Hitoshi Takata

A control design of robotics using the genetic algorithm

This paper presents a new and practical method for a control design of a robotic system. In general, actuators in robotic systems are set with gears whose characteristics are elastic. Since a state feedback-type digital controller is usually used for such a robotic system, the design of the feedback gain of the controller is important, because undesirable vibrations or an overshoot in responses occur for high gains. Therefore the desired response, the output of a reference model, is designed first, and the feedback gains are determined so that the response will coincide with the desired response, which is an optimization problem. The gradient method works to some extent, but it takes a long time to get a satisfactory result. Thus we applied the genetic algorithm (GA) to this nonlinear optimization problem, which gave the very first convergence. The gains obtained have many useful applications. The results of a simulation are also given.

A prediction method of electric power damage by typhoons in Kagoshima via GMDH and NN

Kagoshima Prefecture has suffered from natural disasters by typhoons repeatedly. They hit power systems very badly and sometimes cut off electricity. To ensure the rapid restoration of electricity supply, one needs to predict the amount of damage by typhoon accurately. This paper proposes its prediction method by using the GMDH and NN (neural networks). This method enables us to predict the number of damaged distribution poles and lines from weather forecasts of typhoon. Effectiveness of the method is assured by applying it to the actual data.

Structure Selection and Identification of Hammerstein Type Nonlinear Systems Using Automatic Choosing Function Model and Genetic Algorithm

This paper presents a novel method of structure selection and identification for Hammerstein type nonlinear systems. An unknown nonlinear static part to be estimated is approximately represented by an automatic choosing function (ACF) model. The connection coefficients of the ACF and the system parameters of the linear dynamic part are estimated by the linear least-squares method. The adjusting parameters for the ACF model structure, i.e. the number and widths of the subdomains and the shape of the ACF are properly selected by using a genetic algorithm, in which the Akaike information criterion is utilized as the fitness value function. The effectiveness of the proposed method is confirmed through numerical experiments.

Design of Extremum Seeking Control with Accelerator

In this paper we are concerned with designing an extremum seeking control law for nonlinear systems. This is a modification of a standard extremum seeking controller. It is equipped with an accelerator to the original one aimed at achieving the maximum operating point more rapidly. This accelerator is designed by making use of a polynomial identification of an uncertain output map, the Butterworth filter to smoothen the control, and analog-digital converters. Numerical experiments show how this modified approach can be well in control of the Monod model of bioreactors.

Identification for Nonlinear Systems by the Automatic Choosing Function and the Genetic Algorithm

Abstract This paper deals with an identification method of nonlinear systems based on the automatic choosing function (ACF). A full data region is divided into some subdomains and the unknown nonlinear function to be estimated is approximately described by a linear equation on each subdomain. These linear equations are united into a single one by the ACF smoothly, and thus the resulting model becomes linear in the parameters. Hence these parameters are easily evaluated by the linear least-squares method. Besides the subdomains and the ACF are properly determined by the genetic algorithm.

Continuous-Time Identification of Nonlinear Systems Using Radial Basis Function Network Model and Genetic Algorithm

Abstract This paper deals with an identification method of continuous-time nonlinear systems based on a continuous-time radial basis function (RBF) network model. The higher order derivatives of input and output data are estimated by a delayed state variable filter, or the Butterworth filter. An unknown function of nonlinear term of the objective system is assumed to be approximately represented by an RBF network. The structure of the RBF network model is properly determined by using a genetic algorithm (GA). Moreover the cutoff frequency of the state variable filter are also designed by GA. The unknown weighting parameters of the RBF network and system parameters in the linear terms are estimated by the least-squares method. Simulation results are shown to demonstrate the effectiveness of the proposed method.

FORMAL LINEARIZATION OF NONLINEAR TIME-VARYING DYNAMIC SYSTEMS USING CHEBYSHEV AND LAGUERRE POLYNOMIALS

Abstract This paper is concerned with a formal linearization problem for a general class of nonlinear time-varying dynamic systems. To a given system, a linearization function is made up of Chebyshev polynomials about its state variables. The nonlinear time-varying system is transformed into a linear time-varying system in terms of the linearization function using Chebyshev interpolation to state variables and Laguerre expansion to time variable. An error bound formula of this linearization which is derived in this paper explains that the accuracy of this algorithm is improved as the order of Chebyshev and Laguerre polynomials increases. As its application, a nonlinear observer is designed to demonstrate the usefulness of this formal linearization approach.

Nonlinear feedback control of stabilization problem via formal linearization using Taylor expansion

In this paper we consider a nonlinear feedback control problem for stabilizing multidimensional nonlinear systems using a formal linearization method based on Taylor expansion. Our goal is to design a nonlinear feedback control which stabilizes the nonlinear system in wider region of state space with less restricted conditions. The single-input multidimensional nonlinear system is transformed into an approximated bilinear system with respect to a formal linearization function by a formal linearization method using Taylor expansion. Substituting the ordinary LQ control function to the bilinear terms, a linear system with respect to the formal linearization function is derived and a feedback control is obtained. Finally, we illustrate some simulations to verify our approach.

A Formal Linearization for a General Class of Time-varying Nonlinear Systems by the Cubic Hermite Interpolation and a Nonlinear Observer

A computational method of the formal linearization for time-varying nonlinear systems by using the cubic Hermite interpolation is proposed. We introduce a linearizing function that consists of the state variables, their squares, and the cubes. The nonlinear terms are approximated by the cubic Hermite interpolation and thus a formal linear time-varying system with respect to the linearizing function is acquired. The execution of this method is easily carried out by simple matrix multiplications. A nonlinear observer is synthesized as an application of this method and is verified through numerical example

Identification of continuous-time nonlinear systems via local linear equations united by automatic choosing function and genetic algorithm

Abstract This paper deals with an identification method of continuous-time nonlinear systems using a model expanded by a basis of automatic choosing functions (ACF). Higher order derivatives of input and output data are estimated by a delayed state variable filter, or the Butterworth filter. An unknown nonlinear function to be estimated is approximately described by local linear equations united by ACF. The resulting model is linear in the parameters, which are estimated by the least-squares method. The model structure and Butterworth filter are properly determined by a genetic algorithm. Simulation results are shown to demonstrate the effectiveness of the proposed method.