In this paper, we are concerned with a problem of optimization of the linear observations which are used in the stationary Kalman filter. Especially, we consider the optimization of the gain matrix in the observation. In the previous works one of the authors, an information theoretic criterion, based on a generalized Water Filling Theorem, was introduced to obtain a gain matrix which minimizes the stationary error variance. The merit of this approach is that both analytical and numerical solutions are rather easily obtained compared with the case of the performance criterion which is quadratic in the estimation error and the gain matrix. In this solution process, however, the Riccati equation of the error covariance matrix reduces to a quasi linear equation, and the condition for the existence of the solution of this equation is somewhat stronger than that of the usual Riccati equation. This paper is concerned with the case of the quadratic performance criterion. We propose a new method of numerical optimization by introducing the gradient method and a new rule of updating the angular parameters which are brought by the polar-coordinate representation of an orthogonal matrix. The results of numerical experiments show the efficiency of the algorithm.

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This paper discusses an approach of constructing a state estimator for a class of linear stochastic systems with randomly delayed observation data. State variables of the system is assumed to be observed over a communication network which causes the random delay. In our study, the random delay is assumed to consist of a sum of an average delay and a randomness. The observation data with the random delay can be represented by an observation model with state-dependent additive noise by using the Taylor series expansion around the time behind the average delay. This observation system becomes a stochastic bilinear system. The Kalman filter is constructed as the state estimator for the linear stochastic system based on the bilinear observation system. The effectiveness of the proposed Kalman filter is demonstrated for the several types of input signals such as a sinusoidal wave, a step function, a square wave and so on by numerical simulations.

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This paper treats the filtering and parameter identification for the stochastic hyperbolic systems with jump noise processes. The physical situation of this model can be found in finance problem, e.g., the term structure of the bonds is a typical example. It is well-known that the filtering algorithm including jump processes is not possible to be a closed form like Kalman filter. We eliminate the jump process from the system dynamics by using one observation data and convert the system to the Gaussian frame work. After deriving the Kalman filter and the related likelihood function, the adaptive estimation algorithm is constructed with the aid of parallel filtering scheme. Some numerical examples are demonstrated.

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In this paper, we introduce a strategy which chooses significant features based on information theory in 3-D object recognition. Our optimality criterion is a reduction of uncertainness in a recognition process. If uncertainty and ambiguity of the recognition process can be reduced, object recognition becomes more reliable. A technique to choose the optimal feature based on information theory is already studied for active object recognition. This paper proposes a feature selection strategy for recognizing 3-D objects by extending such a framework. The strategy is constructed by an entropy-based approach using an iterative algorithm. Significant features is chosen based on a set of geometric features consisting of three features in the feature selection strategy. We present 3-D object recognition process, and discuss the validity of the proposed feature selection strategy via some experiments.

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This paper describes a method for target-tracking by a moving camera such as a mobile robot based on a scheme of the fusion of the unsynchronous sensor data. To realize the interaction between the person and the robot, we need not only the location of the target but the relation of the target and the robot such as the motion plan of the target. This study focuses on the sensor data fusion scheme to estimate the relation between the robot and the targets. We apply a fuzzy inference for the sensor data fusion since the result of the fuzzy inference is useful for the fuzzy controller of the moving camera. In addition, the paper discusses the implementation of the fuzzy inference system for the target tracking as an RT component for a distributed component middleware. Experimental results show the feasibility of the proposed method.

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This study aims to develop an intelligent security camera(or Public Security System) for detecting and reacting immediately to criminal acts, especially, a kidnapping case using automobile. We present a system for automated detection of criminal acts that uses the morphological information among detected objects in video sequences to classify the video scenes into kidnapping case or not. Some experimental results of scene recognition by using skeleton analysis are shown. Skeleton analysis is very efficient to represent a structure of the target body. We also consider some technical aspects of the intelligent security camera.

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We propose an efficient and robust method of background image estimation, based on estimation of auto-regressive model coefficients using the Levinson algorithm. The method assumes that changes in brightness between consecutive frames have limited influence on the background image, and that the current background image can be defined using the brightness of the frame preceding it.

