State Of Dynamic System Research Articles

Extreme multistability in symmetrically coupled clocks

Extreme multistability (EM) is characterized by the emergence of infinitely many coexisting attractors or continuous families of stable states in dynamical systems. EM implies complex and hardly predictable asymptotic dynamical behavior. We analyze a model for pendulum clocks coupled by springs and suspended on an oscillating base and show how EM can be induced in this system by specifically designed coupling. First, we uncover that symmetric coupling can increase the dynamical complexity. In particular, the coexistence of multiple isolated attractors and continuous families of stable periodic states is generated in a symmetric cross-coupling scheme of four pendulums. These coexisting infinitely many states are characterized by different levels of phase synchronization between the pendulums, including anti-phase and in-phase states. Some of the states are characterized by splitting of the pendulums into groups with silent sub-threshold and oscillating behavior, respectively. The analysis of the basins of attraction further reveals the complex dependence of EM on initial conditions.

A Deterministic Least Squares Approach for Simultaneous Input and State Estimation

This paper considers a deterministic estimation problem to find the input and state of a linear dynamical system which minimise a weighted integral squared error between the resulting output and the measured output. A completion of squares approach is used to find the unique optimum in terms of the solution of a Riccati differential equation. The optimal estimate is obtained from a two-stage procedure that is reminiscent of the Kalman filter. The first stage is an end-of-interval estimator for the finite horizon which may be solved in real time as the horizon length increases. The second stage computes the unique optimum over a fixed horizon by a backwards integration over the horizon. A related tracking problem is solved in an analogous manner. Making use of the solution to both the estimation and tracking problems a constrained estimation problem is solved which shows that the Riccati equation solution has a least squares interpretation that is analogous to the meaning of the covariance matrix in stochastic filtering. The paper shows that the estimation and tracking problems considered here include the Kalman filter and the linear quadratic regulator as special cases. The infinite horizon case is also considered for both the estimation and tracking problems. Stability and convergence conditions are provided and the optimal solutions are shown to take the form of left inverses of the original system.

A co-optimized approach for state estimation based micro phasor measurement unit allocation in power distribution infrastructure

Due to the highly complex and dynamic electrical characteristics of the 3-phase unbalanced power delivery networks (PDNs), it is challenging for utilities to observe the network entirely. This impediment necessitates the PDNs to become intelligent nowadays in the presence of various smart devices. Micro-phasor measurement units (µPMUs) are expected to play a crucial role in observing the smart power distribution system due to their micro-seconds resolution and millidegree precision accuracy. The placement of µPMUs in PDNs is also very challenging due to their associated costs. So, allocating a minimal number of µPMUs in PDN with fulfilling the topological observability can elucidate the issue of real-time visibility of the entire system. This paper presents a novel co-optimized placement strategy of µPMUs (CPMP) in PDNs that minimizes the µPMU numbers and the estimation error in the buses other than the µPMU assigned nodes. This work also displays a novel dynamic heuristic distribution system state estimation (DDSSE) to estimate the system's unknown states by using only the information of bus voltage phasors at the µPMU specified buses. The DDSSE is used to estimate the root mean square error (RMSE) in estimated voltage magnitudes and angles. Besides this, the efficacy of the grey-wolf optimizer (GWO) is presented in this work to solve the newly formulated placement problem. The results are validated on an Indian 19-bus and 34-bus unbalanced radial distribution system (URDS), and a detailed comparative study of different heuristic algorithms is also analyzed in this work.

LABVIEW IN THE RESEARCH OF FRACTAL PROPERTIES OF THE TOPOLOGY OF NETWORKS AND STOCHASTIC PROCESSES

The advancement and utilization of computer technologies for studying and diagnosing the technical state of dynamic systems are closely linked to scientific and technological progress. Among these technologies, fractal technologies hold a prominent position [1]. Time series data, which record changes in controlled parameters over time, are commonly used for diagnosing technical objects and systems. The use of fractals will also be of interest in assessing the resonant frequency characteristics of oscillatory systems [3]. The informational characteristics of topologically distributed networks (e.g., computer, cellular) significantly depend on their geometry, node placement, and inter-node distances. The fractal dimension, a fundamental characteristic of networks, plays a crucial role in this context [2]. The research paper presents a methodology for modeling and synthesizing large networks using the node density function, which follows a power function with a fractal dimension. This characteristic aligns with Zipf's law of population distribution around urban centers. The paper also provides fractality degree indices for the network diagram. Software tools such as LabVIEW play a significant role in scientific research and experiment automation.

