Sampling Instants Research Articles

A novel looped functional for stability analysis of asynchronous sampled‐data systems

AbstractThis paper is concerned with the stability analysis problems of asynchronous sampled‐data systems via an input‐delay approach. Between two sequential sampling times, a sampled‐data system is controlled by previously sampled states and thus can be modeled as a time‐delay system with a saw‐tooth delay. Inevitably, information at the sampling instants have played essential roles in controlling the systems and reducing the conservatism of the stability criteria. Therefore, to further utilize the information at sampling instants, this paper proposes novel looped functionals consisting of integral state variables and their interval‐normalized terms. Three numerical examples including a practical helicopter system demonstrate the effectiveness of the proposed approaches in terms of allowable sampling intervals.

Sensitivity of transcriptomics: Different samples and methodology alter conclusions in Gulf pipefish (Syngnathus scovelli).

Transcriptome analysis has become a central tool in evolutionary and functional genomics. However, variation among biological samples and analysis techniques can greatly influence results, potentially compromising insights into the phenomenon under study. Here, we evaluate differences in the brain transcriptome between female and male Gulf pipefish (Syngnathus scovelli). We perform comparisons between results from entire pipelines for brain transcriptome assembly, quantification, and analysis. We also offer a unique biological comparison between two sampling instances (Redfish Bay: n = 15, Port Lavaca: n = 7). Our results demonstrate crucial shortcomings with current experimental approaches. We found high variation within our results that was driven by both technical differences between pipelines and biological differences between pipefish samples. In our analysis of highly expressed genes, we found that the choice of methods influenced the degree of contamination or noise included in the identified genes. Notably, genes identified within the same pipeline were more similar than any other comparison. Our differential expression analysis revealed that both methodology and sampling location influenced the quantity and consistency of statistically significant transcripts. In the context of these results, we offer modifications to current practices that may increase the robustness of transcriptome-based conclusions. In particular, the use of a reference-guided assembly and an increase in sample sizes are likely to improve resistance to noise or error.

Enhancing the motion performance of 3-DOF micro/nano-manipulators facing thermo-piezoelectric-mechanical coupling effects

Achieving ultra-high accuracy manipulation with piezoelectric micro/nano-manipulators is significantly hindered by thermal loads uncertainties in the digital control diagram. To address the problem, we propose a sampled-data fixed-time extended state observer based control strategy to enhance the manipulation performance. Initially, we delve into the dynamical model of the micro/nano-manipulator, examining the thermo-piezoelectric-mechanical coupling effects. Following the kinematics decoupling of the 3-DOF model, sampled-data fixed-time extended state observer based control strategy is designed to estimate the system states and total disturbances including thermal impacts and system uncertainties in the sampled-data control architecture, where an output predictor is integrated to forecast system output between consecutive sampling instances, while the observation gains are meticulously crafted to ensure a fixed-time convergence in estimation. Leveraging this estimation framework, a fixed-time feedback controller is designed to compensate the total disturbance and control the system, enabling the system to achieve a tracking convergence, irrespective of the inconsistent initial values stemming from thermal effects disparities. Finally, experimental validation on a piezoelectric thin-sheet-actuated 3-DOF flexible micro/nano-manipulator verifies the effectiveness of the proposed control strategy. Notably, we have observed a minimum enhancement of 26% in spatial trajectory positioning and scanning accuracy in the context of varying thermal loads.

Data-sampled time-varying formation for singular multi-agent systems with multiple leaders

The time-varying formation problem of singular multi-agent systems under sampled data with multiple leaders is investigated in this paper. Firstly, a data-sampled time-varying formation control protocol is proposed in the current study where the communication among followers merely occurred at sampling instants, which can save the controller communication energy significantly. Secondly, necessary and sufficient conditions for the feasibility of the formation function are provided. In addition, an approach is presented to design the formation tracking control under sampled data with multiple leaders. Finally, numerical simulations validate the efficacy of the theoretical results.

