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This paper presents weighted stochastic Riccati (WSR) equations for designing multiple types of optimal controllers for linear stochastic systems. The stochastic system matrices are independent and identically distributed (i.i.d.) to represent uncertainty and noise in the systems. However, it is difficult to design multiple types of controllers for systems with i.i.d. matrices while the stochasticity can invoke unpredictable control results. A critical limitation of such i.i.d. systems is that Riccati-like algebraic equations cannot be applied to complex controller design. To overcome this limitation, the proposed WSR equations employ a weighted expectation of stochastic algebraic equations. The weighted expectation is calculated using a weight function designed to handle statistical properties of the control policy. Solutions to the WSR equations provide multiple policies depending on the weight function, which contain the deterministic optimal, stochastic optimal, and risk-sensitive linear (RSL) control. This study presents two approaches to solve the WSR equations efficiently: calculating WSR difference equations iteratively and employing Newton's method. Moreover, designing the weight function yields a novel controller termed the robust RSL controller that has both a risk-sensitive policy and robustness to randomness occurring in stochastic control design., Comment: This paper is submitted to a journal for possible publication. The copyright of this paper may be transferred without notice, after which this version may no longer be accessible

Nanomechanical systems offer a versatile platform for both fundamental science and industrial applications. Resonating vibration has been demonstrated to enable an ultrasensitive detection of various physical quantities, with emerging applications including signal processing, biological detection and fundamental tests of quantum mechanics. It has also been shown that the mechanical vibration of a nanoscale cantilever can be used to detect electromagnetic analogue-modulated waves. However, signals obtained with nanoscale receivers are so weak that the data transfer often fails; to the best of our knowledge, no successful practical demonstration has yet been reported. Here, we present the first experimental demonstration of the use of nanomechanical systems for digital data transfer with a digital image. Furthermore, our fabrication method achieved a tiny gap around field emitter of vibrational nano-antenna, which enables the receiver to work with quite a low power consumption, on the order of 10nW.

We consider escape from a metastable state of a nonlinear oscillator driven close to triple its eigenfrequency. The oscillator can have three stable states of period-3 vibrations and a zero-amplitude state. Because of the symmetry of period-tripling, the zero-amplitude state remains stable as the driving increases. However, it becomes shallow in the sense that the rate of escape from this state exponentially increases, while the system still lacks detailed balance. We find the escape rate and show how it scales with the parameters of the oscillator and the driving. The results facilitate using nanomechanical, Josephson-junction based, and other mesoscopic vibrational systems for studying, in a well-controlled setting, the rates of rare events in systems lacking detailed balance. They also describe how fluctuations spontaneously break the time-translation symmetry of a driven oscillator.

A nanoscale receiver utilizing the cantilever of a carbon nanotube has been developed to detect phase information included in transmitted signals. The existing receiver consists of a phase detector and demodulator which employ a reference wave and carrier signal, respectively. This paper presents a design method to simplify the receiver in structure with enhancing the performance for the phase detection. The reference wave or carrier signal is not needed in the receiver via the proposed design method., Comment: 8 pages, 1 figure

Because of their nonlinearity, vibrational modes of resonantly driven nanomechanical systems have coexisting stable states of forced vibrations in a certain range of the amplitude of the driving force. Depending on its phase, which encodes binary information, a signal at the same frequency increases or decreases the force amplitude. The resulting force amplitude can be outside the range of bistability. The values of the mode amplitude differ significantly on the opposite sides of the bistability region. Therefore the mode amplitude is very sensitive to the signal phase. This suggests using a driven mode as a bi-directional bifurcation amplifier, which switches in the opposite directions depending on the signal phase and provides an essentially digital output. We study the operation of the amplifier near the critical point where the width of the bistability region goes to zero and thus the threshold of the signal amplitude is low. We also develop an analytical technique and study the error rate near the threshold. The results apply to a broad range of currently studied systems and extend to micromechanical systems and nonlinear electromagnetic cavities., Comment: The originally submitted manuscript

Guaranteeing stability of a designed control system is a challenging problem in data-driven control approaches such as Gaussian process (GP)-based control. The reason is that the inequality conditions, which are used in ensuring the stability, should be evaluated for all states in the state space, meaning that an infinite number of inequalities must be evaluated. Previous research introduced the idea of using a finite number of sampled states with the bounds of the stability inequalities near the samples. However, high-order bounds with respect to the distance between the samples are essential to decrease the number of sampling. From the standpoint of control theory, the requirement is not only evaluating stability but also simultaneously designing a controller. This paper overcomes theses two issues to stabilize GP-based dynamical systems. Second-order bounds of the stability inequalities are derived whereas existing approaches use first-order bounds. The proposed method obtaining the bounds are widely applicable to various functions such as polynomials, Gaussian processes, Gaussian mixture models, and sum/product functions of them. Unifying the derived bounds and nonlinear optimal control theory yields a stabilizing (sub-)optimal controller for GP dynamics. A numerical simulation demonstrates the stability performance of the proposed approach., Comment: 17 pages, 1 figure

In this paper, we present a compressed data structure for moving object trajectories in a road network, which are represented as sequences of road edges. Unlike existing compression methods for trajectories in a network, our method supports pattern matching and decompression from an arbitrary position while retaining a high compressibility with theoretical guarantees. Specifically, our method is based on FM-index, a fast and compact data structure for pattern matching. To enhance the compression, we incorporate the sparsity of road networks into the data structure. In particular, we present the novel concepts of relative movement labeling and PseudoRank, each contributing to significant reductions in data size and query processing time. Our theoretical analysis and experimental studies reveal the advantages of our proposed method as compared to existing trajectory compression methods and FM-index variants.

We consider the problem of coordination via signaling in network congestion games to improve social welfare deteriorated by incomplete information about traffic flow. Traditional studies on signaling, which focus on exogenous factors of congestion and ignore congestion externalities, fail to discuss the oscillations of traffic flow. To address this gap, we formulate a problem of designing a coordination signal on endogenous information about traffic flow and introduce a it self-fulfilling characteristic of a signal that guarantees an outcome flow consistent with the signal itself without causing the unwanted oscillation. An instance of the self-fulfilling signal is shown in the case of a Gaussian signal distribution. In addition, we show simple numerical examples. The results reveal how a self-fulfilling signal suppresses the oscillation and simultaneously improves social welfare through improved network efficiency., Comment: The final publication is available at Springer via http://dx.doi.org/10.1007/s11067-017-9351-4

We show that in periodically driven systems, along with the delta-peak at the driving frequency, the spectral density of fluctuations displays extra features. These can be peaks or dips with height quadratic in the driving amplitude, for weak driving. For systems where inertial effects can be disregarded, the peaks/dips are generally located at zero frequency and at the driving frequency. The shape and intensity of the spectra very sensitively depend on the parameters of the system dynamics. To illustrate this sensitivity and the generality of the effect, we study three types of systems: an overdamped Brownian particle (e.g., an optically trapped particle), a two-state system that switches between the states at random, and a noisy threshold detector. The analytical results are in excellent agreement with numerical simulations.

We study the stationary probability distribution of a system driven by shot noise. We find that, both in the overdamped and underdamped regime, the coordinate distribution displays power-law singularities in its central part. For sufficiently low rate of noise pulses they correspond to distribution peaks. We find the positions of the peaks and the corresponding exponents. In the underdamped regime the peak positions are given by a geometric progression. The energy distribution in this case also displays multiple peaks with positions given by a geometric progression. Such structure is a signature of the shot-noise induced fluctuations. The analytical results are in excellent agreement with numerical simulations.