Device–Edge Collaborative Differentiated Data Caching Strategy Toward AIoT

Caching AIoT data at the edge can reduce the load on cloud centers while providing real-time services for AIoT users. Existing static caching strategies based on popularity prediction fail to meet users’ demands for time-varying entity data, while dynamic caching strategies focus only on evaluating the time-varying state characteristics of entity data, but ignore the differences in popularity among entities, resulting in poor service experience. To this end, a device-edge collaborative differentiated data caching strategy considering static entity popularity as well as dynamic system state is proposed. First, a hot entity recognition method centered on user interests is designed to achieve individual preference estimation by mining users’ long short-term interests, and then achieve group interest prediction based on social computing. Based on this, a dynamic caching optimization method is designed, which considers the timeliness of entity data and communication cost of system to design the objective function of optimal cache decision and then solve it based on reinforcement learning. Simulation results demonstrate that the proposed caching strategy achieves better performance than other benchmark strategies in terms of cache hit rate and search cost.

Stability Indicators of Nonnegative Matrices: Parametric and Sparse Cases

Methods for the algorithmic construction of stability indicators of nonnegative matrices is described, and the application of these indicators to problems of modern mathematical biology and epidemiology is discussed. Specific features of such indicators when they are applied to problems about the parametric loss of stability of trivial equilibrium states of discrete dynamical systems are pointed out. Estimates of the efficiency of algorithms based on the proposed methods for the case of systems determined by sparse matrices are given. Examples of using the constructed algorithms for such systems are discussed.

Criticality in transient behavior of coupled oscillator system toward chimera and synchronization.

Chimera states in spatiotemporal dynamical systems have been investigated in physical, chemical, and biological systems, while how the system is steering toward different final destinies upon spatially localized perturbation is still unknown. Through a systematic numerical analysis of the evolution of the spatiotemporal patterns of multi-chimera states, we uncover a critical behavior of the system in transient time toward either chimera or synchronization as the final stable state. We measure the critical values and the transient time of chimeras with different numbers of clusters. Then, based on an adequate verification, we fit and analyze the distribution of the transient time, which obeys power-law variation process with the increase in perturbation strengths. Moreover, the comparison between different clusters exhibits an interesting phenomenon, thus we find that the critical value of odd and even clusters will alternatively converge into a certain value from two sides, respectively, implying that this critical behavior can be modeled and enabling the articulation of a phenomenological model.

Достаточные условия существования Н∝ -наблюдателя состояния линейных непрерывных динамических систем

<p>The article deals with the problem of finding the observer of the state vector of linear continuous non-stationary dynamical systems with uncertainty of the initial conditions, limited external influences and measurement errors over a finite time interval. Sufficient conditions for the existence of an observer are formulated and proved on the basis of the expansion principle. Relationships are obtained for finding the parameters of the observer and the worst laws of change in external influences and measurement errors. As a limiting case, the problem of observer synthesis for stationary linear dynamical systems on a semi-infinite time interval is considered. Two applied problems of estimating the aircraft state vector based on the results of incomplete and inaccurate measurements are solved.</p>

Recovering the Graph Underlying Networked Dynamical Systems under Partial Observability: A Deep Learning Approach

We study the problem of graph structure identification, i.e., of recovering the graph of dependencies among time series. We model these time series data as components of the state of linear stochastic networked dynamical systems. We assume partial observability, where the state evolution of only a subset of nodes comprising the network is observed. We propose a new feature-based paradigm: to each pair of nodes, we compute a feature vector from the observed time series. We prove that these features are linearly separable, i.e., there exists a hyperplane that separates the cluster of features associated with connected pairs of nodes from those of disconnected pairs. This renders the features amenable to train a variety of classifiers to perform causal inference. In particular, we use these features to train Convolutional Neural Networks (CNNs). The resulting causal inference mechanism outperforms state-of-the-art counterparts w.r.t. sample-complexity. The trained CNNs generalize well over structurally distinct networks (dense or sparse) and noise-level profiles. Remarkably, they also generalize well to real-world networks while trained over a synthetic network -- namely, a particular realization of a random graph.

