Sampling Instants Research Articles

Mathematical Opportunities: Noticing and Acting

Recent studies on the improvement of quality of teaching and learning revealed that teachers should act as a facilitator, coach or guide to foster students’ knowledge and skills. However, teachers’ professional knowledge and skills is one of the determinants of how effectively they can act in accordance with such roles in a classroom setting. To support the development of both pre-service and in-service teachers’ professional skills is thought as a valuable attempt to improve the effectiveness of teaching in schools. Therefore, under a university-school collaboration program, we provided an opportunity for pre-service mathematics teachers to work with students throughout a year and we investigated their pedagogical content knowledge and noticing skills. We aimed to determine whether or not pre-service teachers attended to mathematical opportunities occurred while interacting with students and we analyzed how they responded to those opportunities. In this paper we discussed their responding actions through two sample instances. Such an analysis is likely to contribute to the relevant literature in terms of identifying the nature of pre-service teachers’ in-the-moment noticing as well as evaluating their responding actions for mathematical opportunities.

Quasi-Soft Variable Structure Control of Discrete-Time Systems With Input Saturation

In the effort to improve the convergence rate of linear controllers, at the same time avoiding abrupt input transitions and implementation difficulties of time-optimal ones, soft variable structure control (VSC) may be considered. The classical formulation of soft VSC in continuous time domain assumes smooth, yet instantaneous switching in an infinite pool of controllers, which is not possible in the now commonplace digital control schemes. In discrete-time systems, the control structure may be changed only at the sampling instants, which results at best in quasi-soft behavior. This brief presents a design of quasi-soft VSC system, which by directly covering the discretization effects, permits maintaining the favorable properties of fast convergence and smooth inputs in discrete time domain, thus bringing the realization of soft VSC closer to the industrial reality. The properties of the presented control system are formally proved and verified experimentally.

Robust sampling‐based switching design for piecewise affine systems with application to DC–DC converters

The problem of designing the switching rules for piecewise affine systems which satisfy dwell time constraints is studied. With a proposed sampling-based approach which is different from existing traditional switching laws, the system can be updated and switched only at sampling instants. First, a sufficient condition for stability of piecewise linear affine systems converging to an invariant set is developed in the framework of the sampling-based switching, for which the lengths between successive sampling instants are assumed to be fixed. The corresponding sampled-based switching rules are obtained by solving a family of the linear matrix inequalities. Subsequently, these sampling lengths are extended from a fixed value to a certain interval and robust switching rules are obtained. Systems using these switching rules have the insensitivity to sampling period perturbation. Finally, an application to a DC-DC converter is provided to demonstrate the effectiveness of the proposed method.

Leveraging Label-Specific Discriminant Mapping Features for Multi-Label Learning

As an important machine learning task, multi-label learning deals with the problem where each sample instance (feature vector) is associated with multiple labels simultaneously. Most existing approaches focus on manipulating the label space, such as exploiting correlations between labels and reducing label space dimension, with identical feature space in the process of classification. One potential drawback of this traditional strategy is that each label might have its own specific characteristics and using identical features for all label cannot lead to optimized performance. In this article, we propose an effective algorithm named LSDM, i.e., leveraging label-specific discriminant mapping features for multi-label learning , to overcome the drawback. LSDM sets diverse ratio parameter values to conduct cluster analysis on the positive and negative instances of identical label. It reconstructs label-specific feature space which includes distance information and spatial topology information. Our experimental results show that combining these two parts of information in the new feature representation can better exploit the clustering results in the learning process. Due to the problem of diverse combinations for identical label, we employ simplified linear discriminant analysis to efficiently excavate optimal one for each label and perform classification by querying the corresponding results. Comparison with the state-of-the-art algorithms on a total of 20 benchmark datasets clearly manifests the competitiveness of LSDM.

Efficient Modulation and Processing Method for Closed-Loop Fiber Optic Gyroscope with Piezoelectric Modulator.

