Sampling Instants Research Articles

Reaching Law Based Sliding Mode Control of Sampled Time Systems

In this paper, discrete time reaching law-based sliding mode control of continuous time systems is considered. In sliding mode control methods, usually the assumption of bounded absolute values of disturbances is used. However in many cases, the rate of change of the disturbance is also bounded. In the presented approach, this knowledge is used to improve the control precision and reduce the undesirable chattering. Another advantage of the proposed method is that the disturbance does not have to satisfy the matching conditions. In the paper two new reaching laws are analyzed, one of them ensures the switching quasi-sliding motion and the other the non-switching motion. For both of them, the robustness is assessed by calculating the quasi-sliding mode band width, as well as the greatest possible state error values. Specifically, the state errors are not considered only at the sampling instants, as is usual for discrete time systems, but the bounds on the continuous values “between” the sampling instants are also derived. Then, the proposed approaches are compared and analyzed with respect to energy expenditure of the control signal.

Tracking an Auto-Regressive Process with Limited Communication per Unit Time.

Samples from a high-dimensional first-order auto-regressive process generated by an independently and identically distributed random innovation sequence are observed by a sender which can communicate only finitely many bits per unit time to a receiver. The receiver seeks to form an estimate of the process value at every time instant in real-time. We consider a time-slotted communication model in a slow-sampling regime where multiple communication slots occur between two sampling instants. We propose a successive update scheme which uses communication between sampling instants to refine estimates of the latest sample and study the following question: Is it better to collect communication of multiple slots to send better refined estimates, making the receiver wait more for every refinement, or to be fast but loose and send new information in every communication opportunity? We show that the fast but loose successive update scheme with ideal spherical codes is universally optimal asymptotically for a large dimension. However, most practical quantization codes for fixed dimensions do not meet the ideal performance required for this optimality, and they typically will have a bias in the form of a fixed additive error. Interestingly, our analysis shows that the fast but loose scheme is not an optimal choice in the presence of such errors, and a judiciously chosen frequency of updates outperforms it.

Stability and Stabilization of Aperiodic Sampled-Data Systems Subject to Control Input Saturation: A Set Invariant Approach

This article proposes a new method to deal with the stability analysis and stabilization of aperiodic sampled-data control systems subject to input saturation. An impulsive system representation is employed, with a linear flow and a nonlinear jump dynamics, such that the evolution of the system at the sampling instants can be modeled by a difference inclusion defined by two set-valued maps. We show that to ensure the asymptotic stability it is sufficient to verify that a Lyapunov function decreases by a certain amount only at a grid of possible values for the sampling interval, as long as the increase of the function in continuous-time is conveniently bounded. Simulation results compare our approach with other ones.

A fast MPPT-based anomaly detection and accurate fault diagnosis technique for PV arrays

Catastrophic faults in photovoltaic (PV) arrays, if not detected timely, will significantly reduce the output power and even cause fire risks. Thus, fast and accurate fault detection and diagnosis techniques are of importance to enhance the efficiency, reliability, and safety of PV systems. However, conventional methods fail to detect faults at low mismatch levels and low irradiance levels. In this paper, a sensorless detection technique is thus proposed based on the instantaneous current reduction between two maximum power point tracking (MPPT) sampling instants. Simulations have been conducted to validate its availability to identify anomalies under varying environments, irrespective of the mismatch and irradiance levels. The results clearly demonstrate that the proposed method is less time-consuming but more accurate than the existing techniques. However, due to the presence of blocking diodes, the similarity between faults and certain partial shading (PS) conditions will make them more difficult to be classified. Hence, a unique point on the current–voltage (I-V) curve, namely inflection point, is exploited to accurately distinguish PS conditions, and further determine the mismatch level. More simulation tests under different conditions reveal that the proposed method is effective to quantitatively evaluate the faults. Accordingly, different voltages can be set to differentiate the currents in the faulty string and normal ones as much as possible for efficient fault location.

Event‐triggered adaptive tracking control of uncertain switched nonlinear systems

AbstractThis article is concerned with the event‐triggered adaptive tracking control of switched systems with uncertain nonlinearities and unknown control gains. The switch can occur within two consecutive sampling instants and may trigger new events that raise the mismatch problem and bring the challenge to avoid the Zeno behavior. To address these problems, we propose a novel codesign scheme composed of a switching event‐triggered mechanism and a mode‐dependent adaptive control law. A logarithmic threshold strategy is introduced into the event triggering mechanism. The absence of Zeno is proved from its formal definition. Based on the codesign scheme, the tracking error can be steered to an adjustable neighborhood of the origin. At last, a numerical example is applied to validate the obtained results.