State Super Sampling Soft Actor–Critic Algorithm for Multi-AUV Hunting in 3D Underwater Environment

Reinforcement learning (RL) is known for its efficiency and practicality in single-agent planning, but it faces numerous challenges when applied to multi-agent scenarios. In this paper, a Super Sampling Info-GAN (SSIG) algorithm based on Generative Adversarial Networks (GANs) is proposed to address the problem of state instability in Multi-Agent Reinforcement Learning (MARL). The SSIG model allows a pair of GAN networks to analyze the previous state of dynamic system and predict the future state of consecutive state pairs. A multi-agent system (MAS) can deduce the complete state of all collaborating agents through SSIG. The proposed model has the potential to be employed in multi-autonomous underwater vehicle (multi-AUV) planning scenarios by combining it with the Soft Actor–Critic (SAC) algorithm. Hence, this paper presents State Super Sampling Soft Actor–Critic (S4AC), which is a new algorithm that combines the advantages of SSIG and SAC and can be applied to Multi-AUV hunting tasks. The simulation results demonstrate that the proposed algorithm has strong learning ability and adaptability and has a considerable success rate in hunting the evading target in multiple testing scenarios.

MATHEMATICAL MODELING OF THE DYNAMICS OF AN ELASTIC HALF-MEDIUM WITH A CYLINDRICAL CAVITY REINFORCED BY A SHELL UNDER AXISYMMETRIC LOADS

Purpose. The development of a mathematical model of an elastic semi-medium with a cylindrical cavity reinforced by a shell and a plate that reinforces the surface of the semi-medium based on the finite-element approach. The non-stationary dynamic stress-strain state of this mechanical system under axisymmetric surface loads, which depends on time as a unit Heaviside function was analyzed. The solution of the corresponding static problem was obtained. Based on the obtained results, the dynamic coefficient of the considered mechanical system was calculated.
 Research methods. The finite element method and the Wilson - method were used for solving static and the corresponding dynamic matrix equation correspondingly. The last one allows reducing the differential matrix equation to an iterative sequence of quasi-static problems. To obtain an approximate solution of systems of linear algebraic equations that take place in the process of solving static and a sequence of quasi-statistical problems, the conjugate gradients method was used.
 Results. A finite-element model of the mechanical system of an elastic semi-medium with a cylindrical cavity reinforced by a shell and a plate reinforces the surface of the semi-medium was developed. The non-stationary dynamic stress-deformed state of this mechanical system under action of the surface axisymmetric loads was analyzed. The solution of the corresponding static problem was obtained. Based of the results has been obtained, the dynamic coefficient of the considered mechanical system was determined.
 Scientific novelty. The developed approach allows to take into account the mutual influence of a cylindrical cavity reinforced by a shell and a plate that reinforces the surface of the semi-medium under the action of the non-stationary dynamic loads applied to the surface of the plate.
 Practical value. The developed mathematical models and obtained results can be used in the design of underground structures, in particular mine shafts.

Dynamic State Estimation of Synchronous Machines Using Iterated Square-Root Cubature Kalman Filter and Synchrophasor Measurements

Power system dynamic state estimation is the first prerequisite for control and stability prediction under transient conditions. For a stable and reliable power system, it is crucial and helpful to have accurate, precise, and up-to-date information on the states of the synchronous machines- rotor angle and rotor speed deviation. This paper proposes an application of the Iterated Square-root Cubature Kalman filter (ISCKF) to estimate these main states of synchronous generators. The ISCKF method consists of two step modification - one is the square-root step modification of CKF and the next step is the addition of iterative approach to the square-root CKF method. To demonstrate the performance of the proposed approach during a three-phase short circuit fault, the simulation results, are compared with that of Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF) and Cubature Kalman Filter (CKF). The test systems considered are a single machine infinite bus (SMIB) system, an IEEE 9-bus system and a 19-generator 42-bus test system. The estimation accuracy of the rotor angle using ISCKF method is increased by 6.8–36.54% when compared to that of the CKF method. Similarly, the improvement in accuracy is 4.4–28.57% for estimation of speed deviation.

