Hidekatsu Tokumaru

A real-time learning algorithm for a multilayered neural network based on the extended Kalman filter

The extended Kalman filter (EKF) is well known as a state estimation method for a nonlinear system, and can be used as a parameter estimation method by augmenting the state with unknown parameters. A multilayered neural network is a nonlinear system having a layered structure, and its learning algorithm is regarded as parameter estimation for such a non- linear system. In this paper, a new real-time learning algorithm for a mul- tilayered neural network is derived from the EKF. Since this EKF-based learning algorithm approximately gives the mini- mum variance estimate of the linkweights, the convergence performance is improved in comparison with the backwards error propagation algorithm using the steepest descent tech- niques. Furthermore, tuning parameters which crucially gov- ern the convergence properties are not included, which makes its application easier. Simulation results for the XOR and par- ity problems are provided.

A nonlinear regulator design in the presence of system uncertainties using multilayered neural network

The authors present a novel nonlinear regulator design method that integrates linear optimal control techniques and nonlinear neural network learning methods. Multilayered neural networks are used to add nonlinear effects to the linear optimal regulator (LOR). The regulator can compensate for nonlinear system uncertainties that are not considered in the LOR design and can tolerate a wider range of uncertainties than the LOR alone. The salient feature of the regulator is that the control performance is much improved by using a priori knowledge of the plant dynamics as the system equation and the corresponding LOR. Computer simulations are performed to show the applicability and the limitations of the regulator.

Macroscopic Stability of Interconnected Systems

Abstract Stability concept which is characteristic to a class of large-scale and dynamic systems is introduced. The concept is called macroscopic ctability of interconnected systems. The dynamics of each sub¬system is evaluated by means of a first order system, called a comparison system of the subsystem. Then, conditions which insure macroscopic stability are obtained on the basis of comparison principles for differential inequalities. Finally an example of applications is shown.

The stability of generalized Volterra equations

Abstract In this paper, a particular type of a system of generalized Volterra equations [1], whose solutions are assured to be nonnegative for arbitrary nonnegative initial values, is considered. The extended stability theorem of LaSalle is used for deriving conditions for a nonnegative equilibrium point to be stable with respect to a certain subset of the Euclidean space. The obtained stability theorem has a close relation with Lyapunovs stability condition for linear systems with constant coefficients and is generally less restrictive than conditions known so far.

Recursive least squares circular lattice and escalator estimation algorithms

This note supplements the paper of Sakai [1] about circular lattice filtering with the derivation of optimal recursive least squares circular lattice estimation algorithms. The derivation is based on the geometric method of Lee, Morf, and Friedlander [2]. The same method is also applied to obtain an optimal recursive estimation algorithm for escalator structure of Ahmed and Youn [3].

Global stability of ecosystems of the generalized volterra type

Abstract In this paper, relations between structure and stability of ecosystems of the generalized Volterra type are investigated. Ecosystems of the generalized Volterra type are systems extended from the classic one by Volterra for a deterministic system of one predator and one prey. Structures of ecosystems are classified according to the existence of nonzero cycles and their lengths. The following results are obtained. If a system has no nonzero cycles of length greater than two, it is stable if the structural matrix is a P -matrix. Further, a system with only nonnegative cycles or with symmetric cycles is also stable if the structural matrix is a P -matrix.

Convergence properties of simplified gradient adaptive lattice algorithms

The convergence properties of four simplified gradient adaptive lattice algorithms are analyzed. First, the convergence models that specify the convergence rates are derived. Next, the variances of the estimation errors of the PARCOR coefficients in steady states are calculated. Using these results, the performance of these algorithms is compared.

Diagnosability and Distinguishability Analysis and Its Applications

As systems become more complex, it becomes necessary to understand, simplify, and apply fault diagnosis and fault-tolerant design. Although some graph-theoretical diagnostic models such as self-diagnosis model have been studied, the model can not be applied to most systems due to the assumption that each unit has its own testing capability. This paper presents a graph-theoretical diagnosis model expressed by a set of fallible units, a set of measurements, and an incident matrix indicating binary relation between these two sets. Since this model explicitly separates tested units (fallible units) and testing units (measurements), we can discuss diagnostic aspects from both sides. Diagnosability and distinguishability of the model with multiple faults are discussed from combinatorial point of view. Measures of t-fault diagnosability and t-out-of-s diagnosability which was introduced on the self-diagnosis model are discussed. Conditions for these diagnosabilities are expressed by a topological concept of fault distance. The concept of distinguishability is generalized to multiple fault situations called t-fault distinguishability. A lower bound for the distinguishability is obtained by using fault distance. The new concept of s-distinguishability class (s-dc) is presented. This analysis is recommended in the design of systems to attain a required level of diagnosability and distinguishability as well as in the analysis of present systems to investigate their diagnostic aspects. Two application examples are presented: Diagnosability and distinguishability analysis of error-correcting codes, and design of instrumentation systems of large plants with a required level of diagnosability.

Further condition for the delay-independent stabilization of linear systems

There are two different conditions for the delay-independent stabilization of linear systems by means of state variable feedback including no delays, one of which is also sufficient for decay rate assignability. In this paper a wider condition is presented for delay-independent stabilization. It is proved that this condition includes the conditions so far obtained

Delay-independent stabilization and decay rate assignability of linear systems with limited measurable state variables

Delay-independent stabilization and decay rate assignability of linear systems with limited measurable state variables are considered. To construct control signals, 2n-dimensional linear systems including no delays are introduced. The conditions obtained for delay independent stabilization are contained in systems with measurable state presented previously. The conditions obtained for decay rate assignability for systems with measurable state variables are also sufficient for the present system.