Since Mao initiated the study of stabilization of continuous-time hybrid stochastic differential equations (SDEs) by feedback controls based on discrete-time state observations in 2013, many authors have further studied and developed it. However, so far no work on the pth moment stabilization has been reported. This paper is to investigate how to stabilize a given unstable hybrid SDE by feedback controls based on discrete-time state observations, in the sense of H∞, asymptotic and exponential stability in pth moment for all p > 1. The main techniques used are constructions of the Lyapunov functionals and generalizations of inequalities
Figure 1: (a) Six-time shots of a four-second Japanese threesome pop unit "Perfume" dance motions. (b) Hilbert spectrum (Energy (color)-Frequency (y-axis)-Time (x-axis)) of the dance motion data. e white and red lines are weak and strong beats, respectively. Figure 2: Salsa dance motion with Japanese threesome pop unit "Perfume" choreographies. Decomposing Perfume and Salsa dance into di erent distinct modes (IMFs) using NA-MEMD. Perfume upper body motion IMFs are blended with the Salsa motion IMFs. A new Perfume dance movements with Salsa steps are created.ABSTRACT Human motions (especially dance motions) are very noisy, and it is hard to analyze and edit the motions. To resolve this problem, we propose a new method to decompose and modify the motions using the Hilbert-Huang transform (HHT). First, HHT decomposes a chromatic signal into "monochromatic" signals that are the socalled Intrinsic Mode Functions (IMFs) using an Empirical Mode Decomposition (EMD) [6]. A er applying the Hilbert Transform to each IMF, the instantaneous frequencies of the "monochromatic" signals can be obtained. e HHT has the advantage to analyze non-stationary and nonlinear signals such as human-joint-motions over FFT or Wavelet transform.In the present paper, we propose a new framework to analyze and extract some new features from a famous Japanese threesome pop singer group called "Perfume", and compare it with Waltz and Salsa dance. Using the EMD, their dance motions can be decomposed into motion (choreographic) primitives or IMFs. erefore we can scale, combine, subtract, exchange, and modify those IMFs, and can blend them into new dance motions self-consistently. Our analysis and framework can lead to a motion editing and blending method to create a new dance motion from di erent dance motions.
Motion capture data are widely used in different research fields such as medical, entertainment, and industry. However, most motion researches using motion capture data are carried out in the time-domain. To understand human motion complexities, it is necessary to analyze motion data in the frequency-domain. In this paper, to analyze human motions, we present a framework to transform motions into the instantaneous frequency-domain using the Hilbert-Huang transform (HHT). The empirical mode decomposition (EMD) that is a part of HHT decomposes nonstationary and nonlinear signals captured from the real-world experiments into pseudo monochromatic signals, so-called intrinsic mode function (IMF). Our research reveals that the multivariate EMD can decompose complicated human motions into a finite number of nonlinear modes (IMFs) corresponding to distinct motion primitives. Analyzing these decomposed motions in Hilbert spectrum, motion characteristics can be extracted and visualized in instantaneous frequency-domain. For example, we apply our framework to (1) a jump motion, (2) a foot-injured gait, and (3) a golf swing motion.
This paper used a model predictive control with an additional term to develop a modified longitudinal guidance law to reduce landing risk in an automatic carrier landing system. The landing risk model was established by using a longitudinal trajectory and touchdown point predictive principle. A traditional MPC was then involved in designing a modified automatic carrier landing system guidance law for the proposed model. The nonlinear landing mathematic model of an F/A-18 carrier-based aircraft was initially established. Considering the processed procedure in the model predictive control algorithm, the corresponding linear landing model was derived on the basis of the equilibrium states of the F/A-18. Second, landing trajectory in the longitudinal plane was analysed so that the predictive principle of the trajectory trend was reasonably addressed. Depending on the experimental sample data of a pilot model, some linear imitating envelopes are transformed from the corresponding nonlinear trajectory clusters. Furthermore, a touchdown point prediction model was further established based on the predicted trajectory and touchdown point. Third, the traditional model predictive control was introduced to integrate the landing risk term in the performance cost function to develop a novel modified algorithm that not only guides the aircraft to automatically approach and land on the carrier, but also eliminates landing risk during the final carrier approach. Linear matrix inequalities were imported to substitute algebraic inequalities derived from this new algorithm to increase calculating speed. A simulation mission was conducted on a semi-physical platform and compared with the traditional model predictive control without the additional term. The theoretical results validated the correctness and robustness of the modified algorithm and its capability to eliminate landing risk during terminal carrier approach.
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