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This paper considers a problem on data compression of “Digital-Ink" which is a sequence of data sampled from the traced curve at a sampling rate. In particular, considering the case when there are some slips of pen during the handwriting input due to a frictionless sheet on the display, etc., we develop a robust method of digital-ink compression by employing optimal smoothing spline method based on B-splines. It is shown that L₁ smoothing spline can be used effectively for excluding the influence due to the pen slips. The performance is examined by some experimental studies.

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To support pan-contextual access to complex scene images, a pattern sensitive re-sampling scheme is introduced. By restricting ‘what-to-be-observed’ in future scenes to really existing objects exhibiting connected distributions of visual saliency, in this scheme, chromatic diversity and brightness distribution are jointly identified with invariant measure to be associated with fractal attractors. Through infinitely divisible representation of capturing probability, the image features are interpolated as mathematical expectation of infinite resolution. The re-sampling scheme has been verified by using naturally complex scene images.

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This study aims to develop a simple gaze tracking interface on laptop PC, for usability of the handicapped. In place of using EOG and IR-CCD, we developed the tracking interface by using digital processing under natural light. In order to reduce the installation costs, we used a CCD camera integrated into a laptop. Eye gaze estimation is carried out by simple projection of the correspondence between coordinate of cornea and laptop ' s display. We show some experimental results and future works.

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Various heating treatments are performed in the medical field throughout the world. To monitor the temperature distribution in the treatment area, it is strongly recommended to develop a noninvasive temperature measuring technique. Due to the fact that the temperature change can generate minute difference in the physical parameter in tissues, it becomes very difficult to measure the temperature change noninvasively for the deep target. Recent development of electromagnetic wave technique enables noninvasive temperature measurement inside the material using Magnetic Resonance Imaging (MRI). In this paper, the temperature distribution is recorded using MRI by measuring the phase of longitudinal relaxation time of proton. Furthermore, moxibustion treatment which is one of the techniques of acupuncture and moxibustion therapy was selected as the heat source. The result of temperature distribution map and the simulation were compared and reported. The paper will show that the noninvasive temperature distribution measurement is an innovative methodology for research in the traditional oriental medicine.

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In a financial market where risky securities are affected by hidden economic factors, we consider an optimal consumption/investment problem for the expected HARA utility of the investor's wealth on infinite time horizon. We report some results on the related Hamilton-Jacobi-Bellman equation, which is, after some transformation, a second order linear degenerate elliptic equation. Using its solution, an optimal consumption/investment strategy is specified.

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The purpose of the paper is to statistically quantify the effectiveness of unconventional monetary policy which the FRB implemented after the collapse of Lehman Brothers in September, 2008. The first quantity easy monetary policy refereed to QE1 is implemented from March of 2009 through March of 2010 and that of QE2 is from Nov. of 2010 through June of 2011. The statistical problem we have is the shortage of sample size. The estimation results by small sample size tend to have the bias. Honda and Tachibana (2011), who estimate the Japan's QE, to avoid the bias, expanded small sampling periods to large ones by using dummy variables. We apply their method to USA case and analyze the comprehensive economic impact and transmission mechanisms of the monetary policy in USA. Analysis using the structural Vector Auto Regressions (SVAR) model has shown the following three observations. First, QE1 and QE2 raise aggregate output through transmission paths of stock price, home price and exchange rates. Second, QEs decreased vix (Volatility index), so that investors would like to take risks in stock market trading. Third, QEs raise longer term interest rates via the income, price-level, and Fisher effects. These results suggest that the unconventional monetary policy in USA has been effective as a means to ease the economic slump.

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This paper investigates the effect of “quantitative easing monetary policy (QEMP)” which the Bank of Japan (BOJ) adopted from March 2001 through June 2006, by changing operating target for money market from interest rate to the monetary base that is defined as the sum of “Cash” and “Reserves at the BOJ”. The paper confirms that the monetary policy has contributed to the recovery of the prolonged deflation. First we estimate vector autoregressive (VAR) model, which consists of the reserves, stock, exchange rate and real GDP. Next we decompose money stock into transaction money and precautionary money to evaluate the transmission mechanism of the effect of reserves on the real economy by taking into account the financial anxiety. We have found a quantitative easing shock firstly increase transaction money and then raise output and price, which dispel the anxiety. We also confirm that a liquidity trap did not exist during the period of quantitative easing monetary policy.