This paper presents a simple method for compensating the Sagnac phase shift in an interferometric fiber-optic gyroscope (I-FOG) with a piezoelectric modulator. The common advantages of I-FOGs with closed-loop compensation are linearized output characteristics and insensitivity to the light source power, including its time and thermal-induced fluctuations. Whereas closed-loop operation is normally achieved via ramp modulation requiring an electro-optic modulator, all-fiber architectures with a piezoelectric modulator are mostly limited to open loop. Nevertheless, such setups can more conveniently utilize a less expensive single-mode fiber with depolarized light and do not require any custom-made components. The proposed method allows us to combine the advantages of both approaches. Closed-loop compensation is ensured by adding further sinusoidal modulation to the common biasing modulation, such that the Sagnac phase shift is compensated solely at the sampling instants. We describe and experimentally demonstrate the proposed approach, utilizing a test setup to compare our closed-loop solution with open-loop operation. The results denote that the method provides a cost-efficient manner of performance improvement compared to the open-loop I-FOGs based on a piezoelectric modulator.

A symplectic moving horizon estimation algorithm with its application to the Earth—Moon L2 libration point navigation

Accurate state estimations are perquisites of autonomous navigation and orbit maintenance missions. The extended Kalman filter (EKF) and the unscented Kalman filter (UKF), are the most commonly used method. However, the EKF results in poor estimation performance for systems are with high nonlinearity. As for the UKF, irregular sampling instants are required. In addition, both the EKF and the UKF cannot treat constraints. In this paper, a symplectic moving horizon estimation algorithm, where constraints can be considered, for nonlinear systems are developed. The estimation problem to be solved at each sampling instant is seen as a nonlinear constrained optimal control problem. The original nonlinear problem is transferred into a series of linear-quadratic problems and solved iteratively. A symplectic method based on the variational principle is proposed to solve such linear-quadratic problems, where the solution domain is divided into sub-intervals, and state, costate, and parametric variables are locally interpolated with linear approximation. The optimality conditions result in a linear complementarity problem which can be solved by the Lemke’s method easily. The developed symplectic moving horizon estimation method is applied to the Earth-Moon L2 libration point navigation. And numerical simulations demonstrate that though more time-consuming, the proposed method results in better estimation performance than the EKF and the UKF.

Theorem and Algorithm Checking for Courses on Logic and Formal Methods

The RISC Algorithm Language (RISCAL) is a language for the formal modeling of theories and algorithms. A RISCAL specification describes an infinite class of models each of which has finite size; this allows to fully automatically check in such a model the validity of all theorems and the correctness of all algorithms. RISCAL thus enables us to quickly verify/falsify the specific truth of propositions in sample instances of a model class before attempting to prove their general truth in the whole class: the first can be achieved in a fully automatic way while the second typically requires our assistance. RISCAL has been mainly developed for educational purposes. To this end this paper reports on some new enhancements of the tool: the automatic generation of checkable verification conditions from algorithms, the visualization of the execution of procedures and the evaluation of formulas illustrating the computation of their results, and the generation of Web-based student exercises and assignments from RISCAL specifications. Furthermore, we report on our first experience with RISCAL in the teaching of courses on logic and formal methods and on further plans to use this tool to enhance formal education.

Multi-level Semantic Feature Augmentation for One-shot Learning.

The ability to quickly recognize and learn new visual concepts from limited samples enables humans to quickly adapt to new tasks and environments. This ability is enabled by semantic association of novel concepts with those that have already been learned and stored in memory. Computers can start to ascertain similar abilities by utilizing a semantic concept space. A concept space is a high-dimensional semantic space in which similar abstract concepts appear close and dissimilar ones far apart. In this paper, we propose a novel approach to one-shot learning that builds on this core idea. Our approach learns to map a novel sample instance to a concept, relates that concept to the existing ones in the concept space and, using these relationships, generates new instances, by interpolating among the concepts, to help learning. Instead of synthesizing new image instance, we propose to directly synthesize instance features by leveraging semantics using a novel auto-encoder network we call dual TriNet. The encoder part of the TriNet learns to map multi-layer visual features from CNN to a semantic vector. In semantic space, we search for related concepts, which are then projected back into the image feature spaces by the decoder portion of the TriNet. Two strategies in the semantic space are explored. Notably, this seemingly simple strategy results in complex augmented feature distributions in the image feature space, leading to substantially better performance. The codes and models are released in the github: https://github.com/tankche1/ Semantic-Feature-Augmentation-in-Few-shot-Learning.