Energy-to-Peak State Estimation for Switched Neutral-Type Neural Networks With Sector Condition via Sampled-Data Information.

In this article, the energy-to-peak state estimation problem is investigated for a class of switched neutral neural networks subject to the external perturbations with bounded energy. Both the values of the measurement outputs and switching signal of the subsystems are only available for the controllers at the discrete sampling instants. Unlike the results for nonswitched neural networks, the coexistence of the switching and sampling actions directly causes the asynchronous phenomena between the indexes of subsystems and their corresponding controllers. To address this situation, the piecewise time-dependent Lyapunov-Krasovskii functional and slow switching mechanism are introduced. Under the developed theorem conditions, we prove that the designed state estimator exponentially tracks the true value of the neural state with the accessible sampled-data information. Also, the influence of the exogenous perturbations on the peak value of the estimation error is constrained at a prescribed level. Finally, a neutral cellular neural network with switching parameters is employed to substantiate the effectiveness and applicability of the theoretical results.

Novel Techniques for a Verified Simulation of Fractional-Order Differential Equations

Verified simulation techniques have been investigated intensively by researchers who are dealing with ordinary and partial differential equations. Tasks that have been considered in this context are the solution to initial value problems and boundary value problems, parameter identification, as well as the solution of optimal control problems in cases in which bounded uncertainty in parameters and initial conditions are present. In contrast to system models with integer-order derivatives, fractional-order models have not yet gained the same attention if verified solution techniques are desired. In general, verified simulation techniques rely on interval methods, zonotopes, or Taylor model arithmetic and allow for computing guaranteed outer enclosures of the sets of solutions. As such, not only the influence of uncertain but bounded parameters can be accounted for in a guaranteed way. In addition, also round-off and (temporal) truncation errors that inevitably occur in numerical software implementations can be considered in a rigorous manner. This paper presents novel iterative and series-based solution approaches for the case of initial value problems to fractional-order system models, which will form the basic building block for implementing state estimation schemes in continuous-discrete settings, where the system dynamics is assumed as being continuous but measurements are only available at specific discrete sampling instants.

Periodic Event-Triggered Suboptimal Control With Sampling Period and Performance Analysis.

In this paper, the periodic event-triggered suboptimal control (PETSOC) method is developed for continuous-time linear systems. Different from event-triggered control, where the triggering condition is monitored continuously, the developed PETSOC method only verifies the triggering condition periodically at sampling instants, which further reduces computational resources. First, the control gain of the PETSOC is designed based on the algebraic Riccati equation. Subsequently, the periodic event-triggering condition is proposed for the suboptimal control method, which is only verified at sampling instants periodically. The sampling period is determined and analyzed based on the continuous form of the triggering condition. Moreover, the stability and the performance upper bound of the closed-loop system with the PETSOC are proved. Finally, the effectiveness of the developed PETSOC is validated through simulation on an unstable batch reactor.

Adaptive observer design for a class of Lipschitz nonlinear systems with multirate outputs and uncertainties: Application to attitude estimation with gyro bias

AbstractThe design of an adaptive observer for a class of multi‐input multi‐output Lipschitz nonlinear systems with uncertainties and multirated outputs is proposed in this paper. The sampling instants of the different outputs can be asynchronous and irregular. The exponential convergence of the proposed observer is proved with the help of a Lyapunov approach. The stability is ensured, provided that some conditions, including a persistent excitation condition and a maximum value condition on the sample rate of each output, are verified. The performances of the observer are illustrated through simulations of the attitude estimation problem using sensors from an inertial measurement unit and considering gyro bias.

Active Learning for Effectively Fine-Tuning Transfer Learning to Downstream Task

Language model (LM) has become a common method of transfer learning in Natural Language Processing (NLP) tasks when working with small labeled datasets. An LM is pretrained using an easily available large unlabelled text corpus and is fine-tuned with the labelled data to apply to the target (i.e., downstream) task. As an LM is designed to capture the linguistic aspects of semantics, it can be biased to linguistic features. We argue that exposing an LM model during fine-tuning to instances that capture diverse semantic aspects (e.g., topical, linguistic, semantic relations) present in the dataset will improve its performance on the underlying task. We propose a Mixed Aspect Sampling (MAS) framework to sample instances that capture different semantic aspects of the dataset and use the ensemble classifier to improve the classification performance. Experimental results show that MAS performs better than random sampling as well as the state-of-the-art active learning models to abuse detection tasks where it is hard to collect the labelled data for building an accurate classifier.