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Effects of information and estimations in portfolio maximization problems of expected utility with respect to terminal wealth are considered. In this paper, assuming several strategies whose differences come from information of markets and estimations of a parameter, we theoretically and numerically study their effects to expected utility and distributions of wealth at the maturity, and characters of paths where the strategy works well or bad.

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In this paper, we mainly concern about nonlinear BSDE which is often used to describe the case of constraint on the wealth of an investor. Unlike the linear case, we can show that under a certain situation, both buyer and seller can create arbitrage opportunities in the derivative market. We utilize the relation between BSDE and PDE in order to obtain a boundary of solution. As a result, we succeeded in establishing a sufficient condition which guarantees the existence of arbitrage opportunities in the market as well as the limitation of an arbitrage.

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We propose the optimal execution strategy including the limit order. The arrival of the counterpart market order of our limit order is modelled by the Poisson process reduced from the Cox process. We formulate the limit order and market order by the regular stochastic control and impulse control respectively. The performance criterion consists of the terminal wealth and the inventory penalty function which copes with the uncertainty of the limit order. We solve the corresponding Hamilton-Jacobi-Bellman quasi variational inequality numerically using the implicit method. The result of the numerical simulation with the obtained optimal strategy gives a quantitative evaluation of the advantage to include the limit order into the execution strategy.

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In this paper, first as a basic formula for the discrete stochastic calculus , we give the multidimensional version of the discrete Itˆo formula. Then we price a certain type of lookback options in the discrete Black Sholes Model and find the discrete hedging strategy of these exotic options. We note that these results are concrete example of discrete Kennedy martingales.

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A new tool to measure the degree of randomness of a given sequence, named as the RMT-test, is introduced and applied on machine-generated random numbers as well as real-world data sequences. The tool consists of two parts: the qualitative evaluation that is aimed to visualize the degree of randomness, and the quantitative evaluation that is aimed to distinguish subtle differences of randomness among highly random sequences based on moment analysis, in which the moments of the actual eigenvalue distributions of the correlation matrix to the corresponding theoretical expression derived by the random matrix theory. The RMT-test is applied to solve practical problems by comparing the randomness of real data, such as the output of cryptographic hash functions MD5 and SHA-1, and high-frequency time series of stock prices. It is found that the stock of higher randomness tends to perform better than the stock of lower randomness in the following time period.

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A generalized Cauchy process has been extensively studied since it gives one of the three universal distributions in Beck-Cohen superstatistics. There are many stochastic processes which give Cauchy type distributions in non-equilibrium open systems. However, their different features of intermittency and associated nonlinear structures are not elucidated completely. This paper exhibits a class of generalized Cauchy processes with their temporal features in the first, second and third order systems. A theoretical method for discriminating their various stochastic models is also discussed.

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In this paper, for the purpose of evaluating the degradation level of the performance in application with the estimated parametric model in which the estimated parameters have the disturbance, we consider the relation between the robustness of parameter estimation and the model order. In this paper, the robustness of the estimated parameter is defined as the degradation level of the performance. After the application performance cost function is derived, the gradient at the estimated parameter is focused to evaluate the disturbance level of the performance in the application. As a result, when identifying the model with the true structure by maximum-likelihood method, the disturbance level is simply given as the function of the model order. And it is shown that the larger the model order is, the more the estimated parameter lacks the robustness in the application. In addition, the relation between the robustness and a information criterion is introduced.

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We consider partially observed discrete-time linear stochastic systems and assume that some entries of the system matrices are unknown. We propose a new method which identifies those unknown entries and the state vectors of those systems simultaneously. The key idea of the proposed method is utilization of the pseudomeasurement which is a fictitious and additional observation process on the unknown entries and will be modified so as to work for the partially observed systems. Augmenting the pseudomeasurement with the original observation process, we derive the new identification method by applying the extended Kalman filter. The proposed method is consistent with the conventional method (without pseudomeasurement) and so they can easily be unified to be a single iterative process for simultaneous identification and state estimation by switching the coefficient matrix of the augmented observation process.

