Set Membership Research Articles

Adaptive MPC for constrained systems with parameter uncertainty and additive disturbance

In this study, the authors propose an adaptive model predictive control (MPC) algorithm for constrained linear systems in state space subject to uncertain model parameters and disturbances. An iterative set membership identification algorithm is first presented to update the uncertain parameter set at each time step. Based on the shrunken uncertain parameter set, an MPC controller is then designed to robustly stabilise the uncertain systems subject to state and input constraints. The algorithm can efficiently reduce the size of the uncertain parameter set in min-max MPC setting, and therefore improve the control performance. The algorithm is proved to ensure constraint satisfaction, recursive feasibility and input-to-state practical stability of the closed-loop system even in the presence of system uncertainties. A numerical example and a brief comparison with traditional min-max MPC are provided to demonstrate the efficiency of the proposed algorithm.

Identification of optimal wind, solar and hybrid wind-solar farming sites using fuzzy logic modelling

In this paper, an analytical framework is developed using fuzzy logic to evaluate optimal sites for wind, solar and hybrid wind-solar farms; using criterial components for energy optimization through climatological, topographic and human factors. The model is applied through a case study to the island of Mauritius which bears a highly complex topography. Through this computation, fuzzy constraints including wind and solar power, site elevation, settlement areas, and proximity to grid lines are all fitted to different fuzzy membership sets and the individual satisfaction degrees of each were calculated and aggregated into overall satisfaction degrees. Decision maps of highly suitable regions for hybrid wind-solar farming were then highlighted revealing two potential sites on the island for hybrid wind-solar farming; revealing a total generation potential of energy per year of 161.58 GWh at Le Morne and 281.28 GWh at La Laura-Malenga. The findings of this study aim to guide energy and urban planners to better identify optimum sites for wind, solar and hybrid wind-solar farm construction whilst making optimal use of land resources to achieve both sustainable dimensions and energy economic resilience.

Distributed Interpolatory Algorithms for Set Membership Estimation

This work addresses the distributed estimation problem in a set membership framework. The agents of a network collect measurements which are affected by bounded errors, thus implying that the unknown parameters to be estimated belong to a suitable feasible set. Two distributed algorithms are considered, based on projections of the estimate of each agent onto its local feasible set. The main contribution of the paper is to show that such algorithms are asymptotic interpolatory estimators, i.e. they converge to an element of the global feasible set, under the assumption that the feasible set associated to each measurement is convex. The proposed techniques are demonstrated on a distributed linear regression estimation problem.

Two Low Computational Complexity Improved Multiband Structured Subband Adaptive Filter Algorithms

The improved multiband-structured subband adaptive filter (IMSAF) applies the input regressors at each subband to speed up the convergence rate of MSAF. When the projection order is increased, the convergence rate of the IMSAF algorithm improves at the cost of increased complexity. The present research introduces two new IMSAF algorithms with low computational complexity feature. In the first algorithm, the selective partial update approach (SPU) is extended to IMSAF algorithms and SPU-IMSAF is established. In SPU-IMSAF, the filter coefficients are partially updated at each subband for every adaptation. In the second algorithm, the set-membership (SM) strategy is utilized in IMSAF and SM-IMSAF is established. The SM-IMSAF has fast convergence rate, low steady-state error and low computational complexity features at the same time. Also, by combining SM and SPU methods, the SM-SPU-IMSAF is introduced. Simulation results demonstrate the good performance of the proposed algorithms.

