This paper proposes an identification method for a class of nonlinear systems using a neural network and a noise model. A three-layer neural network is used as a plant model of the nonlinear system, and the noise model is applied as a whitening filter. Since noise can not be observed directly, an identification method is proposed in which the neural network and the noise model are calculated with the bootstrap method. We are able to obtain the approximate maximum estimated value of the nonlinear system, where the estimated value is determined based on Akaike's information criterion. Simulation results are shown to show the effectiveness of the proposed method. The validity of the obtained model is investigated by evaluating the covariance of an estimate error, means, and residual tests. Finally, the simulation result of the undisturbed output and the output of the obtained model are compared and it is shown that a neural network following the undisturbed output and a whitening filter are obtained.
This paper deals with classification problem, such as diagnosis, in which classes are defined by categorical forms. Supposing there are some sample data, and each datum has n kinds of characteristic values. The problem to classify these samples into given m classes based on their characteristic values has been discussed for a long period of time. However, classic methods including the discriminant analysis are difficult to be applied to actual problems, because the assumption of multivariate normal distribution and equality of variance-covariance matrices are needed. In this paper we propose a classification method using the associatron as an associative memory machine. We extend the associatron so as to have stable three leveled outputs following in the steps of a method given by Kanagawa et al. Examples of diagnosis of liver disease and the problem of iris classification are demonstrated.
In linear ω-periodic discrete-time systems, eigenvalues of the state transition matrix over the time interval nω dominate stability, where n is the dimension of the state vector. The periodic discrete-time system is called to be sample observable when the state can be determined from observation of output at only one time within one period. Under the assumption that eigenvalues of the monodromy matrix in an open-loop system are distinct, it is shown that the closed-loop system can be stabilized by applying the sampled output nω-periodic hold control if and only if the open-loop system is stabilizable and sample detectable at some time t0.
The back propagation method on the basis of the gradient method is often utilized as a learning rule of a neural network. This paper proposes a back propagation method using the least mean-square method for the output recurrent neural network. The approach consists of the decision of the input vector and the parameter estimation of each layer. The input vector of the output layer is corrected to decrease the output error corresponding to learning rate and the learning value of the other layer. The parameter is calculated using the least-square method from the obtained input and output of each layer. The identification result for the linear oscillation system shows the effectiveness of the proposed algorithm which is not based on the gradient method. It is shown that better estimate is obtained by the proposed algorithm compared with the classical back propagation method.
In this paper, we propose a new frequency-domain validation test for uncertainty models having white noises and norm-bounded unmodeled dynamics. In this method, a statistical whiteness test is integrated into the deterministic model validation methodology and we consider the whiteness test based on the averaged periodogram of data segments in order to reduce the validation problem into a convex problem with less computation burden. One of the distinguished features of our method is that the quality of the validation test can be improved by increasing the data segments because of the whiteness test. Also, one of the merits of our frequency-domain validation test is that we need a priori information in time-domain only. A numerical example is given to illustrate the effectiveness of the proposed method.
In the genetic algorithms (GAs), maintenance of the diversity of the population is an important issue to enhance their optimization and adaptation ability. The authors have proposed the thermodynamical genetic algorithm (TDGA), which can maintain the diversity explicitly and systematically by evaluating the diversity of the population as entropy and by selecting offspring so as to minimize the free energy. In applications of the GA to problems of adaptation to changing environments, maintenance of the diversity is an essential requirement because it is a key factor of the GA in yielding novel search points continuously for adaptation. This paper discusses adaptation to changing environment by means of TDGA. The authors propose a control method of the temperature, an adjustable parameter in the TDGA. That is, the temperature is controlled by a feedback technique so as to regulate the level of the entropy of the population. The adaptation ability of the proposed method is confirmed by computer simulation taking time-varying knapsack problems as examples.
In this paper, we discuss convergence of iterative learning control based on the gradient method for linear discrete-time systems. First, it is shown that residuals generated by the algorithm converge exponentially and therefore, observation errors or disturbance does not cause divergence. Second, the convergence conditions are expressed as strictly positive realness of the ratio of transfer functions. Conditions for the strictly positive realness is presented when there exists uncertainty of parameters in the transfer function and it is known that they are in given intervals. We also propose a simple sufficient condition for the strictly positive realness, which is based on a special structure of the problem. Finally, we illustrate design procedure based on the results given in this paper. Applications of the results to sampled-data systems are also discussed.