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This paper studies grey-box modeling for mechanical systems in the frequency domain. A two-step grey-box modeling algorithm is developed: The state of the grey-box model is estimated by an initial model, and an improved model is then computed from the state. The effectiveness of the proposed algorithm is shown by a rotary type pendulum system.

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In this paper, we will develop an online statistical change detection method, which is used for detection of changes in a system under surveillance in closed-loop. A recursive algorithm of closed loop subspace model identification is presented, which is based on the matrix inversion lemma. The relation between the proposed recursive algorithm and the predictor-based subspace identification method (PBSID) is clarified from the viewpoint of a matrix-valued least squares problem. A test signal generated sequentially by the recursive algorithm is studied and its asymptotic whiteness is proved explicitly. The proposed online change detection method is based on a likelihood ratio test to examine the change in the covariance of the aforementioned test signal.

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Ionospheric anomaly is one of the major error sources that affect the performance of the GPS (Global Positioning System). In particular, ionospheric scintillation may cause GPS satellite signal loss, and multiple losses can degrade the availability of positioning/navigation services such as GBAS (Ground-Based Augmentation Systems). In order to improve the tracking performance of GPS receivers under scintillation conditions, a tracking loop aided by INS (Inertial Navigation System) has been developed and flight tests to evaluate it were conducted around the island of Ishigaki where ionosphere scintillation frequently occurs. Evaluation of phase tracking performance was carried out off-line using a software-defined GPS receiver which processes stored IF (Intermediate Frequency) data. The use of INS enabled a longer integration time of GPS signals, which increased the signal-to-noise ratio (SNR). As a result, the INS-aided tracking loop achieved continuous phase tracking even under strong scintillation conditions.

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ln this paper, a practical method for improving GPS-PPP(Global Positioning System-Precise Point Positioning) accuracy in urban canyons are presented by using a barometric pressure sensor. Several techniques to improve PPP quality are also integrated into a PPP algorithm which is available in case that there are few (only two or three) visible satellites from automobiles moving on the street in urban canyons. Therefore, this paper verifies the usefulness to integrate barometric pressure information into these methods.

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In this paper we present a carrier-phase-based RTK-PPP algorithm with multiple antennas which are disposed with solid geometrical distances and with the common receivers' clock errors, based on GR models. We present GR equations for multiple antennas, and derive the Kalman filtering formula of very precise point positioning in urban cayons.

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In this paper, the regional ionospheric VTEC models for GNSS (Global Navigation Satellite System) positioning in the local area like as Japan are investigated. The ionosphere is modeled based on VTEC (Vertical Total Electron Content) estimation methods. In order to model regional VTEC distribution from regional data, GEONET (Gnss Earth Observation NETwork) data are used and obtained from the GSI (Geospatial Information Authority of Japan). In our previous research, Least Squares method has been applied. In this paper, we propose the method by applying Kalman Filter. In the experiments, the ionospheric VTEC is modeled by the previous and proposed methods.

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Ionosheric delay is one of the major error sources in GNSS (Global Navigation Satellite System) positioning. For single frequency system, it is very important to effectively correct the ionospheric delay and the so-called Klobuchar model has been widely used due to its well known properties such as computational simplicity. The Klobuchar model is one of the global ionospheric models, and it can correct about 50% RMS ionospheric errors[1]. On the other hand, there are some models that can achieve better accuracy than the Klobuchar model, the SCHA (Spherical Cap Harmonics Analysis) model is one of such models. By the SCHA model, it has been reported that the ionospheric delays can be well modeled in the regional area such as the sky over Japan[2, 3]. In this paper, we investigate the parameter which is assumed to be constant in the Klobuchar model as well as Klobuchar like models in [4, 5, 6], and try to improve the model accuracy by assuming the parameter as a function of the geomagnetic latitude. Also, the positioning results based on the Klobuchar like models are compared by experiments using long term (half year) observation data.