Morton filters: fast, compressed sparse cuckoo filters

Approximate set membership data structures (ASMDSs) are ubiquitous in computing. They trade a tunable, often small, error rate ($$\epsilon $$) for large space savings. The canonical ASMDS is the Bloom filter, which supports lookups and insertions but not deletions in its simplest form. Cuckoo filters (CFs), a recently proposed class of ASMDSs, add deletion support and often use fewer bits per item for equal $$\epsilon $$. This work introduces the Morton filter (MF), a novel CF variant that introduces several key improvements to its progenitor. Like CFs, MFs support lookups, insertions, and deletions, and when using an optional batching interface raise their respective throughputs by up to 2.5$$\times $$, 20.8$$\times $$, and 1.3$$\times $$. MFs achieve these improvements by (1) introducing a compressed block format that permits storing a logically sparse filter compactly in memory, (2) leveraging succinct embedded metadata to prune unnecessary memory accesses, and (3) more heavily biasing insertions to use a single hash function. With these optimizations, lookups, insertions, and deletions often only require accessing a single hardware cache line from the filter. MFs and CFs are then extended to support self-resizing, a feature of quotient filters (another ASMDS that uses fingerprints). MFs self-resize up to 13.9$$\times $$ faster than rank-and-select quotient filters (a state-of-the-art self-resizing filter). These improvements are not at a loss in space efficiency, as MFs typically use comparable to slightly less space than CFs for equal $$\epsilon $$.

Monte Carlo and Reconstruction Membership Inference Attacks against Generative Models

Abstract We present two information leakage attacks that outperform previous work on membership inference against generative models. The first attack allows membership inference without assumptions on the type of the generative model. Contrary to previous evaluation metrics for generative models, like Kernel Density Estimation, it only considers samples of the model which are close to training data records. The second attack specifically targets Variational Autoencoders, achieving high membership inference accuracy. Furthermore, previous work mostly considers membership inference adversaries who perform single record membership inference. We argue for considering regulatory actors who perform set membership inference to identify the use of specific datasets for training. The attacks are evaluated on two generative model architectures, Generative Adversarial Networks (GANs) and Variational Autoen-coders (VAEs), trained on standard image datasets. Our results show that the two attacks yield success rates superior to previous work on most data sets while at the same time having only very mild assumptions. We envision the two attacks in combination with the membership inference attack type formalization as especially useful. For example, to enforce data privacy standards and automatically assessing model quality in machine learning as a service setups. In practice, our work motivates the use of GANs since they prove less vulnerable against information leakage attacks while producing detailed samples.

Unsupervised Learning with Contrastive Latent Variable Models

In unsupervised learning, dimensionality reduction is an important tool for data exploration and visualization. Because these aims are typically open-ended, it can be useful to frame the problem as looking for patterns that are enriched in one dataset relative to another. These pairs of datasets occur commonly, for instance a population of interest vs. control or signal vs. signal free recordings. However, there are few methods that work on sets of data as opposed to data points or sequences. Here, we present a probabilistic model for dimensionality reduction to discover signal that is enriched in the target dataset relative to the background dataset. The data in these sets do not need to be paired or grouped beyond set membership. By using a probabilistic model where some structure is shared amongst the two datasets and some is unique to the target dataset, we are able to recover interesting structure in the latent space of the target dataset. The method also has the advantages of a probabilistic model, namely that it allows for the incorporation of prior information, handles missing data, and can be generalized to different distributional assumptions. We describe several possible variations of the model and demonstrate the application of the technique to de-noising, feature selection, and subgroup discovery settings.

Learning-based predictive control for linear systems: A unitary approach

A comprehensive approach addressing identification and control for learning-based Model Predictive Control (MPC) for linear systems is presented. The design technique yields a data-driven MPC law, based on a dataset collected from the working plant. The method is indirect, i.e. it relies on a model learning phase and a model-based control design one, devised in an integrated manner.In the model learning phase, a twofold outcome is achieved: first, different optimal p-steps ahead prediction models are obtained, to be used in the MPC cost function; secondly, a perturbed state-space model is derived, to be used for robust constraint satisfaction. Resorting to Set Membership techniques, a characterization of the bounded model uncertainties is obtained, which is a key feature for a successful application of the robust control algorithm.In the control design phase, a robust MPC law is proposed, able to track piece-wise constant reference signals, with guaranteed recursive feasibility and convergence properties. The controller embeds multistep predictors in the cost function, it ensures robust constraints satisfaction thanks to the learnt uncertainty model, and it can deal with possibly unfeasible reference values. The proposed approach is finally tested in a numerical example.