Sampled‐data output feedback stabilization for a class of switched stochastic nonlinear systems

SummaryThis paper investigates a global sampled‐data output feedback stabilization problem for a class of switched stochastic nonlinear systems whose output and system mode are available only at the sampling instants. An observer is designed to estimate the unmeasurable state and thus a sampled‐data controller is constructed with the sampled estimated state. As a distinctive feature, a merging virtual switching signal is introduced to describe the asynchronous switching generated by detecting the system mode via a sampler. By choosing an appropriate piecewise Lyapunov function, it is proved that the proposed sampled‐data controller with allowable sampling period can stabilize the considered switched stochastic nonlinear systems under an average dwell‐time condition. Finally, two simulation results are presented to illustrate the effectiveness of the proposed method.

Rigor and Reproducibility: A Systematic Review of Salivary Cortisol Sampling and Reporting Parameters Used in Cancer Survivorship Research.

Salivary cortisol is a commonly used biomarker in cancer survivorship research; however, variations in sampling protocols and parameter reporting limit comparisons across studies. Standardized practices to provide rigor and reproducibility of diurnal salivary cortisol sampling and reporting are not well established. Previous systematic reviews examining relationships between diurnal salivary cortisol and clinical outcomes have resulted in mixed findings. It remains unclear which sampling protocols and reporting parameters offer the greatest utility for clinical research. This review examines diurnal salivary cortisol sampling protocols and reporting parameters to evaluate whether a standardized approach is recommended. A comprehensive search of intervention studies among adult cancer survivors including diurnal salivary cortisol resulted in 30 articles for review. Sampling protocols ranged from 1 to 4 days with the majority of studies sampling cortisol for 2 days. Sampling instances ranged from 2 to 7 times per day, with the majority collecting at 4 time points per day. Diurnal cortisol slope and cortisol awakening response (CAR) were the most commonly reported parameters associated with clinical outcomes. Flattened cortisol slopes, blunted CARs, and elevated evening cortisol concentrations were associated with poorer psychosocial and physiological outcomes. Based on our review, we propose that a rigorous, standardized diurnal salivary cortisol sampling protocol should include sampling at key diurnal times across ≥3 consecutive days to report diurnal cortisol parameters (i.e., CAR and slope) and objective measures of participant protocol adherence. Diminishing budgetary resources and efforts to minimize participant burden dictate the importance of standardized cortisol sampling protocols and reporting parameters.

Delay-Dependent Fuzzy Sampled-Data Synchronization of T–S Fuzzy Complex Networks With Multiple Couplings

This paper studies the problem of synchronization for a class of Takagi–Sugeno (T–S) fuzzy complex networks, where the node dynamics may include partial coupling, diffusion coupling, discrete-time coupling, and delayed coupling. A fuzzy sampled-data control strategy that takes into account the time-delay effect is designed to solve the synchronization problem of such networks. Synchronization criteria are established for complex networks with the target node by constructing a modified time-dependent Lyapunov functional and using a mathematical induction approach. In contrast to most existing results, the constructed Lyapunov functional is neither necessarily positive on sampling intervals nor needlessly continuous at sampling instants. Moreover, a corresponding greater aperiodic sampling interval is obtained. Numerical simulation is presented to demonstrate the feasibility and validity of the proposed strategies.