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Randomized algorithms for optimal power flow problems are presented. A standard optimal power flow problem is to minimize a fuel cost satisfying power flow equations and some inequalities consisting of the limits on control variables and the operating limits of a power system. Then, the robust optimal power flow problem is considered when uncertain active and reactive power is injected into the power system. Although both problems are highly nonconvex, the proposed algorithms always stop within the finite number of iterations and find a suboptimal solution which is a feasible in a probabilistic sense. It is shown that the maximum number of random samples is a polynomial of the size of the problems.

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The integration of renewable energy into an electric grid introduces new challenges to achieve optimal operating point for the power flow problem, because of randomness in generation and the distance between generation and consumption. These challenges can be overcome by using storage with appropriate capacity and efficient strategy to charge and discharge. In this work, we introduce a model of the power flow problem with storage so that it can be used to inject active and reactive power into the grid. We formulate an optimal power flow problem for a distribution grid with storage as a multi-period control problem based on the deterministic and stochastic nature of load and generation. We propose a multi-objective optimization function, in which the operating objectives are as follows: i) injecting reactive power into the power system for decreasing distribution loss and voltage deviation; and ii) maximizing renewable energy integration with minimum curtailment.

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In car-navigation systems, car position measurement estimates the car's position and heading angle from the out-puts of a GPS receiver and sensors, and calculates the position on a link that represents a road and is recorded in a digital road map. We focus on the latter process, which is map matching. If there are large errors in the car's estimated position and heading angle as well as in link position and direction angle, map matching selects an incorrect link. We previously proposed a map-matching method that calculates the criterion from the error variances of the positions and direction angles of the links, too. However, this method must in advance measure the error variances of the positions and direction angles of the links, which are different from one area to another. This paper proposes a map-matching method with a function to calculate the error variances of the position and direction angle of the links in a digital road map and that can remove the previous measurement work. The performance of this function was evaluated, and the performance of this map-matching method was compared with that of the conventional method by using numerical computation.

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In this paper, we experimentally investigate the cooperative balancing task on a virtual coupled inverted pendula (CIP) model, performed by a pair of an invisible artificial controller and a human subject, where experimental participants were not allowed to watch the movement of the artificial partner during experiments. The experimental result on Lyapunov exponents implies that the human subjects who never have experienced the balancing tasks with visible controller, seems to try to make the artificial controller neutrally stable as well as the subjects who have already experienced. Therefore, the result implies that at least as to the human subjects in the present study, there are no influence of learning with the visible controller on the stabilities of the task with invisible controller.

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This research investigates the deterioration of rotating equipment with misalignment via actual experimental data. Data to use the analysis of the deterioration are obtained from an acceleration sensor. Not only the deterioration prediction but also the residual life prediction is conducted by using on-line estimation through weighted least square method. In this research, to evaluate the prediction method, the deterioration is analyzed via multiple experimental data obtained from rotating equipment with misalignment.

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The aim of this research is to evaluate the behavior of small scaled wind turbine system against strong wind input using electromagnetic stall control system. In general, the wind turbine system is generating energy from the revolution of blades. The revolution of blades is depended on the velocity of wind. Therefore, if there is strong wind then the revolution of blade is increased and consequently more energy will be generated. Therefore, generally the wind turbine systems are located in the gale area in order to generate energy efficiency. However, there are some limitations of the revolution of blades or the angular velocity of blades, especially in small-scaled turbine. If the angular velocity exceeds the limit of revolution, then wind turbine system may breakdown. Thus in this paper, in order to avoid the malfunction of small-scaled wind turbine system, electromagnetic stall control (ESC) is suggested. ESC can control the angular velocity without having any connection with shaft. Thus, we would control angular velocity much efficiently than the conventional stall control method such friction stall control. As a consequence, we could verify the reliability of ESC system.

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The results of experiments on balancing a virtual inverted pendulum with over-damped dynamics are reported. Three types of pendulum, namely, an inverted stick, a triangle pendulum, and a vibrating spring were used in experiments and subjects of different age, gender, and skill of balancing participated in these experiments. It is demonstrated that the main characteristics of human balancing under the analyzed conditions, in particular, the phase portraits and the distribution functions of the pendulum angle and the angular velocity are universal in form. Only the characteristic scales depend on the subject features and the difficulty of balancing.

