequency domain analysis of the reduced order equivalents. State perturbation in the state space model has also been considered in full as well as reduced order system dynamics and eigenvalue analysis for system stability.

Application of the Euler and Runge–Kutta Generalized Methods for FDE and Symbolic Packages in the Analysis of Some Fractional Attractors

Abstract This paper applies the Euler and the fourth-order Runge–Kutta methods in the analysis of fractional order dynamical systems. In order to illustrate the two techniques, the numerical algorithms are applied in the solution of several fractional attractors, namely the Lorenz, Duffing and Liu systems. The algorithms are implemented with the aid of Mathematica symbolic package. Furthermore, the Lyapunov exponent is obtained based on the Euler method and applied with the Lorenz fractional attractor.

On the statistical mechanics of structural vibration

The analysis of the structural dynamics of a complex engineering structure has much in common with the subject of statistical mechanics. Both are concerned with the analysis of large systems in the presence of various sources of randomness, and both are concerned with the possibility of emergent laws that might be used to provide a simplified approach to the analysis of the system. The aim of the present work is to apply a number of the concepts of statistical mechanics to structural dynamic systems in order to provide new insights into the system behaviour under various conditions. The work is foundational, in that it is based on employing the fundamental equations of motion of the system in conjunction with various definitions of entropy, and no recourse is made to emergent laws that are accepted in thermodynamics. The analysis covers closed (undamped and unforced) and open (forced and damped) systems, linear and nonlinear systems, and both single systems and coupled systems. The fact that the system itself can be random leads to a number of results that differ from those found in classical statistical mechanics, where the initial conditions might be considered to be random but the Hamiltonian is taken to be well defined. For example, the occurrence of a stationary state in a closed system normally requires nonlinearity and coarse-graining of the statistical distribution, but neither condition is required for a random system. For coupled systems it is shown that under certain conditions both Statistical Energy Analysis (SEA) and Transient Statistical Energy Analysis (TSEA) are emergent laws, and insights are gained as to the validity of these laws. The analysis is supported by a number of numerical examples to illustrate key points.

Controllability criteria of fractional differential dynamical systems with non-instantaneous impulses

AbstractThis manuscript prospects the controllability criteria of non-instantaneous impulsive Volterra type fractional differential systems. By enroling an appropriate Gramian matrix that is often defined by the Mittag-Leffler function and with the assistance of Laplace transform, the necessary and sufficiency conditions for the controllability of non-instantaneous impulsive Volterra-type fractional differential equations are derived by using algebraic approach and Cayley–Hamilton theorem. An important feature present in our paper is that we have taken non-instantaneous impulses into the fractional order dynamical system and studied the controllability analysis, since this do not exist in the available source of literature. Inclusively, we have provided two illustrative examples with the existence of non-instantaneous impulse into the fractional dynamical system. So this demonstrates the validity and efficacy of our obtained criteria of the main section.