Innovation-saturated Koopman Kalman filter for distribution system dynamic state estimation against measurement outliers

Sensor errors, model uncertainty, changes in the surrounding environment, data loss, or malicious network attacks can all result in outliers, which can pollute the measurement process of the distribution system. In this study, to address this problem, a dynamic state estimation method for distribution systems based on innovation-saturated Koopman Kalman filter (IS-KKF) was proposed. The Koopman Kalman filter (KKF) is model-free and data-driven, and estimates nonlinear dynamics through the conventional linear Kalman filter. To make the Koopman Kalman filter robust to measurement outliers, the innovation saturation mechanism applies a saturation function to it. To correct the state estimation, this mechanism is applied to the filtering process. When outliers occur, the distorted innovation is saturated to prevent the state estimation results from being destroyed. Adaptive adjustment of the saturated boundary is a feature of this mechanism. Extensive simulations were carried out on the IEEE 118-bus test system to verify the effectiveness and robustness of the proposed method. The simulation results demonstrate that the proposed method can effectively reject outliers with different amplitudes, types, and continuous times, has significant computational efficiency, and does not require additional measurement redundancy.

Observation-Based Filtering of State of a Nonlinear Dynamical System with Random Delays

Observation-Based Filtering of State of a Nonlinear Dynamical System with Random Delays

Space–Time Structures in the Auroral Oval: Approaches to Modeling

The interaction of the magnetospheric–ionospheric (MI) system surrounding the Earth with the environment (solar wind) occurs in the form of a series of transient processes at different scales. The largest of them, magnetic storms, are obviously triggered by disturbances in the solar wind (direct driving). The role of the internal dynamics of the MI system, which is caused to a large extent by the nonlinearity and temporal delays of the loading–unloading processes of energy and particle from the solar wind into the magnetosphere, becomes more significant at smaller scales (substorms, pseudobreakups, injections, and activations). A typical dynamic state of the MI system is characterized as self-organized criticality or turbulence, which are characterized by statistical scale invariance (scaling) in the fluctuation distributions of many characteristics. The dynamics of the MI system is projected into the region of the auroral oval, the very existence of which is due to this dynamics. The space–time structure of auroral disturbances largely reflects the structure of processes in the MI plasma. The description of this structure is important both for studying the fundamental study of plasma processes and for many topical applied problems related to the propagation of radio waves in the ionosphere and vital activity at high latitudes. The paper discusses approaches and developments for constructing a model of the space–time structure of the auroral oval, based on fractal and multifractal characteristics.

Distributed extended high‐gain observers for the generalized strict‐feedback system

AbstractTwo distributed extended high‐gain observers are studied for the generalized strict‐feedback system in presence of external disturbance. The system state dynamics are reconstructed admissibly based on the limited measured output. First, a distributed high‐gain observer is constructed to ensure the semiglobal ultimate uniform convergence of the state estimation error between the estimated state in each local observer and system state, for any prescribed initial system values. However, the dimension of the proposed distributed observer is n + 1 and the high‐gain parameter is powered up to n + 1. Therefore, a 2(n + 1)‐dimension distributed high‐gain low‐power observer is delicately designed, with the high‐gain parameter powered fixed to 2. The formulated distributed observer is easy‐implementation and the estimation error can reach fast convergence. Finally, a chaotic oscillator and a pendulum‐cart system are introduced to verify the effectiveness of the theoretical results.

Adaptive Asymmetric Time-Varying Integral Barrier Lyapunov Control-Based Trajectory Tracking of Autonomous Vehicles

This paper investigates the lane following and changing maneuvers of autonomous vehicles in the presence of unknown disturbances, taking into account the dynamic system states and input constraints. The integrated longitudinal-lateral and yaw rate dynamics of the vehicle are simultaneously considered to improve the tracking accuracy and system stability when navigating under critical conditions. Then, an adaptive asymmetric time-varying integral barrier Lyapunov control and dynamic surface control scheme are developed to design the active front steering controller, longitudinal controller, and direct yaw moment control controller, which is capable of constraining the system states and control signals within the predefined boundary. In addition, the radius basis function neural network (RBFNN) is employed to estimate the lumped disturbances caused by the parametric uncertainties, external disturbances, and unmodeled dynamics, and the command filter system is used to avoid the explosion of terms phenomenon. Due to the fast and accurate torque response characteristics of the in-wheel motors, the optimization-based method is then implemented to effectively allocate the driving/braking torque to each in-wheel motor so as to improve vehicle performance. The stability of the closed-loop system is comprehensively demonstrated by means of the Lyapunov theory. Finally, the quantitative and qualitative comparisons in different diving scenarios using the Carim-Simulink joint environment are carried out to illustrate the effectiveness and validation of the proposed method.