A less conservative stability criterion for sampled‐data system via a fractional‐delayed state and its state‐space model

SummaryThis paper introduces a state‐space model based on a fractional‐delayed state for a sampled‐data system described as a linear system under aperiodic sampling intervals. The new state‐space model exploits the information on the sampled‐data system and the fractional‐delayed state, which is defined on the sampling interval. The fractional‐delayed state and its state‐space model are utilized to construct the Lyapunov functional, which consists of the traditional Lyapunov function and a looped functional whose boundary conditions are zeros at sampling instants. Based on the Lyapunov functional, a stability criterion and a robust stability criterion are derived in terms of linear matrix inequalities. Simulation results show the effectiveness of the proposed criterion.

Mixed [formula omitted] sampled-data output feedback control design for a semi-linear parabolic PDE in the sense of spatial [formula omitted] norm

This paper addresses distributed mixed H2∕H∞ sampled-data output feedback control design for a semi-linear parabolic partial differential equation (PDE) with external disturbances in the sense of spatial L∞ norm. Under the assumption that a finite number of local piecewise measurements in space are available at sampling instants, a static sampled-data output feedback controller is suggested, where the sampling interval in time is bounded. The local piecewise measurements bring additional difficulty for the exponential stability and performance analysis since the existing Poincaré-Wirtinger inequality in 1D spatial domain is not applicable. By constructing an appropriate Lyapunov–Krasovskii functional candidate and employing Wirtinger’s inequalities, a variant of Poincaré-Wirtinger inequality in 1D spatial domain, as well as Agmon’s inequality, it is shown that the suggested static sampled-data output feedback controller not only guarantees the output exponential stability of the resulting closed-loop PDE in the spatial L∞ norm but also ensures the mixed H2∕H∞ performance index defined in the spatial L∞ norm, if the sufficient conditions presented in terms of standard linear matrix inequalities (LMIs) are fulfilled. The satisfactory and better performance of the suggested sampled-data feedback controller is demonstrated by numerical simulation results of an illustrative example.

Time-varying formation for linear multi-agent systems based on sampled data with multiple leaders

This paper investigates the time-varying formation problem of a linear multi-agent system (MAS) based on sampled data with multiple leaders. The leader group and the follower group form the MAS. Followers are driven to reach the time-varying formation where the center of the formation is the convex combination of the states of the leaders. First, a time-varying formation control protocol with sampled data is proposed, while communication among followers is only occurred at sampling instants, which reduces the waste of communication energy significantly. Second, sufficient conditions for the MAS achieving the desired time-varying formation under sampling with multiple leaders are derived. In the theoretical analysis, a Lyapunov function is constructed to derive sufficient conditions based on formation protocol with sampled data for the MAS reaching time-varying formation. In addition, under formation control with sampled data, the problems of time-varying formation of MAS with one leader and time-invariant formation of MAS with multiple leaders are the special cases of the problem discussed in this paper. Finally, one example is presented to demonstrate the obtained theoretical analysis.

Sampled-data adaptive observer for state-affine systems with uncertain output equation

The problem of sampled-data observer design is addressed for a class of state- and parameter-affine nonlinear systems. The main novelty in this class lies in the fact that the unknown parameters enter the output equation and the associated regressor is nonlinear in the output. Wiener systems belong to this class. The difficulty with this class of systems comes from the fact that output measurements are only available at sampling times causing the loss of the parameter-affine nature of the model (except at the sampling instants). This makes existing adaptive observers inapplicable to this class of systems. In this paper, a new sampled-data adaptive observer is designed for these systems and shown to be exponentially convergent under specific persistent excitation conditions that ensure system observability and identifiability. The new observer involves an inter-sample output predictor that is different from those in existing observers and features continuous trajectories of the state and parameter estimates.

