This paper studies a novel approach to analysis of switched dynamical systems in perspective of bifurcation and multiobjective optimization. As a first step, we analyze a simple switched dynamical system based on a boost converter with photovoltaic input. First, in a bifurcation phenomenon perspective, we consider period doubling bifurcation sets in the parameter space. Second, in a multiobjective optimization perspective, we consider a trade-off between maximum input power and stability. The trade-off is represented by a Pareto front in the objective space. Performing numerical experiments, relationship between the bifurcation sets and the Pareto front is investigated.

This paper considers a velocity control problem for merging and splitting maneuvers of vehicle platoons. In this paper, an external device sends velocity commands to some vehicles in the platoon, and the others adjust their velocities autonomously. The former is pinning control, and the latter is consensus control in multi-agent control. We propose a switched pinning control algorithm. Our algorithm consists of three sub-methods. The first is an optimal switching method of pinning agents based on an MLD (Mixed Logical Dynamical) system model and MPC (Model Predictive Control). The second is a representation method for dynamical platoon formation with merging and splitting maneuver. The platoon formation follows the positional relation between vehicles or the formation demand from the external device. The third is a switching reduction method by setting a cost function that penalizes the switching of the pinning agents in the steady-state. Our proposed algorithm enables us to improve the consensus speed. Moreover, our algorithm can regroup the platoons to the arbitrary platoons and control the velocities of the multiple vehicle platoons to each target value.

In this research, we propose an effective stability analysis method to impacting systems with periodically moving borders (periodic borders). First, we describe an n-dimensional impacting system with periodic borders. Subsequently, we present an algorithm based on a stability analysis method using the monodromy matrix for calculating stability of the waveform. This approach requires the state-transition matrix be related to the impact phenomenon, which is known as the saltation matrix. In an earlier study, the expression for the saltation matrix was derived assuming a static border (fixed border). In this research, we derive an expression for the saltation matrix for a periodic border. We confirm the performance of the proposed method, which is also applicable to systems with fixed borders, by applying it to an impacting system with a periodic border. Using this approach, we analyze the bifurcation of an impacting system with a periodic border by computing the evolution of the stable and unstable periodic waveform. We demonstrate a discontinuous change of the periodic points, which occurs when a periodic point collides with a border, in the one-parameter bifurcation diagram.

This paper proposes a natural facial and head behavior recognition method using hybrid dynamical systems. Most existing facial and head behavior recognition methods focus on analyzing deliberately displayed prototypical emotion patterns rather than complex and spontaneous facial and head behaviors in natural conversation environments. We first capture spatio-temporal features on important facial parts via dense feature extraction. Next, we cluster the spatio-temporal features using hybrid dynamical systems, and construct a dictionary of motion primitives to cover all possible elemental motion dynamics accounting for facial and head behaviors. With this dictionary, the facial and head behavior can be interpreted into a distribution of motion primitives. This interpretation is robust against different rhythms of dynamic patterns in complex and spontaneous facial and head behaviors. We evaluate the proposed approach under natural tele-communication scenarios, and achieve promising results. Furthermore, the proposed method also performs favorably against the state-of-the-art methods on three benchmark databases.

This paper presents a novel identification method for hybrid dynamical system models, where parameters have stochastic and time-varying characteristics. The proposed parameter identification scheme is based on a modified implementation of particle filtering, together with a time-smoothing technique. Parameters of the identified model are considered as time-varying random variables. Parameters are identified independently at each time step, using the Bayesian inference implemented as an iterative particle filtering method. Parameters time dynamics are smoothed using a distribution based moving average technique. Modes of the hybrid system model are handled independently, allowing any type of nonlinear piecewise model to be identified. The proposed identification scheme has low computation burden, and it can be implemented for online use. Effectiveness of the scheme is verified by numerical experiments, and an application of the method is proposed: analysis of driving behavior through identified time-varying parameters.