Space–Time Structures in the Auroral Oval: Approaches to Modeling

The interaction of the magnetospheric–ionospheric (MI) system surrounding the Earth with the environment (solar wind) occurs in the form of a series of transient processes at different scales. The largest of them, magnetic storms, are obviously triggered by disturbances in the solar wind (direct driving). The role of the internal dynamics of the MI system, which is caused to a large extent by the nonlinearity and temporal delays of the loading–unloading processes of energy and particle from the solar wind into the magnetosphere, becomes more significant at smaller scales (substorms, pseudobreakups, injections, and activations). A typical dynamic state of the MI system is characterized as self-organized criticality or turbulence, which are characterized by statistical scale invariance (scaling) in the fluctuation distributions of many characteristics. The dynamics of the MI system is projected into the region of the auroral oval, the very existence of which is due to this dynamics. The space–time structure of auroral disturbances largely reflects the structure of processes in the MI plasma. The description of this structure is important both for studying the fundamental study of plasma processes and for many topical applied problems related to the propagation of radio waves in the ionosphere and vital activity at high latitudes. The paper discusses approaches and developments for constructing a model of the space–time structure of the auroral oval, based on fractal and multifractal characteristics.

Dynamic state estimation of power systems considering maximum correlation entropy and quadratic function

Uncertainties such as abnormal system inputs, strong model nonlinearities, outliers and impulsive noise unavoidably exist in the power system dynamic state estimation (SE) (DSE). The existing Kalman filter-based DSE methods cannot deal with the uncertainties well and can be improved further. In this paper, a robust DSE method based on the maximum correlation entropy (MCE), quadratic function (QF) and the cubature Kalman filter is proposed to reduce the effects caused by the uncertainties. The MCE-QF based estimator is robust and can alleviate the influence of uncertainties. A new SE error covariance is derived by using the robust statistical tool, influence function. The robustness and estimation precision of the proposed DSE method is demonstrated by conducting simulations on a synchronous generator under different cases.

System Design Principles: adaptation to time for long living autonomous systems

The article presents the principles of creating systems with the adaptation to the operation time. In the literature on systems design the adaptation mostly concerned: 1) the unknown object structure; 2) the unknown object parameters; 3) unknown parameters of input signals; 4) the unknown functions of system state dynamics; and 5) unknown environment conditions. It usually assumed that the control process is intended to achieve a certain, usually optimal state of the system, - such way the “adaptive system concept” are close to “optimal system concept”. The other approach for system design with these conditions is robustness, as robust control does not need a priori information about the bounds on these uncertain or time-varying parameters; robust control guarantees that if the changes are within given bounds the control law need not be changed, while adaptive control is concerned with control law changing itself. In the last 10 – 15 years there was introduced the new approach as “resilient systems”. “Resilience engineering” may look like “repairing engineering” – it is assumed that errors or malfunctions occur “for sure” and the system should respond appropriately to this.
 The system operation time, as the cause of adaptation, was very rare considered, mostly when reliability issues are discussing. The proposed approach is new. The proposed principles should be used with known approaches of dependable system design, – these are engineering and information theory redundancy. Both approaches must be used in the design phase and are unchanged structural parameters of the system during operations. There were concerned mostly “long-living systems” and the same task of reliability.
 Proposed principles can be used in the development of the systems designed for continuous operation with absence of the possibility of external human intervention to restore system performance or some maintenance procedures. By «system» in this article are meant «Complex Adaptive Systems» (CAS). Currently, the proposed approach can be attributed to the development of "Artificial General Intelligence" (AGI). Examples of such systems include space-based and underwater-based robotic systems. By “Adaptability of the system to time” – in the sense of control process – it is meant a certain structural reconfiguration of the system, considering the non-stationary nature of stochastic processes of errors, damages, and system failures.
 The formulation of principles is of a general declarative nature – at this stage the author gives preference to the essence of the proposal, rather than its formalization. The article does not provide specific design guidelines, but contains some examples of possible applications, mainly to highlight the essence of the proposals.