Credit Anomaly Detection Method based on Bayesian Networks

Due to the virtual nature of online transactions and the underdeveloped personal credit risk assessment system of Internet finance lending platforms in China, these platforms often struggle to verify the creditworthiness of applicants prone to fraud and default, leading to loan losses. As a result, risk control has become the core of Internet lending platforms. Modern risk control relies on statistical and data mining techniques to analyze and model data, uncover patterns that indicate loan defaults, and identify anomalies. This paper proposes a Bayesian network-based credit anomaly detection method, which detects anomalies by calculating and ranking the joint anomaly probabilities of sample instances. The technique operates under unsupervised learning and can effectively handle missing and imbalanced data. This method analyzes a loan credit dataset with 32,581 samples and 12 features of the customers. The result of the analysis demonstrates the feasibility and effectiveness of this method in detecting anomalies in online loans.

Enhanced Looped Lyapunov Functional for Sampled-Data Control for T-S Fuzzy Systems with Time Delay

This paper addresses the problem of sampled-data control in T-S fuzzy systems with time delays. Initially, a negative-definite criterion is developed for the matrix containing membership functions with the help of the idea of a switching mechanism. Building upon this criterion, a membership-function-based looped Lyapunov functional is introduced. Furthermore, a sampling-time-dependent looped Lyapunov functional is constructed, incorporating crucial information about the sampling instance. Notably, this functional matrix is not constrained to satisfy positive-definiteness, and it varies with each sampling point. By utilizing the enhanced looped Lyapunov functional, less conservative stability conditions and a new controller criterion for the T-S fuzzy system with time delays are derived. This demonstrates that our proposed stability conditions allow for a larger sampling interval compared to existing work. Finally, the proposed method’s effectiveness is demonstrated through the validation of two simulation examples.

Direct Identification of the Continuous Relaxation Time and Frequency Spectra of Viscoelastic Materials

Relaxation time and frequency spectra are not directly available by measurement. To determine them, an ill-posed inverse problem must be solved based on relaxation stress or oscillatory shear relaxation data. Therefore, the quality of spectra models has only been assessed indirectly by examining the fit of the experiment data to the relaxation modulus or dynamic moduli models. As the measures of data fitting, the mean sum of the moduli square errors were usually used, the minimization of which was an essential step of the identification algorithms. The aim of this paper was to determine a relaxation spectrum model that best approximates the real unknown spectrum in a direct manner. It was assumed that discrete-time noise-corrupted measurements of a relaxation modulus obtained in the stress relaxation experiment are available for identification. A modified relaxation frequency spectrum was defined as a quotient of the real relaxation spectrum and relaxation frequency and expanded into a series of linearly independent exponential functions that are known to constitute a basis of the space of square-integrable functions. The spectrum model, given by a finite series of these basis functions, was assumed. An integral-square error between the real unknown modified spectrum and the spectrum model was taken as a measure of the model quality. This index was proved to be expressed in terms of the measurable relaxation modulus at uniquely defined sampling instants. Next, an empirical identification index was introduced in which the values of the real relaxation modulus are replaced by their noisy measurements. The identification consists of determining the spectrum model that minimizes this empirical index. Tikhonov regularization was applied to guarantee model smoothness and noise robustness. A simple analytical formula was derived to calculate the optimal model parameters and expressed in terms of the singular value decomposition. A complete identification algorithm was developed. The analysis of the model smoothness and model accuracy for noisy measurements was carried out. The equivalence of the direct identification of the relaxation frequency and time spectra has been demonstrated when the time spectrum is modeled by a series of functions given by the product of the relaxation frequency and its exponential function. The direct identification concept can be applied to both viscoelastic fluids and solids; however, some limitations to its applicability have been pointed out. Numerical studies have shown that the proposed identification algorithm can be successfully used to identify Gaussian-like and Kohlrausch–Williams–Watt relaxation spectra. The applicability of this approach to determining other commonly used classes of relaxation spectra was also examined.