Non-fragile sampled-data control of network systems subject to time-delay

ABSTRACTThis paper studies the consensus problem of non-linear network systems subject to time-delay through aperiodic sampled-data control, which is more desirable and flexible than periodic sampling control. By receiving the relative information of the neighboring nodes, each node can obtain control input signals at the discrete sampling instants. A new stability criterion is established for network systems via using a time-dependent Lyapunov functional and the free-weighting matrix method. The maximum upper bound of sampling interval can be achieved by solving Linear matrix inequality optimization problem. Under the basic work of a non-fragile sampled-data controller, network systems with time-delay are asymptotically stable. In the end, two numerical simulation examples can be provided to illustrate the validity of the application of the proposed algorithm.

Inter-sample output predictor based sampled-data ADRC supporting high precision control of VCM servo systems

Ultra high precision servo control systems usually require fast sampling rate to achieve desired digital control performance, where output sampling restrictions (such as sensor bandwidth) pose major challenges for such applications. In this paper, we propose a novel sampled-data multi-rate active disturbance rejection control (ADRC) architecture under sampling rate restrictions, where a digital extended state observer (ESO) with inter-sample output prediction structure is employed to construct inter-sample dynamics between two consecutive sampling instants, such that high frequency disturbances can be better rejected. The convergence of the estimation and the stability of the closed-loop system are analyzed based on Lyapunov function method and separation principle. The proposed control architecture is implemented on a voice coil motor (VCM) actuated micro–nano servo gantry, demonstrating significant performance improvement over existing single-rate or multi-rate ADRC methods.

Synchronization Control for Network Systems With Communication Constraints.

A novel control strategy for synchronization control for network systems with communication constraints is presented in this paper. The dynamics of nodes in the network are nonidentical. The communication topology of network is weakly connected with communication constraints. The designed distributed controller for each node has two parts: reference generator (RG) and regulator. All RGs adopt the communication channels to exchange local information and track the target trajectory. Meanwhile, regulator can ensure that nonidentical node achieves synchronization with its RG. In order to reduce the communication frequency between node and its regulator, a sampled-date control strategy is utilized. The upper bound of the aperiodic sampling instants is calculated through the small-gain theorem, where the closed-loop system is equivalently formulated as the feedback interconnection of a linear time-invariant system and an integral sampled-data operator. Finally, some simulation results are given to demonstrate the effectiveness of the controller design strategy.

Sampled-data control of a class of switched nonlinear systems under asynchronous switching

This paper focuses on an output feedback stabilization problem for a class of switched nonlinear systems in non-strict feedback form under asynchronous switching via sampled-data control. Since the output of the considered systems is measurable only at the sampling instants, an observer is designed with a tunable scaling gain to estimate the state, and then a sampled-data controller is constructed with the sampled estimated state. As a distinctive feature, a merging virtual switching signal is introduced to describe the asynchronous switching generated by detecting the activation of the subsystem. By choosing an appropriate Lyapunov function, it is proved that the constructed controller with dwell time constraint can globally stabilize the considered systems under asynchronous switching. Finally, the effectiveness of the proposed method is illustrated by two examples.

Robust self-triggered MPC with fast convergence for constrained linear systems

In this paper, a robust self-triggered model predictive control (MPC) scheme is proposed for linear discrete-time systems subject to additive disturbances, state and control constraints. To reduce the amount of computation on controller sides, MPC optimization problems are only solved at certain sampling instants which are determined by a novel self-triggering mechanism. The main idea of the self-triggering mechanism is to choose inter-sampling times by guaranteeing a fast decrease in optimal costs. It implies a fast convergence of system states to a compact set where it is ultimately bounded and a reduction of computation times to stabilize the system. Once the state enters a terminal region, the system can be stabilized to a robust invariant set by a state feedback controller. Robust constraint satisfaction is ensured by utilizing the worst-case set-valued predictions of future states in such a way that recursive feasibility is guaranteed for all possible realisations of disturbances. In the case where a priority is given to reducing communication costs rather than improvement in control performance in a neighborhood of the origin, a feedback control law based on nominal state predictions is designed in the terminal region to avoid frequent feedback. Performances of the closed-loop system are demonstrated by a simulation example.