Stabilization of Aperiodic Sampled-Data Boolean Control Networks: A Delay Approach

In this article, a novel method for the global stochastic stability analysis of aperiodic sampled-data Boolean control networks (BCNs) is introduced. In our article, the sampling instants of aperiodic sampled-data control (ASDC) are uncertain and only the activation frequencies of the sampling interval are known. Using the semitensor product of matrices, a BCN under ASDC can be transformed into a Boolean network (BN) with stochastic delays. Specifically, the ASDC is represented as a delayed control. Here, the time-varying delay is a random variable generated by a Markov chain and its transition probability matrix can be obtained by the activation frequencies of the sampling interval. Notably, the value of the time-varying delay is less than the upper bound of the sampling interval and when its present value is given, there are only two possible values that can be taken at the next moment. Subsequently, by using the Lyapunov function and augmented method, a sufficient condition for the global stochastic stability of BCNs under ASDC is provided. In particular, the aforementioned results are applicable to the sampled-data control with constant sampling interval. Finally, a numerical example is presented to demonstrate our results.

Bias correction for direct spectral estimation from irregularly sampled data including sampling schemes with correlation

The prediction and correction of systematic errors in direct spectral estimation from irregularly sampled data taken from a stochastic process is investigated. Different sampling schemes are investigated, which lead to such an irregular sampling of the observed process. Both kinds of sampling schemes are considered, stochastic sampling with non-equidistant sampling intervals from a continuous distribution and, on the other hand, nominally equidistant sampling with missing individual samples yielding a discrete distribution of sampling intervals. For both distributions of sampling intervals, continuous and discrete, different sampling rules are investigated. On the one hand, purely random and independent sampling times are considered. This is given only in those cases, where the occurrence of one sample at a certain time has no influence on other samples in the sequence. This excludes any preferred delay intervals or external selection processes, which introduce correlations between the sampling instances. On the other hand, sampling schemes with interdependency and thus correlation between the individual sampling instances are investigated. This is given whenever the occurrence of one sample in any way influences further sampling instances, e.g., any recovery times after one instance, any preferences of sampling intervals including, e.g., sampling jitter or any external source with correlation influencing the validity of samples. A bias-free estimation of the spectral content of the observed random process from such irregularly sampled data is the goal of this investigation.

Aperiodic sampled-data control of distributed networked control systems with time-delay

This paper proposes a hybrid aperiodic sampled-data mechanism for the control of interconnected subsystems with time-delay. The proposed aperiodic sampled-data mechanism comprises of two stages. In the first stage, the next sampling instant for each subsystem is computed using self-triggering strategy. Thereafter, in the second stage, an event-triggering condition is checked at these sampling instants for each subsystem and signal is transmitted to the controller only if the event-triggering condition is violated. Further, to reduce the computational complexity involved in the proposed triggering mechanism, another triggering mechanism with integrated event-triggering and self-triggering is developed. Also, an upper bound on delay for each subsystem is computed to ensure the stability of distributed networked control system. The results proposed are validated using a simulation example. A comparison of the proposed technique with other triggering mechanisms in terms of sampling instants, number of transmissions to the controller, maximum delay bound and other performance measures is drawn through simulation example.

Sampled-Data Adaptive Fuzzy Control of Switched Large-Scale Nonlinear Delay Systems

A decentralized adaptive fuzzy sampled-data control problem for switched large-scale nonlinear systems with time-varying delays is considered in this article. Fuzzy logic systems are applied to handle unknown nonlinear terms. A novel fuzzy adaptive law is proposed utilizing only the information of the system states at sampling instants. Moreover, a proper CLF and a new decentralized adaptive sampled-data control law are constructed to ensure that all states of the CLS are bounded. The developed strategy’s effectiveness is verified with two examples.

Aperiodic Sampled-Data H∞Filtering for Lipschitz Nonlinear Systems: An Impulsive System Approach

This paper is concerned with the H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering for Lipschitz nonlinear systems under aperiodically sampled measurements. The developed filter is a hybrid system, whose states undergo a change or reset at sampling instants. The resulting filtering error system is then modelled as a kind of nonlinear impulsive systems. By introducing a time-varying Lyapunov functional candidate, a sufficient condition for the existence of desired filter is derived to ensure the filtering error system asymptotic stability and guarantee an H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance. The optimal H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance and corresponding filter gain matrix can be obtained by solving a convex problem with linear matrix inequalities (LMIs) constrains. Two examples are given to show the effectiveness of the theoretical results, and our results are less conservative than existing ones through comparisons.

