Masayoshi Eguchi

A novel approach to the nonlinear H ∞ regulator problem

This paper presents a theoretical approach to the nonlinear H∞ regulator problem. From a fixed point theoretic point of view, it is shown that the nonlinear H∞ state feedback law is characterized as a fixed point of a mapping and its suboptimal solution can be obtained using standard optimization techniques. A simple numerical example is included to verify that the resulting feedback law actually enhances the robustness of a system.

Integral manifold andH? control in weak nonlinear systems

For a weak nonlinear system the authors obtained sufficient conditions for locking the solution of a differential equation system of the weak nonlinear type within a stable integral manifold, while satisfying the saddle point conditions of the optimal control evaluation function. The resulting solution can be used as a state feedback solution for the problem of H∞ regulator in weak nonlinear systems. By using the P solution of a Riccati matrix, sufficient conditions for obtaining the state feedback rule were derived from the results of discussion relating to the integral manifold. Then, the effectiveness of feedback of the weak nonlinear type was confirmed by simulation in a simple system. In addition, the Lyapunov function was used to evaluate stability of a closed-loop system obtained based on this feedback rule.

A self‐recovering communication buffer based on the concept of cellular automaton

This paper presents a self-recovering buffer memory for communication systems based on the concept of cellular automaton. The model proposed is a FIFO-type (First-in, First-out-type) memory which meets the conditions for a communication buffer and incorporates the principles of cellular automaton. By binding together a number of cells which can perform basic FIFO operations, it is found that each cell is capable of determining whether or not it is holding the first valid data in a queue based on information about its own status and it s neighboring cell. It also is observed that this model possesses a capacity for self recovery which always enables the buffer to return to a normal state in the event of an internal transient fault. Furthermore, by representing each cell with a sequential circuit, this buffer memory is prototyped with a gate array and its applicability is verified comparing it with existing FIFO design methods.

A topology for discrete spaces and its application in scratch detection for surface inspections

In conventional digital image processing, topological properties have been studied only for selected types of neighborhoods such as a 4- or 8-pixels connection. This paper analyzes properties of a finite topological space by defining it as a topological space with no restriction on the shape of a neighborhood. This leads to the identification of topological properties which are independent of the shape of a neighborhood and can be applied to image processing using neighborhoods other than a 4- or 8-connection. Since a finite topological space can treat only a single neighborhood this cannot be applied to image processing which uses multiple neighborhoods simultaneously. A finite topological space has been extended to a formal topological space having multiple neighborhoods, and its properties are analyzed in this paper. This theory is then applied to image processing. It has been difficult to detect scratches on a surface with patterns, such as a hard disk or a hairline-finished metal, by using a conventional digital topology because the scratches often consist of many small blocks and their images are stained by noise. The properties obtained through the formal topology have successfully been applied to these problems, and its effectiveness has been confirmed.

Existence of a Low-Order Integral Manifold and Non-linear Regulator Problems

Abstract A set of sufficient conditions which confine the solution of weak non-linear differential equations to some low order stable integral manifold are derived by applying the fixed point theorem. These conditions can be weakened substantially if the initial values of the differential equations are confined to some bounded region. These results are then applied to weak non-linear optimal regulator problems. Sufficient conditions are derived for the existence of a non-linear feedback control law which meets the neccesary conditions for optimality. An algorithm for calculating the feedback control law is proposed. Simulations using the algorithm exhibited favorable results.