Інноваційні фактори забезпечення економічної безпеки аграрного сектору

Статтю присвячено визначенню інноваційних факторів забезпечення економічної безпеки аграрного сектору у напрямку формування ефективної державної політки й обґрунтуванню відповідних стратегічних імперативів розвитку галузі.
 Метою статті є дослідження науково-прикладних засад оцінки факторів формування державної політики інноваційного розвитку аграрного сектору як напрямку забезпечення його економічної безпеки та підтримки конкурентоспроможності.
 Наукова новизна. Запропонована класифікація інноваційних факторів, що впливають на формування державної політики забезпечення економічної безпеки аграрного сектору: науково-освітній потенціал; впровадження інноваційних розробок; інноваційна зовнішньоекономічна спеціалізація держави; розвиток мережевих технологій; поширення серед населення та доступність сучасних інформаційних технологій. Побудована імітаційна модель забезпечення економічної безпеки аграрного сектору економіки, яка дозволяє дослідити вплив окремих напрямів розвитку інтелектуального та інноваційного потенціалу, визначити заходи активізації інноваційно-інвестиційної діяльності суб’єктів аграрного сектору для забезпечення їх економічної безпеки.
 Висновки. Встановлено, що на сучасному етапі соціально-економічних трансформацій в країні результати наукової, науково-технічної та інноваційної діяльності є вирішальними факторами, що визначають перехід до інноваційного типу розвитку аграрного сектору, забезпечують її високу ефективність та економічну безпеку у ринковому середовищі. Систематизовано інноваційні фактори забезпечення економічної безпеки аграрного сектору та показники їх оцінки (Науково-освітній потенціал. Впровадження інноваційних розробок. Інноваційна зовнішньоекономічна спеціалізація держави. Розвиток мережевих технологій. Поширення серед населення та доступність сучасних інформаційних технологій).
 Для ефективної інноваційно-інвестиційної політики держави у сфері розвитку аграрного сектору та забезпечення його економічної безпеки важливим елементом є створення інноваційної та інвестиційної спроможності галузі, яка забезпечує їх конкурентоспроможність. Незважаючи на невідворотність процесів посилення залежності успіхів агровиробників від інноваційності агробізнесу, на практиці у вітчизняному агропромисловому секторі темпи продукування і впровадження інновацій залишаються низькими.
 Запропоновано визначати забезпечення економічної безпеки аграрного сектору через результативний показник інноваційного розвитку – валову додану вартість. Пропонується використання методу імітаційного моделювання, зокрема на основі концепції системної динаміки, для виявлення сценаріїв інноваційного розвитку аграрного сектору з метою забезпечення його економічної безпеки та підвищення конкурентоспроможності. Імітаційна модель побудована у відповідності до встановлених зав’язків між факторами інноваційної спроможності в аграрному секторі, які забезпечують його економічну безпеку. Усі цикли в моделі є контурами додаткового зворотного зв’язку, що має призводити до поширення позитивних тенденцій у моделі. Динаміка складових імітаційної моделі визначається побудованими економетричними моделями взаємозв’язків між показниками інтелектуального та інноваційного потенціалу й результатами діяльності.

Stabilization of Arbitrary Switched Nonlinear Fractional Order Dynamical Systems: Application to Francis Hydro-Turbine Governing System

This paper is a theoretical and practical study on the stabilization of fractional order Lipschitz nonlinear systems under arbitrary switching. The investigated system is a generalization of both switched and fractional order dynamical systems. Firstly, a switched frequency distributed model is introduced as an equivalent for the system. Subsequently, a sufficient condition is obtained for the stabilizability of the system based on the Lyapunov approach. Finally, the results are extended to synthesis mode-dependent state feedback controller for the system. All the results are expressed in terms of coupled linear matrix inequalities, which are solvable by optimization tools and directly reducible to the conditions of the integer order nonlinear switching systems as well as the conventional non-switched nonlinear fractional order systems. The proposed method has various practical implications. As an example, it is utilized to control Francis hydro-turbine governing system. This system is represented as a switching structure and supposed to supply a load suffering abrupt changes driven by an arbitrary switching mechanism. The simulation results support the usefulness of the method.

Targeted Adversarial Learning Optimized Sampling.

Boosting transitions of rare events is critical to simulations of chemical and biophysical dynamic systems in order to close the time scale gaps between theoretical modeling and experiments. We present a novel approach, called targeted adversarial learning optimized sampling (TALOS), to modify the potential energy surface in order to drive the system to a user-defined target distribution where the free-energy barrier is lowered. Combining statistical mechanics and generative learning, TALOS formulates a competing game between a sampling engine and a virtual discriminator, enables unsupervised construction of bias potentials, and seeks for an optimal transport plan that transforms the system into a target. Through multiple experiments, we show that on-the-fly training of TALOS benefits from the state-of-art optimization techniques in deep learning and thus is efficient, robust, and interpretable. TALOS is also closely connected to the actor-critic reinforcement learning and hence leads to a new way of flexibly manipulating the many-body Hamiltonian systems.

A numerical approximation method for fractional order systems with new distributions of zeros and poles

A multiple-zero-pole (MZP) method is proposed for general SISO fractional order dynamic systems in this paper. Based on amplitude–frequency curve, a new rational approach to fractional differentiator is designed. There are three advantages of MZP method. 1) A more generalized form of approximation system is proposed by design the distribution of zeros and poles in a new way. 2) The same fractional differentiator can be approximated in many different forms. 3) The robustness of the approximation system is enhanced by using integer order integrators to construct fractional differentiator. The feasibility of the method is assessed in the illustrative examples, and the simulations prove the effectiveness.