Nonuniform Sampling Rate Conversion:An Efficient Approach

We present a discrete-time algorithm for nonuniform sampling rate conversion that presents low computational complexity and memory requirements. It generalizes arbitrary sampling rate conversion by accommodating time-varying conversion ratios, i.e., it can efficiently adapt to instantaneous changes of the input and output sampling rates. This approach is based on appropriately factorizing the time-varying discrete-time filter used for the conversion. Common filters that satisfy this factorization property are those where the underlying continuous-time filter consists of linear combinations of exponentials, e.g., those described by linear constant-coefficient differential equations. This factorization separates the computation into two parts: one consisting of a factor solely depending on the output sampling instants and the other consists of a summation -- that can be computed recursively -- whose terms depend solely on the input sampling instants and its number of terms is given by a relationship between input and output sampling instants. Thus, nonuniform sampling rates can be accommodated by updating the factors involved and adjusting the number of terms added. When the impulse response consists of exponentials, computing the factors can be done recursively in an efficient manner.

Dual-Rate Data-Driven Virtual Reference Feedback Tuning: Improvement in Fast-Tracking Performance and Ripple-Free Design

In this study, a data-driven design method is proposed for a dual-rate system, where the sampling interval of a plant output is restricted and is an integer multiple of the holding interval of a control input. In our proposed method, single-rate virtual reference feedback tuning (S-VRFT), where the holding interval is the same as the sampling interval, is extended to the dual-rate virtual reference feedback tuning (D-VRFT) system. In D-VRFT, a controller is decided using a set of input/output data used in S-VRFT, and it is easy to extend S-VRFT to D-VRFT and implement D-VRFT. In this study, intersample oscillations caused in such a dual-rate control system is prevented because a weighting filter is introduced for penalizing the control input deviation between the sampling instants. The filter is designed as an integrator for weighting the low-frequency domain. The improvement in fast-tracking performance as well as the ripple-free property are demonstrated through both the numerical and experimental results.

Local Sampled-Data Gain-Scheduling Control of quasi-LPV Systems

Abstract This paper deals with the problem of sampled-data gain-scheduling control design for affine quasi-LPV systems. As the control implementation is based on sample-data and its update occurs only at specific sampling instants, the state-dependent scheduling functions of the controller are piecewise continuous. This characteristic causes a mismatch between the system model and the controller parameters, namely asynchronous scheduling functions of the controller with respect to the plant during the inter-sampling behavior. To cope with this phenomenon, a polytopic description of the inter-sampling is constructed based on bounding assumptions on the scheduling functions and their time derivatives. Then, regarding a time-delay approach, a constructive and numerically implementable LMI-based synthesis condition is derived, and a convex procedure is proposed for enlarging the estimate of the region of attraction of the origin of the closed-loop system. The time-derivative bounds of the scheduling functions are explicitly accounted into the local analysis to ensure the method’s implementation. A numerical example is provided to illustrate the proposed methodology.

A 2-Level Iterated Tabu Search Algorithm for the Quadratic Assignment Problem

In this paper, a 2-level iterated tabu search (ITS) algorithm for the solution of the quadratic assignment problem (QAP) is considered. The novelty of the proposed ITS algorithm is that the solution mutation procedures are incorporated within the algorithm, which enable to diversify the search process and eliminate the search stagnation, thus increasing the algorithm’s efficiency. In the computational experiments, the algorithm is examined with various implemented variants of the mutation procedures using the QAP test (sample) instances from the library of the QAP instances – QAPLIB. The results of these experiments demonstrate how the different mutation procedures affect and possibly improve the overall performance of the ITS algorithm.

Optimal sampling pattern for free final time linear quadratic regulator: the scalar case

The optimal sampling problem is the selection of the optimal sampling instants together with the optimal control actions such that a given cost function is minimised. In this article, we solve the optimal sampling problem for free final time linear quadratic regulator with scalar dynamical system. The solution provides the optimal sampling instants, control actions and the optimal final time in a recursive and constructive way for any arbitrary number of samples , as it is not based on asymptotic arguments. An application example shows the feasibility of the approach.