Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Editorial Section
  • Masaharu Adachi
    原稿種別: FOREWORD
    2022 年 13 巻 2 号 p. 169
    発行日: 2022年
    公開日: 2022/04/01
    ジャーナル フリー
  • Tomoyuki Sasaki, Hidehiro Nakano
    原稿種別: Invited Review Paper
    2022 年 13 巻 2 号 p. 170-195
    発行日: 2022年
    公開日: 2022/04/01
    ジャーナル フリー

    Swarm intelligence (SI) algorithms have been studied in solving real-world optimization problems called black-box optimization problems. Typical features of SI algorithms are: (1) being a population-based metaheuristics; (2) using fitness values of a given objective function; and (3) having very simple search rules which search agents follow. As such, SI algorithms have been applied to various black-box optimization problems. Particle swarm optimization is one of powerful SI algorithms, in which a swarm consists of plural particles as solution candidates. Particles directly fly a search space and share their own information each other, and thus PSO can find good quality of solutions. However, a PSO swarm is easily stuck in solving optimization problems whose search space is high-dimensional and complicated. In order to solve such problems, large numbers of particles and reference frame invariance are needed for PSO algorithms. Herein, we suggest a piecewise-linear particle swarm optimizer (PPSO) which is a deterministic PSO. PPSO has two simple search modes switched to another mode dynamically, whose search dynamics are complex. As such, PPSO algorithm can be implemented on hardware with low hardware costs because PPSO algorithm must not require many random number generators. In addition, PPSO algorithm can find a good quality of solution in solving complex optimization problems. We studied search performances of PPSO compared to PSO algorithms and provide theoretical analysis of reference frame invariance for PPSO. In order to verify search performances and theoretical analysis, we performed numerical simulations.

Special Section on Nonlinear Science Workshop on the Journal
Regular Section
  • Zhuanglin Mei, Toshiki Oguchi
    原稿種別: Paper
    2022 年 13 巻 2 号 p. 477-492
    発行日: 2022年
    公開日: 2022/04/01
    ジャーナル フリー

    This paper considers the identification problem of network structures for networked dynamical systems. We define the network structure as a coupling function describing the network connectivity and the nonlinear data exchange functions in the network, and attempt to identify the coupling function from potentially noisy measurement data. We develop an identification method of network structures applicable even to network systems consisting of nonlinear systems and nonlinear coupling functions by using the Koopman operator theory. First, we design observable functions as basis functions of a functional space, and determine the Koopman operators associated with the dynamics of the network. Then, the coupling function is identified as a projection on the span of the observables. Also, we make use of the sparse identification techniques to reduce requirements on data amounts and improve robustness with respect to measurement noise. Numerical examples show that the proposed method is applicable to a wide range of nonlinear systems, including chaotic systems with nonlinear coupling functions, and yields better performance than some existing methods. Identification results for two different nonlinear network systems with nonlinear coupling functions show the usefulness of the proposed method.