The iterated extended set membership filter applied to relative localization between autonomous vehicles based on GNSS and UWB ranging

AbstractThis paper presents a novel Iterated Extended Set Membership Filter (IESMF) with an application to relative localization. For safe operation of formations of automatic vehicles, consistent uncertainty estimates are of crucial importance. Here, a localization filter that provides ellipsoidal regions that are guaranteed to contain another vehicles position is presented. The proposed iterative update step can appreciably reduce the size of the a posteriori state ellipsoid. The idea of using SIVIA as a baseline to quantify conservativeness is introduced. Another novelty is that we take into account parametric uncertainty of the observation equation.The proposed filter is applied to a two unmanned aircraft systems (UAS) localization problem in simulation with observation noise obtained from real sensors. Simulation results illustrate the effective reduction of filter conservativeness by a small number of iterative updates.

Research on Evaluation of Linux in Aerospace Based on Improved FAHP

The evaluation and selection of embedded operating system are very important for manned spaceflight engineering. Considering the fuzziness and hierarchy of the evaluation process, a fuzzy analytic hierarchy process (FAHP) based on variation coefficient method and Criteria Importance Though Intercrieria Correlation (CRITIC) method is proposed to be applied to comprehensive evaluation of real-time Linux in space embedded system. The evaluation system, evaluation set and Gaussian distribution membership function are constructed, and the weight values of each criterion and index are determined by variation coefficient method and CRITIC method. The measured data are used for quantitative indexes such as real-time performance, and the expert scoring method is used for qualitative indexes such as reliability and compatibility, and verifies the validity of the model through simulation. The results show that the improved FAHP can quickly and intuitively judge the performance characteristics of Linux system and its derivatives, and provide a method for scientific and effective evaluation of space embedded operating system.

Adaptive model predictive control for linear time varying MIMO systems

A robust, adaptive Model Predictive Control (MPC) approach for asymptotically stable, constrained linear time-varying (LTV) systems with multiple inputs and outputs is proposed. The approach consists of two-steps, carried out on-line with a receding horizon strategy. In the first one, a real-time Set Membership identification algorithm exploits the measured input–output data and the available prior knowledge to build and refine a set of admissible models of the plant (Feasible Parameter Set, FPS). This set is guaranteed to contain also the true system dynamics under the considered working assumptions. In the second step, a robust finite-horizon optimal control problem is formulated and solved. The variation of system dynamics is taken into account by inflating the FPS over the prediction horizon, according to worst-case bounds, assumed a priori, on the parameters’ rate of change. The resulting optimal control sequence guarantees that the outputs of all possible plants inside the FPS satisfy the operational constraints, also considering all possible future parameter changes. The main theoretical properties of the proposed approach are demonstrated and the method is showcased in numerical simulations, highlighting the fundamental improvement over previous approaches not designed for LTV systems.

Graph MBO on Star Graphs and Regular Trees. With Corrections to DOI 10.1007/s00032-014-0216-8

The graph Merriman–Bence–Osher scheme produces, starting from an initial node subset, a sequence of node sets obtained by iteratively applying graph diffusion and thresholding to the characteristic (or indicator) function of the node subsets. One result in [14] gives sufficient conditions on the diffusion time to ensure that the set membership of a given node changes in one iteration of the scheme. In particular, these conditions only depend on local information at the node (information about neighbors and neighbors of neighbors of the node in question). In this paper we show that there does not exist any graph which satisfies these conditions. To make up for this negative result, this paper also presents positive results regarding the Merriman–Bence–Osher dynamics on star graphs and regular trees. In particular, we present sufficient (and in some cases necessary) results for the set membership of a given node to change in one iteration.