A digital map is a simple dynamical system that is related to various digital dynamical systems including cellular automata, dynamic binary neural networks, and digital spiking neurons. Depending on parameters and initial condition, the map can exhibit various periodic orbits and transient phenomena to them. In order to analyze the dynamics, we present two simple feature quantities. The first and second quantities characterize the plentifulness of the periodic phenomena and the deviation of the transient phenomena, respectively. Using the two feature quantities, we construct the steady-versus-transient plot that is useful in the visualization and consideration of various digital dynamical systems. As a first step, we demonstrate analysis results for an example of the digital maps based on analog bifurcating neuron models.

Verification of temporal logic properties plays a crucial role in proving the desired behaviors of continuous systems. In this paper, we propose an interval method that verifies the properties described by a bounded signal temporal logic. We relax the problem so that if the verification process cannot succeed at the prescribed precision, it outputs an inconclusive result. The problem is solved by an efficient and rigorous monitoring algorithm. This algorithm performs a forward simulation of a continuous-time dynamical system, detects a set of time intervals in which the atomic propositions hold, and validates the property by propagating the time intervals. In each step, the continuous state at a certain time is enclosed by an interval vector that is proven to contain a unique solution. We experimentally demonstrate the utility of the proposed method in formal analysis of nonlinear and complex continuous systems.

This paper presents a nonlinear model of human brain activity in response to visual stimuli according to Blood-Oxygen-Level-Dependent (BOLD) signals scanned by functional Magnetic Resonance Imaging (fMRI). A BOLD signal often contains a low frequency signal component (trend), which is usually removed by detrending because it is considered a part of noise. However, such detrending could destroy the dynamics of the BOLD signal and ignore an essential component in the response. This paper shows a model that, in the absence of detrending, can predict the BOLD signal with smaller errors than existing models. The presented model also has low Schwarz information criterion, which implies that it will be less likely to overfit the experimental data. Comparison between the various types of artificial trends suggests that the trends are not merely the result of noise in the BOLD signal.

A dynamic controller, based on the Stability Transformation Method (STM), has been used to stabilize unknown and unstable periodic orbits (UPOs) in dynamical systems. An advantage of the control method is that it can stabilize unknown UPOs. In this study, we introduce a novel control method, based on STM, to stabilize UPOs in DC-DC switching power converters. The idea of the proposed method is to apply temporal perturbations to the switching time. These perturbations are calculated without information of the locations of the target orbits. The effectiveness of the proposed method is verified by numerical simulations and laboratory measurements.

Many controllers are implemented on digital platforms as periodic control tasks. But, in embedded systems, an amount of resources are limited and the reduction of resource utilization of the control task is an important issue. Recently, much attention has been paid to a self-triggered controller, which updates control inputs aperiodically. A control task by which the self-triggered controller is implemented skips the release of jobs if the degradation of control performances by the skipping can be allowed. Each job computes not only the updated control inputs but also the next update instant and the control task is in the sleep state until the instant. Thus the resource utilization is reduced. In this paper, we consider self-triggered predictive control (stPC) of mixed logical dynamical (MLD) systems. We introduce a binary variable which determines whether the control inputs are updated or not. Then, we formulate an stPC problem of mixed logical dynamical systems, where activation costs are time-dependent to represent the preference of activations of the control task. Both the control inputs and the next update instant are computed by solving a mixed integer programming problem. The proposed stPC can reduce the number of updates with guaranteeing stability of the controlled system.

This letter studies a digital return map that is a mapping from a set of lattice points to itself. The digital map can exhibit various periodic orbits. As a typical example, we present the digital logistic map based on the logistic map. Two fundamental results are shown. When the logistic map has a unique periodic orbit, the digital map can have plural periodic orbits. When the logistic map has an unstable period-3 orbit that causes chaos, the digital map can have a stable period-3 orbit with various domain of attractions.

Kudekar et al. proved an interesting result in low-density parity-check (LDPC) convolutional codes: The belief-propagation (BP) threshold is boosted to the maximum-a-posteriori (MAP) threshold by spatial coupling. Furthermore, the authors showed that the BP threshold for code-division multiple-access (CDMA) systems is improved up to the optimal one via spatial coupling. In this letter, a phenomenological model for elucidating the essence of these phenomenon, called threshold improvement, is proposed. The main result implies that threshold improvement occurs for spatially-coupled general graphical models.

