Koopman operator is a composition operator defined for a dynamical system described by nonlinear differential or difference equation. Although the original system is nonlinear and evolves on a finite-dimensional state space, the Koopman operator itself is linear but infinite-dimensional (evolves on a function space). This linear operator captures the full information of the dynamics described by the original nonlinear system. In particular, spectral properties of the Koopman operator play a crucial role in analyzing the original system. In the first part of this paper, we review the so-called Koopman operator theory for nonlinear dynamical systems, with emphasis on modal decomposition and computation that are direct to wide applications. Then, in the second part, we present a series of applications of the Koopman operator theory to power systems technology. The applications are established as data-centric methods, namely, how to use massive quantities of data obtained numerically and experimentally, through spectral analysis of the Koopman operator: coherency identification of swings in coupled synchronous generators, precursor diagnostic of instabilities in the coupled swing dynamics, and stability assessment of power systems without any use of mathematical models. Future problems of this research direction are identified in the last concluding part of this paper.
In this paper, we consider output dead-beat controllability of discrete-time polynomial systems. First, we derive an output dead-beat stability condition. Based on this stability condition, second, we derive an output dead-beat controllability condition. If our controllability condition holds, it is possible to design an output dead-beat feedback controller in the polynomial form by solving a finite set of algebraic equations.
Neuromorphic systems aiming at mimicking some characteristics of the nervous systems of living humans or animals have been developed since the late 1980s', taking benefit of intrinsic properties and increasing performances of the successive silicon fabrication technologies. A regain of interest has been observed in the middle of the 2010s', which manifests itself from the emergence of large-scale projects integrating various computational and hardware perspectives, by the increased interest and involvement of industry and the growth of the volume of scientific publications. This paper reviews research directions and methods of neuromorphic microelectronics hardware, the developed hardware and its performance, and discusses current issues and potential future developments.
The size frequency distribution of Japanese place-name is analyzed. The list of municipalities and town-area names are extracted from the zip code table and their size frequency distributions are measured. The distribution of town-area names obeys a power law behavior while the distribution of municipality names is well fitted by a lognormal distribution. A simple mathematical model of the municipality and town-area evolution and their naming process is suggested.
In this paper, we propose a new potential method of nonlinear resistive circuits to solve the max-flow/min-cut problems. The important point is that simultaneous analysis of the max-flow and the min-cut can be made based on the dynamics of a single state in the circuit. Although the max-flow problem and the min-cut problem are in duality, the respective algorithms are different in conventional methods. In other words, the simultaneous analysis for the max-flow/min-cut problems does not exist. Our proposed method enables the simultaneous analysis only by nonlinear resistive circuit analysis. Additionally, the min-cut can be found from the node voltages directly. The node voltages enable the finding of all min-cuts easily when a graph has multiple min-cuts, which are found when plural cuts with the same min-cut capacity exist in the same graph. In conventional min-cut algorithms, it is hard to obtain multiple min-cuts. Moreover, our proposed method has a huge advantage of being suitable for hardware implementation. When the proposed circuit model is designed with the integrated circuit such as analog type Programmable Logic Device, Memristor or Phase Change Memory which can change graph structure and branch conductance, the novel min-cut solution with real-time processing can be expected.
This paper considers an electric power grid with multiple synchronous machines exhibiting coupled swing dynamics and aims at developing a hierarchical diagnosis of loss of transient stability of the machines, which we term as swing instabilities. We introduce a standard energy function for the power grid and decompose it into individual energy functions of a collective system of the grid, of the motions relative to the collective system, and of the infinite bus. This decomposition enables us to extract distinctive behaviors embedded in the swing instabilities in terms of energy. We numerically apply the individual energy functions in the proposed decomposition to analysis of swing instabilities in the IEEE New England 39-bus test system. We then propose a hierarchical diagnosis of the swing instabilities based on the decomposition and discuss its validity by approximating the individual energy functions along solutions representing the grid's instabilities.
An improvement for clock synchronization in wireless sensor networks (WSNs) is presented, which is obtained by analyzing a temporal frequency variation observed in internal clock circuits. Clock synchronization is an essential building component in WSNs for distributed sensing. Flooding time synchronization protocol (FTSP) is one of the highest-precision synchronization protocols for WSNs, which has been implemented on certain WSN testbeds. We carry out systematic experiments of FTSP with a Mica2Dot testbed to understand how synchronization precision is affected by a dynamic frequency variation in the clock circuit with a button battery. Our observations clarify that the following two elements are essential for better clock synchronization; (i) a short-term frequency variation in the clock circuit, and (ii) the resulting error in clock drift (i.e., skew) estimation from the linear regression in FTSP. Based on these findings, we propose a simplistic improvement for robust and more precise clock synchronization, utilizing two sets of simultaneous estimations of skew between sender and receiver nodes. Through systematic experiments and analysis, we confirm this improvement realizes a higher synchronization precision in a stable network environment, while it maintains robustness of time synchronization even in a worst case of unstable networks.
An optimization method based on piecewise-rotational chaotic system (OPRC) is proposed. OPRC is a kind of multi-point searching methods in order to find an optimal solution, and these searching points are updated by piecewise-rotational chaotic dynamics. OPRC is a simple optimizer because these searching points are governed by simple dynamics which contains no stochastic terms. OPRC has significantly better performance than particle swarm optimization and our previous method based on another chaotic system. The relationship between the performance of OPRC and the time-series of the proposed chaotic system is analyzed. Then we clarify that OPRC obtains better solutions when the autocorrelation of the time-series takes negative values with damped oscillation.