Time-varying formation tracking of multi-agent systems with multiple leaders based on aperiodic time-triggered intermittent control

In this article, the distributed aperiodic time-triggered intermittent control protocol (DATICP) is presented for the time-varying formation tracking of multi-agent systems (MASs) with multiple leaders. Firstly, we present the mathematical description of DATICP. The characteristic of DATICP lies in that for each agent, its control signal is updated at aperiodic sampling instants on work time intervals and disappears on rest time intervals. Secondly, based on a mixed time-dependent Lyapunov functional (MTLF), the exponential stability theorem of the derived system is established. Thirdly, according to the theorem, sufficient conditions are given to achieve time-varying formation tracking for MASs with multiple leaders by DATICP. As a result, a corollary is obtained which compromises conservativeness and complexity. Finally, two simulation examples are offered for illustration.

Distributed Observer for Linear Systems with Multirate Sampled Outputs Involving Multiple Delays

This paper focuses on the design of a continuous distributed observer for linear systems under multirate sampled output measurements involving multiple delays. It is mathematically proved that the continuous distributed observer can achieve estimation in a sensor network environment, where output measurements from each sensor are available at different sampling instants, whether these times are periodic or aperiodic, and despite the presence of multiple time-varying delays. Each sampled and delayed measurement represents a node of the network, necessitating a dedicated observer for each node, which has access to only part of the system’s output and communicates with its neighbors according to a given network graph. The exponential convergence of the error dynamics is ensured by Lyapunov stability analysis, which accounts for the influence of the sampled and delayed measurements at each node. To demonstrate the effectiveness of the proposed observer, simulation tests were conducted on the tracking control of chasing satellites in low Earth orbit (LEO), encompassing both small and large sampling rates and delays. The continuous distributed observer with sampled output measurements exhibited convergence in scenarios with different sampling intervals, even in the presence of time-varying delays, achieving asymptotic omniscience, as demonstrated in the convergence analysis.

Sampled-Data Exponential Synchronization of Complex Dynamical Networks with Saturating Actuators.

This paper investigates the problem of exponential synchronization control for complex dynamical systems (CDNs) with input saturation. Considering the effects of transmission delay, a memory sampled-data controller is designed. A modified two-sided looped functional is constructed that takes into account the entire sampling period, which includes both current state information and delayed state information. This functional only needs to be positive definite at the sampling instants. Sufficient criteria and the controller design method are provided to ensure the exponential synchronization of CDNs with input saturation under the influence of transmission delay, as well as the estimation of the basin of attraction. Additionally, an optimization algorithm for enlarging the region of attraction is proposed. Finally, a numerical example is presented to verify the effectiveness of the conclusion.

Adaptive Transmission Interval-Based Self-Triggered Model Predictive Control for Autonomous Underwater Vehicles with Additional Disturbances

Most existing model predictive control (MPC) methods overlook the network resource limitations of autonomous underwater vehicles (AUVs), limiting their applicability in real systems. This article addresses this gap by introducing an adaptive transmission, interval-based, and self-triggered model predictive control for AUVs operating under ocean disturbances. This approach enhances system stability while reducing resource consumption by optimizing MPC update frequencies and communication resource usage. Firstly, the method evaluates the discrepancy between system states at sampling instants and their optimal predictions. This significantly reduces the conservatism in the state-tracking errors caused by ocean disturbances compared to traditional approaches. Secondly, a self-triggering mechanism was employed, limiting information exchange to specified triggering instants to conserve communication resources more effectively. Lastly, by designing a robust terminal region and optimizing parameters, the recursive feasibility of the optimization problem is ensured, thereby maintaining the stability of the closed-loop system. The simulation results illustrate the efficacy of the controller.

Memory synchronisation of delayed neural networks via variable sampling control

This paper tackles the challenge of memory synchronisation of delayed neural networks by implementing a variable sampling control approach. On the one hand, in the light of constructing novel Lyapunov functionals, the conservativeness of the criteria obtained for delayed neural networks is significantly reduced. On the other hand, in light of memory sampling method, the transmission delay is introduced in sampling control scheme, and the information can be fully utilised. The constructed Lyapunov functionals have an advantage, i.e. it is not necessary to be positive on sampling intervals, and also to be continuous at the sampling instants. Finally, to demonstrate the effectiveness and advantages of the proposed methods, two experimental simulations are conducted for delayed neural networks. Two simulations provide empirical evidence supporting the validity of the techniques developed in this study, highlighting their potential for practical application in delayed neural network systems.