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Understanding how humans control unstable systems is central to many research problems, with applications ranging from quiet standing to aircraft landing. Increasingly much evidence appears in favor of event-driven control hypothesis: human operators are passive by default and only start actively controlling the system when the discrepancy between the current and desired system states becomes large. The present study proposes a stochastic model describing the transitions between the passive and the active phase of control behavior, which is based on the concept of random walk in double-well potential. Unlike the conventionally used model of fixed threshold, the proposed model is intrinsically stochastic and thus conforms to the physiological interpretation of the threshold as a probabilistic rather than deterministic notion. The model is studied numerically and is confronted to the experimental data on virtual stick balancing. The results confirm the validity of the model and suggest that the double-well potential can be used in modeling human control behavior in a diverse range of applications.

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This paper is concerned with output synchronization of nonlinear agents over a switching communication network. Under the assumption that the topology of the network is an i.i.d. stochastic process, a sufficient condition for synchronization was derived by Takaba (2012) in terms of a linear matrix inequality including the expected value of graph Laplacians. However, such an expected value may not be available in practical situations, we attempt to extend the above synchronization condition to the case where the expected Laplacian belongs to a prescribed polytopic set. Simulation results are also included.

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In this paper, we propose visual support ways for articulation in pronunciation correction and investigate the effect through some experiences. The way which we have proposed is realized by display of formants and shapes of mouth and tongue, which are derived based on the formants of speaker's voice. These displays can lead supported ones to recognize their pronunciation different from correct pronunciation.

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This paper discusses human brain activities of frontal lobe under glucose tolerance test. The results of the test are treated and evaluated numerically using oxidized hemoglobin densities which are measured by near infrared spectroscopy. We apply multivariable estimated models of auto-regressive form with upper triangular estimates. They are given by hierarchical decomposition analysis, which show properties of each stage.

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Artificial respirators are widely used for patients with little or no autonomous breathing ability. Doctors are required to pay scrupulous attention for the use of the artificial respirators. And doctors must set the artificial respirator in consideration of each patient's pulmonary characteristic. However, we do not understand the pulmonary characteristic of the patient by the measurement of data. Therefore, the setting of the artificial respirator is decided by the experience and the intuition of the doctor now. Purpose of this study are to develop a method to estimate the static P － V curve and the pulmonary elastance of the patient and to set a ventilation condition of the artificial respirator. The static P － V curve and the pulmonary elastance expresses the important feature of the lung, and the static P － V curve is a basis for deciding the air-way pressure limit value. In our previous work, we have presented an estimation technique of the pulmonary elastance by fuzzy logic. Parameters of the pulmonary elastance (f_E(V)) are different in each fuzzy rules. Then, it is said that other parameters do not change in a short time(one cycle breath). Nevertheless, in the previous study, these parameters were estimated to be different values in parameters estimation of each fuzzy rule. It is considered that the estimated precision of the static P － V curve is influenced by these values. We solve this problem using new estimation procedure. In addition, a ventilation condition of the artificial respirator is set using estimated static P － V curve.

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A mathematical model of Caprine arthritis encephalitis (CAE) that has a great economic impact in goat farming Transmission path of CAE virus is mainly by vertical transmission through breast milk. Droplet infection and sexual infection is known as other transmission path. From these facts, mathematical model of CAE was created based on the model of spread of sexually transmitted disease (STD) in the human case. The model is analyzed to determine the stability.

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This paper is concerned with a bifurcation analysis of a stochastic lumped parameter system. The P-bifurcation (Phenomenological bifurcation) and the D-bifurcation (Dynamical bifurcation) are major analytical methods for the stochastic bifurcation. The P-bifurcation studies a stationary measure corresponding to the one-point motion, while the D-bifurcation approach is based on the stability of invariant measures. Since the P-bifurcation is based on the one point-motion, there is a possibility to miss certain branches in bifurcation diagrams. So, we study the bifurcation in the stochastic lumped parameter system by the D-bifurcation approach.

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The work is devoted to possible generalizations of the Langevin equation based on the notion of the intermediate point determining the contribution of nonlinear random forces and different channels of noise action.

