In this paper, the author investigates the statistical moments such as expectations and variancesfor a class of fuzzy random sets, where the fuzzy random set is considered as a model of the capriciousvague perception of a crisp phenomenon or a crisp random phenomenon.First, the class of fuzzy random sets, which has been proposed by author[1–3], where the vagueperception of a crisp phenomenon fluctuates slightly but randomly by the state of a capriciousperson’s mind, is refined and its expectation and variance are introduced.Secondly, the refined class of fuzzy random sets is extended to the models for the capricious vagueperceptions of crisp random phenomena, and their expectations and variances are investigated fromthe viewpoint of the multi-valued logic.
This paper is concerned with the control strategy by vaccination of the infectious disease spreadin the populations consisting of the susceptible, the infected and the recovered (SIR). In the realisticspread of the infectious disease, changes in the environment and the weather cause some kinds ofrandom fluctuations in the infection and the recovery rates, etc. Moreover, medical facilities havegenerally the maximal capacity for treatment of diseases. Taking these facts into consideration, wepropose the stochastic infectious model with vaccination and saturated treatment, and we considerthe stochastic optimal vaccination problem for the SIR model with saturated treatment using thestochastic maximum principle and the four-step scheme. We construct a feasible optimal vaccinationsystem. By numerical simulations, we validate the efficacy of the optimal vaccination strategy.
This paper considers a problem on the non-negative derivative constraints on the cubic smoothingspline curves using normalized uniform B-splines as the basis functions. In particular, we derive acondition for monotonic constraints over interval based on the study of Fritsch and Carlon. Moreover,we present how these results are incorporated in the optimal smoothing spline problems. Theperformance is examined by a numerical example.
The author has been developing a navigation system for safety for mobile robots, mobility scooters and pedestrians by using depth sensors which can capture range data of image size. If the geometrical relation between the sensor and the space is completely known, each point of the captured range data can be classified into three groups: upper than the ground, on the ground, and lower than the ground. However, it is essential to be able to deal with the unpredictable change of the posture of the sensor due to the movement of the attached body. The author already developed a real-time estimation scheme of the posture including pitch angle, roll angle, and height from the observed data in the framework of optimization. In this paper, the author proposes an estimation scheme based on the state space model and apply Extended Kalman filter for the same application problem. We will compare the algorithms by experimental results and will show the usefulness of the proposed algorithm.
In this paper, we experimentally study cooperative human balancing tasks performed by a pair ofa human subject and an artificial controller, based on the coupled inverted pendula (CIP) model. Inorder to examine what kind of influence does the feedback gain of the controller on dynamic stabilitiesof the cooperative balancing tasks, we experimentally estimate Lyapunov exponents of balancingerrors of the system of human subject and artificial controller, in which the human subject is incooperation with the artificial controller having several different feedback gains. The result impliesthat the human subject seems to try to make the artificial controller minimally or neutrally stable.
We proposed a stochastic (or statistical) Equivalent linearization - Gaussian Sum Filter(: EqGSFilter) for discrete time nonlinear Systems. Subsequently, in this paper, we investigate and showthe further results related to the EqGS Filter. Especially we discuss a method to apply Gauss-Hermite quadrature rules for evaluation of the conditional expected values of the quantities requiredto design the EqGS filter. Finally, we show the estimation results of AR modeling comparison withthe extended Kalman and the equivalent linearization filters.
In this paper, the ionospheric models for GNSS (Global Navigation Satellite System) positioningin the local area like as Japan are investigated and the prediction models are discussed. The ionosphericdelay is modeled by applying SCHA (Spherical Cap Harmonic Analysis). It is well knownthat the ionosphere varies according to solar activity. Therefore, ionospheric effect on GNSS positioningvaries with not only the position but also the local time, and it has a periodicity. The periodiccharacteristics of the ionosphere are investigated by SCHA ionospheric models. The purpose of thisresearch is to predict the ionospheric delay model for the real time positioning. Based on our investigation,the ionospheric delays are predicted with AR (Auto-Regression) model. Furthermore thecapability for ionospheric model prediction is discussed. In the experiments, the proposed predictionmodels are compared with Klobuchar model.