Sampled-data event-triggered control with sampling-independent positive guarantees on inter-event times

To fit with a digital environment in networked control systems, sampled-data event-triggered control (ETC) has been proposed where the event-triggering mechanisms sense and process information only at discrete sampling instants (not necessarily periodically). One deficiency in the previous study on sampled-data ETC is the lack of analysis on transmission performance, which yields the potential occurrence of an undesirable phenomenon that the minimum inter-event time is always equal to the minimum inter-sampling interval, no matter how small the latter is. To overcome this drawback, in this paper, we propose a novel sampled-data ETC scheme such that the lower bounds of inter-event times have sampling-independent positive guarantees. A linear networked control system is considered under observer-based controllers, external disturbances, and multiple communication channels. The improved transmission performance is due to the utilization of dynamic event-triggering conditions and some mean-rate error signals, which are the ratios between network-induced errors and some time-increasing functions. After modeling the closed-loop dynamics into a hybrid system, sufficient conditions on the upper bound of inter-sampling intervals and parameters in ETC are provided to ensure input-to-state stability (rather than its practical version) and sampling-independent positive guarantees simultaneously. Furthermore, a new tradeoff relationship between the sampling and transmission performance is revealed: a faster sampling frequency is conducive to improving inter-event times. Finally, a linearized model of an inverted pendulum is simulated to illustrate the efficiency and feasibility of the obtained results.

Local synchronization for non-linear stochastic functional systems under sampling control

This paper presents a local exponential driving-response synchronization framework for stochastic non-linear functional systems (NLSFSs) under the sampling control. In contrast to previous studies of local synchronization of deterministic functional systems, we extend this to local synchronization of stochastic functional systems. For the sampling control, we define a partition of sampling instants. Combined with Halanay inequality and stochastic analysis technique, we also prove that under some sufficient conditions, including the maximum sampling interval, i.e. the upper bound of the partition, the NLSFSs can be locally synchronized under the sampling control with the partition. Our results show that the synchronization is dependent on the time delay, stochastic disturbance, and the maximum sampling interval. Then the results are applied to a class of circuit systems, and some synchronization criteria for the systems are provided. Finally, a numerical example is showcased and the simulation results illustrate the effectiveness of our theoretical results.

An Improved Onboard Adaptive Aero-Engine Model Based on an Enhanced Neural Network and Linear Parameter Variance for Parameter Prediction

Achieving measurable and unmeasurable parameter prediction is the key process in model-based control, for which an accurate onboard model is the most important part. However, neither nonlinear models like component level models or LPV models, nor linear models like state–space models can fully meet the requirements. Hence, an original ENN-LPV linearization strategy is proposed to achieve the online modelling of the state–space model. A special network structure that has the same format as the state–space model’s calculation was applied to establish the state–space model. Importantly, the network’s modelling ability was improved through applying multiple activation functions in the single hidden layer and an experience pool that records data of past sampling instants, which strengthens the ability to capture the engine’s strongly nonlinear dynamics. Furthermore, an adaptive model, consisting of a component-level model with adaptive factors, a linear Kalman filter, a predictive model, an experience pool, and two ENN-LPV networks, was developed using the proposed linearization strategy as the core process to continuously update the Kalman filter and the predictive model. Simulations showed that the state space model built using the ENN-LPV linearization strategy had a better model identification ability in comparison with the model built using the OSELM-LPV linearization strategy, and the maximum output error between the ENN-LPV model and the simulated engine was 0.1774%. In addition, based on the ENN-LPV linearization strategy, the adaptive model was able to make accurate predictions of unmeasurable performance parameters such as thrust and high-pressure turbine inlet temperature, with a maximum prediction error within 0.5%. Thus, the effectiveness and the advantages of the proposed method are demonstrated.