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The problems we consider in this paper arose in a probabilistic treatment of card shuffling. However we treat them as stochastic discrete time switching systems. When a deck of n cards is used the state space has n! elements so that for even small n the problem becomes very difficult to handle. We show that we can reduce the dimension of the state space first to the number of partitions n into non-negative integer parts and then using this we reduce the state space to size n for a particular type of shuffle. We demonstrate the procedure in this paper with a deck of size 5.

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In this paper, existence of chaotic oscillation in nonlinear systems is studied. Firstly, a method invoking one dimensional piecewise continuous map(PCM) in order to study various types of oscillations in nonlinear dynamical systems described by ordinary differential equations. The systems studied in this paper are of Van der Pol-Mathieu type. Secondly, the sine circle maps are obtained from the data sequence of state variables of nonlinear systems, then the PCM is obtained to approximates the sine circle map by root mean square method. The PCM consists of two linear lines lie in the two domains divided by a cut-off parameter. Furthermore, Lyapunov exponents of the motions in the PCM are studied to existence for chaotic motions and to existence for periodic motions. Finally, computational experiments on the nonlinear systems and on the PCM show that the proposed method is effective to study the existence of chaotic oscillations and periodic oscillations in nonlinear dynamical systems such as Van der Pol-Mathieu type.

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In recent years, damage caused by torrential rain is occurring frequently in global scale. In order to prevent the damage caused by this, more accurate forecast system is needed. However, it is difficult to predict guerrilla rainstorm that occurs locally within widespread torrential rainfall. Therefore, it must be predict accurately the amount of torrential rain in anticipation of few minutes as much as possible. We develop short term forecasting method of growth and disappearance phenomenon of rainfall that based on the fact that torrential rainfall tend to develop and disappear within the period of 30 minutes to 1 hour. To measure the rainfall level and velocity of nucleus of rain drop, we use the high resolution radar. For an immediate and rapid and precise prediction of guerrilla rainstorm, at first, we develop the state transition algorithm to predict the rain-level. But for the short term prediction, it is not suitable for general methods. To overcome the weakness of the general state transition methods, we introduce the rapid state-transition ones based on short-period sampling data. Furthermore, to achieve the more precise prediction scheme, we also introduce the estimation method of the coordinates of center of gravity movement of rain cloud. The effectiveness of the newly proposed hybrid prediction algorithm that consist of short term state transition method and estimation of center of gravity of rain cloud was verified by numerical simulation for actual rain-level data. As a result, the prediction accuracy was remarkably improved.

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The rotor-router model is a class of deterministic processes on graphs which can simulate the random walks. In this model, each vertex has a rotor-router which indicates the walker's movement. Every walker moves on the graph following the rotor-router's instructions. In this paper, we propose a model with independent and identically distributed initial rotor-routers on the line. We show limit theorems for the total time spent in the positive side and negative side of the line.

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This paper presents a convergence analysis of multi-agent consensus algorithm with noisy communication. A stochastic approximation method is applied to an average consensus algorithm and the relation between the consensus accuracy and the number of iteration is clarified. A bound of the variation of the agents at the specific number of iterations is also derived with a probabilistic guarantee.

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Bilinear systems are ubiquitous in dynamics and control literature. The concept of bilinear systems is attributed to input-output coupling terms. Stochastically influenced bilinear systems are described via bilinear stochastic differential equations. Bilinear systems are attractive and popular for two reasons: (i) first, they offer closed-form solutions for time-varying as well as time-invariant settings (ii) they preserve some of the qualitative characteristics of non-linear stochastic systems. In this paper, we construct a mathematical theory of a scalar time-varying bilinear ‘Stratonovich’ stochastic differential equation with a vector random input by deriving its closed-form solution and related results. Secondly, the analytic result of the paper is applied to a series RL circuit Stochastic Differential Equation (SDE), a bilinear stochastic dynamic circuit. This paper accomplishes the noise analysis of the bilinear dynamic circuit by deriving the mean and variance equations as well. The theory of this paper hinges on the ‘Stratonovich calculus’, and characteristic function of the vector Brownian motion. This paper will be of interest to dynamists, stochasticians looking for advances in bilinear systems and their control. More precisely, this paper opens up research directions in stability and control of bilinear stochastic systems by exploiting the analytic results of this paper.

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