Nonessentiality of Reservoir’s Fading Memory for Universality of Reservoir Computing

This article describes a novel sufficient condition concerning approximations with reservoir computing (RC). Recently, RC using a physical system as the reservoir has attracted attention. Because many physical systems are modeled as state-space systems, it is necessary to guarantee the approximations given by reservoirs represented as nonlinear state-space systems. There are two problems with existing approaches: a reservoir must have a property called fading memory and must be represented as a set of maps between input and output signals on the bi-infinite-time (BIT) interval. These two conditions are too strict for reservoirs represented as nonlinear state-space systems as they require the reservoir to have a unique equilibrium state for the zero input. This article proposes an approach that employs operators from right-infinite-time (RIT) inputs to RIT outputs. Furthermore, we develop a novel extension of the Stone–Weierstrass theorem to handle discontinuous functions. To apply the extended theorem, we define functionals corresponding to operators and introduce a metric on the domain of the functionals. The resulting sufficient condition does not require the reservoir to have fading memory or continuity with respect to inputs and time. Therefore, our result guarantees the approximations with very common reservoirs and provides a rationale for physical RC. We present an example of a physical reservoir without fading memory. With the example reservoir, the RC model successfully approximates NARMA10, a benchmark task for time series predictions.journal articl

Multi-Pendulum Synchronization Using Constrained Agreement Protocols

(c) 2009 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.Digital Object Identifier: 10.4108/ICST.ROBOCOMM2009.5834This paper considers the problem of coordinating multiple pendula attached to mobile bases. In particular, the pendula should move in such a way that their motion is synchronized, which calls for two problems to be solved simultaneously, namely a constrained optimal control problem for each pendulum, and a constrained agreement problem across the network of pendula. A novel way of manipulating the initial conditions in the consensus equation is presented that will solve the latter of these problems, and simulation results are presented that support the viability of the proposed approach

Formation shape control with distance and area constraints

This paper discusses a formation control problem in which a target formation is defined with both distance and signed area constraints. The control objective is to drive spatially distributed agents to reach a unique target rigid formation shape (up to rotation and translation) with desired inter-agent distances. We define a new potential function by incorporating both distance terms and signed area terms and derive the formation system as a gradient system from the potential function. We start with a triangle formation system with detailed analysis on the equilibrium and convergence property with respect to a weighting gain parameter. For an equilateral triangle example, analytic solutions describing agents’ trajectories are also given. We then examine the four-agent double-triangle formation and provide conditions to guarantee that both triangles converge to the desired side distances and signed areas.Z. Sun was supported by the Australian Prime Minister’s Endeavour Postgraduate Award from Australian Government. Sugie is supported by JSPS KAKENHI Grant Number JP16K14284. Azuma is supported by JSPS KAKENHI Grant Number JP15H00814. Sakurama is supported by JSPS KAKENHI Grant Number JP15K06143

Power Processing for Advanced Power Distribution and Control

A power packet dispatching system is proposed to realize the function of power on demand. This system distributes electrical power in quantized form, which is called power processing. This system has extensibility and flexibility. Here, we propose to use the power packet dispatching system as the next generation power distribution system in self-established and closed system such as robots, cars, and aircrafts. This paper introduces the concept and the required researches to take the power packet dispatching system in practical phase from the total viewpoints of devices, circuits, power electronics, system control, computer network, and bio-inspired power consumption

Tree of motility – A proposed history of motility systems in the tree of life

Motility often plays a decisive role in the survival of species. Five systems of motility have been studied in depth: those propelled by bacterial flagella, eukaryotic actin polymerization and the eukaryotic motor proteins myosin, kinesin and dynein. However, many organisms exhibit surprisingly diverse motilities, and advances in genomics, molecular biology and imaging have showed that those motilities have inherently independent mechanisms. This makes defining the breadth of motility nontrivial, because novel motilities may be driven by unknown mechanisms. Here, we classify the known motilities based on the unique classes of movement-producing protein architectures. Based on this criterion, the current total of independent motility systems stands at 18 types. In this perspective, we discuss these modes of motility relative to the latest phylogenetic Tree of Life and propose a history of motility. During the ~4 billion years since the emergence of life, motility arose in Bacteria with flagella and pili, and in Archaea with archaella. Newer modes of motility became possible in Eukarya with changes to the cell envelope. Presence or absence of a peptidoglycan layer, the acquisition of robust membrane dynamics, the enlargement of cells and environmental opportunities likely provided the context for the (co)evolution of novel types of motility

Dynamic Quantization of Nonlinear Control Systems

This paper addresses a problem of finding an optimal dynamic quantizer for nonlinear control subject to discrete-valued signal constraints, i.e., to the condition that some signals must take a value on a discrete and countable set at each time instant. The quantizers to be studied are in the form of a nonlinear difference equation which maps continuous-valued signals into discrete-valued ones. They are evaluated by a performance index expressing the difference between the resulting quantized system and the unquantized system, in terms of the input-output relation. In this paper, we present a closed-form solution, which globally minimizes the performance index. This result shows the performance limitation of a general class of dynamic quantizers. In addition to this, some results on the structure and the stability are given in order to clarify the mechanism of the best dynamic quantization in nonlinear control systems