Information Reconstruction on an Infinite Tree for a $$4\times 4$$-State Asymmetric Model with Community Effects

The information reconstruction problem on an infinite tree, is to collect and analyze massive data samples at the $n$th level of the tree to identify whether there is non-vanishing information of the root, as $n$ goes to infinity. This problem has wide applications in various fields such as biology, information theory and statistical physics, and its close connections to cluster learning, data mining and deep learning have been well established in recent years. Although it has been studied in numerous contexts, the existing literatures with rigorous reconstruction thresholds established are very limited. In this paper, motivated by a classical deoxyribonucleic acid (DNA) evolution model, the F$81$ model, and taking into consideration of the Chargaff's parity rule by allowing the existence of a guanine-cytosine content bias, we study the noise channel in terms of a $4\times 4$-state asymmetric probability transition matrix with community effects, for four nucleobases of DNA. The corresponding information reconstruction problem in molecular phylogenetics is explored, by means of refined analyses of moment recursion, in-depth concentration estimates, and thorough investigations on an asymptotic $4$-dimensional nonlinear second order dynamical system. We rigorously show that the reconstruction bound is not tight when the sum of the base frequencies of adenine and thymine falls in the interval $\left(0,1/2-\sqrt{3}/6\right)\bigcup \left(1/2+\sqrt{3}/6,1\right)$, which is the first rigorous result on asymmetric noisy channels with community effects.

A Tangential Block Lanczos Method for Model Reduction of Large-Scale First and Second Order Dynamical Systems

In this paper, we present a new approach for model reduction of large scale first and second order dynamical systems with multiple inputs and multiple outputs. This approach is based on the projection of the initial problem onto tangential subspaces to produce a simpler reduced-order model that approximates well the behaviour of the original model. We present an algorithm named: adaptive block tangential Lanczos-type algorithm. We give some algebraic properties and present some numerical experiences to show the effectiveness of the proposed algorithms.

FEA based discrete-time sliding mode control of uncertain continuum mechanics MIMO vibrational systems

In this paper, a novel method for control of uncertain MIMO flexible systems is proposed. The control system is constructed such that it is capable of stabilizing a flexible dynamical system based on rigid approximation of continuum dynamics, resulting in facilitation of modeling and control procedures for complicated vibrational systems. In order to ensure system stability in real-time applications, the control system is obtained in discrete-time basis. To these ends, a sliding hyper-plane based sliding mode control (SMC) algorithm is constructed featuring sliding functions for individual subsystems. An approximated dummy model of the real system is used alongside the dynamical system in order to estimate parametric and unstructured uncertainties which are evaluated through comparisons between the dummy model, data obtained from the real system and corresponding mathematical model. Conventional SMC techniques introduce undesired effects of chattering which result in amplifying vibrations in flexible systems. To address this issue, an alternate algorithm based on selection of control signals within appropriate bounds is used in order to eliminate chattering and provide superior performance in comparison with conventional SMC techniques. The accuracy of proposed method has been verified through ANSYS® mechanical APDL-based simulations and its effectiveness has been verified in multiple operating conditions.

Controllability of Nonlinear Stochastic Fractional Higher Order Dynamical Systems

Abstract This paper deals with the study of controllability of stochastic fractional dynamical systems with 1 < α ≤ 2. Necessary and sufficient condition for controllability of linear stochastic fractional system is obtained. Sufficient conditions for controllability of stochastic fractional semilinear systems, integrodifferential systems, systems with neutral term, systems with delays in control and systems with Lévy noise is formulated and established. The solution is obtained in terms of Mittag-Leffler operator functions by considering bounded operators. The Banach fixed point theorem is used to obtain the desired results from an equivalent nonlinear integral equation of the given system.

On reduced-complexity robust adaptive control of switched Euler–Lagrange systems

State-of-the-art adaptive or robust adaptive techniques for several classes of uncertain switched systems demand structural knowledge of the system dynamics in order to appropriately select the regressor terms in the adaptive law. As a result, the number of unknown parameters to be adapted increases with system complexity, which can lead to very complex adaptive laws. In this work we propose, for the relevant class of Euler–Lagrange systems subject to time-dependent slow switching, a switched robust adaptive control framework with reduced complexity: the number of unknown parameter to be adapted is independent on the system complexity, whereas the regressor terms in the adaptive laws do not require any structural knowledge of the system dynamics. Stability analysis is provided to illustrate the benefit of the proposed design, and the performance of the controller is verified using a switched system stemming from the combination of mooring and free-hanging operations in dynamic positioning of offshore ships.