An enhanced looped-functional framework for stability analysis of sampled-data systems

This paper enhances the looped-functional framework for sampled-data systems by using continuous Lyapunov functionals instead of xT(t)Px(t). The continuous Lyapunov functionals exploit the maximum allowable sampling interval compared with the traditional Lyapunov function xT(t)Px(t) in the conventional looped-functional framework. The enhanced looped-functional framework ensures the negativeness of the continuous Lyapunov functionals concerning the sampling instants and guarantees the stability of the sampled-data systems. Based on these continuous Lyapunov functionals, this paper constructs novel Lyapunov functionals with the looped-functional which not only exploits all available vectors related to sampling intervals but also introduces an additional interval which is zero at t=tk+1. Also, this paper proposes the stability criteria based on the enhanced looped-functional framework for the sampled-data systems with the asynchronous and synchronous samplings, respectively. The numerical examples show the effectiveness of the proposed framework.

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Nonlinear optimal control for robotic exoskeletons with electropneumatic actuators

Koopman operator-based multi-model for predictive control

AbstractThis work describes a new model structure developed for prediction in Model Predictive Control (MPC). The model has a multi-model structure in which independent sub-models are employed for the consecutive sampling instants. The model lifts process states into a high-dimensional space in which a linear process description is applied. Depending on the influence of the manipulated variables on lifted states, three general model versions are described and model identification algorithms are derived. As a result of the multi-model structure, model parameters are found analytically from computationally uncomplicated least squares problems using the Extended Dynamic Mode Decomposition algorithm, but the evolution of states over the horizon used in MPC is taken into account. Next, the MPC algorithm for the described model is derived. It requires solving online simple quadratic optimisation tasks. The effectiveness of three considered model configurations and three versions of the lifting functions is examined for a nonlinear DC motor benchmark. Their impact on model accuracy, complexity, possible control accuracy and MPC calculation time is thoroughly discussed. Finally, a more complex polymerisation reactor process is considered to showcase the practical applicability of the presented approach to modelling and MPC.

Aperiodic sampled‐data stabilization of switched singular systems with asynchronous switching: A hybrid control approach

AbstractThis article investigates the sampled‐data stabilization problem for a class of switched singular systems with aperiodic sampling. The asynchronous switching between the plant and the switched controller caused by sampling is considered. Unlike normal systems, the conventional zero‐order hold type sampled‐data control law may be inapplicable to singular systems. This is because under that control law, the algebraic equations of singular systems may have no solutions at sampling instants. To cope with this problem, a new hybrid control law composed of a mode‐dependent impulsive controller and a mode‐dependent sampled‐data state feedback controller is devised. The impulsive controller adjusts the values of differential substate at sampling instants so that the algebraic equations are solvable. Then, by constructing a novel piecewise sampling‐time‐dependent Lyapunov function and using the average dwell time method as well as convex technique, a sampling‐range‐dependent sufficient condition for exponential stability of the resulting closed‐loop system is established. Moreover, an optimization‐based method is proposed to solve the hybrid controller gains. Simulation results on two examples including a mechanical arm system show the effectiveness of the proposed control method.

Consensus of linear multi‐agent systems under switching topology by sampled‐data output feedback control

AbstractThis paper studies both synchronous and asynchronous consensus problems for linear multi‐agent systems under switching topology. A novel distributed continuous‐discrete observer is established by solely using the relative sampled output messages, which needs neither to store messages from neighboring agents nor estimate the information of itself and all neighbors. Based on the estimation provided by the distributed observer, a distributed output feedback control with digital form is synthesized, which allows each agent to update the value of its controller at the synchronous/asynchronous sampling instants. It is of interest to see that, for the class of chain‐integrator multi‐agent systems, the proposed control approach allows the sampling periods to be chosen freely and thus would be more practical in some situations from the perspective of energy saving. The theoretical results are illustrated by formation flying of spacecraft and synchronization of multiple double‐integrators.