Phase structure of nonlinear dynamical system is governed by the vector field and decides the trajectories. Accordingly, the power spectra of trajectories include the structural field effect on the phase space. In this paper, we develop a method for analyzing phase structure using power spectra of trajectories and reconstitute a potential function in the system.

A digital spiking neuron is a wired system of shift registers that can generate spike-trains having various spike patterns by adjusting the wiring pattern between the registers. Inspired by the ultra-wideband impulse radio, a novel theoretical synthesis method of the neuron for application to spike-pattern division multiplex communications in an artificial pulse-coupled neural network is presented. Also, a novel heuristic learning algorithm of the neuron for realization of better communication performances is presented. In addition, fundamental comparisons to existing impulse radio sequence design methods are given.

This paper presents a novel parallel boost converter using switched capacitors The switches are controlled not only by periodic clock but also by voltage-mode threshold that is a key to realize strong stability, fast transient and variable output. The dynamics is described by a piecewise linear equation, the mapping procedure is applicable and the system operation can be analyzed precisely.

Quad-core cpus have been a common desktop configuration for today's office. The increasing number of processors on a single chip opens new opportunity for parallel computing. Our goal is to make use of the multi-core as well as multi-processor architectures to speed up large-scale data mining algorithms. In this paper, we present a general parallel learning framework, Cut-And-Stitch, for training hidden Markov chain models. Particularly, we propose two model-specific variants, CAS-LDS for learning linear dynamical systems (LDS) and CAS-HMM for learning hidden Markov models (HMM). Our main contribution is a novel method to handle the data dependencies due to the chain structure of hidden variables, so as to parallelize the EM-based parameter learning algorithm. We implement CAS-LDS and CAS-HMM using OpenMP on two supercomputers and a quad-core commercial desktop. The experimental results show that parallel algorithms using Cut-And-Stitch achieve comparable accuracy and almost linear speedups over the traditional serial version.

This paper studies switched dynamical systems based on a simplified model of two-paralleled dc-dc buck converters in current mode control. In the system, we present novel four switching rules depending on both state variables and periodic clock. The system has piecewise constant vector field and piecewise linear solutions: they are well suited for precise analysis. We then clarify parameter conditions that guarantee generation of stable 2-phase synchronization and hyperchaos for each switching rule. Especially, it is clarified that stable synchronization is always possible by proper use of the switching rules and adjustment of clock period. Presenting a simple test circuit, typical phenomena are confirmed experimentally.

This paper studies a simple spiking oscillator having piecewise constant vector field. Repeating vibrate-and-fire dynamics, the system exhibits various spike-trains and we pay special attention to chaotic spike-trains having line-like spectrum in distribution of inter-spike intervals. In the parameter space, existence regions of such phenomena can construct infinite window-like structures. The system has piecewise linear trajectory and we can give theoretical evidence for the phenomena. Presenting a simple test circuit, typical phenomena are confirmed experimentally.

In this article, we introduce a new concept for the future information environment, called an "ambient information environment (AmIE)." We first explain it, especially emphasizing the difference from the existing ubiquitous information environment (UbIE), which is an interaction between users and environments. Then, we focus on an ambient networking environment (AmNE) which supports the AmIE as a networking infrastructure. Our approach of a biologically inspired framework is next described in order to demonstrate why such an approach is necessary in the AmIE. Finally, we show some example for building the AmNE.

Analysis of cascading outages in power systems is important for understanding why large blackouts emerge and how to prevent them. Cascading outages are complex dynamics of power systems, and one cause of them is the interaction between swing dynamics of synchronous machines and protection operation of relays and circuit breakers. This paper uses hybrid dynamical systems as a mathematical model for cascading outages caused by the interaction. Hybrid dynamical systems can combine families of flows describing swing dynamics with switching rules that are based on protection operation. This paper refers to data on a cascading outage in the September 2003 blackout in Italy and shows a hybrid dynamical system by which propagation of outages reproduced is consistent with the data. This result suggests that hybrid dynamical systems can provide an effective model for the analysis of cascading outages in power systems.