Evaluating generalization through interval-based neural network inversion

Typically, measuring the generalization ability of a neural network relies on the well-known method of cross-validation which statistically estimates the classification error of a network architecture thus assessing its generalization ability. However, for a number of reasons, cross-validation does not constitute an efficient and unbiased estimator of generalization and cannot be used to assess generalization of neural network after training. In this paper, we introduce a new method for evaluating generalization based on a deterministic approach revealing and exploiting the network’s domain of validity. This is the area of the input space containing all the points for which a class-specific network output provides values higher than a certainty threshold. The proposed approach is a set membership technique which defines the network’s domain of validity by inverting its output activity on the input space. For a trained neural network, the result of this inversion is a set of hyper-boxes which constitute a reliable and \(\varepsilon\)-accurate computation of the domain of validity. Suitably defined metrics on the volume of the domain of validity provide a deterministic estimation of the generalization ability of the trained network not affected by random test set selection as with cross-validation. The effectiveness of the proposed generalization measures is demonstrated on illustrative examples using artificial and real datasets using swallow feed-forward neural networks such as Multi-layer perceptrons.

Extended Tsukamoto's inference method for solving multi-objective linguistic optimization problems

Multi-objective linguistic optimization problems (MOLOPs) are quite useful in modeling a number of real life problems. The decision variables used to define the problem constraints and the objective functions take linguistic values in MOLOPs. In those MOLOPs, where the values of objective functions are unknown at all the points of the variable space, the link between the values of decision variables and objective functions is defined using if-then rules. MOLOPs formulated in this way were often solved using the Tsukamoto's inference method. However, the Tsukamoto's method can solve MOLOPs if the consequents in the if-then rules are defined as monotonic functions. Also, the solution obtained from Tsukamoto's method is a precise number. So in the present work, we propose a novel extension of Tsukamoto's inference method. The extended Tsukamoto's inference method can overcome both the above limitations. That is, it can solve MOLOPs where the consequents are defined as non-monotonic functions as well as monotonic functions. Also the extended Tsukamoto's method generates intervals instead of unique numbers, in the solution. From these intervals, we then generate type-1 fuzzy set membership functions and compare them using two of their fuzzy set uncertainty measures viz. centroid and fuzziness. Furthermore, we generate linguistic recommendations for these generated type-1 fuzzy set membership functions, as humans understand linguistic information naturally. We have also demonstrated the applicability of the proposed extended Tsukamoto's inference method to the case study for student's performance evaluation. We strongly believe that our proposed method is a novel one and will provide directions to future research.

Monitoring patient health based on medical records using fuzzy logic method

The Fuzzy Logic concept was first introduced by Prof. Lotfi Zadeh from the University of California at Berkeley in 1965, and presented not as a control methodology, but as a way of processing data by allowing the use of partial set membership compared to the crisp set membership or non-membership. Along with the development of computer technology, the concept of fuzzy logic is increasingly needed by people, because this concept is able to provide information needed in the decision making process. This study aims to analyze and design intelligent systems to monitor the health development of inpatients. The method used is the Fuzzy Logic method. This method will predict the level (degree) of health of each patient based on the amount of drug use and the durationof diagnosis process. The tools used to analyze and design the system are Unified Modeling Language. The results of this research are monitoring the health development of patients using the Fuzzy Logic method.

On equivalence of major relaxation methods for minimum ellipsoid covering intersection of ellipsoids

This paper investigates the problem on the minimum trace or volume ellipsoid covering intersection of ellipsoids. This problem can be solved by three major relaxation methods involving semi-definite programming relaxation, S-procedure relaxation and parameterized bounding ellipsoid relaxation. They are proposed from the different ideas or viewpoints, so that it is difficult to judge which relaxation method is the most suitable for the different practical implementations. To the best of our knowledge, the problem of proving the convexity of the optimization problem derived by the third relaxation method remains open. By rigorous analysis, we reveal the equivalence among the three relaxation methods, and address the open problem, i.e., the optimization problem derived by the third relaxation method can be equivalently transformed to a convex optimization problem. The computation complexity of these relaxation methods are also discussed, and the equivalent result is helpful to set membership filter and multisensor fusion obtaining a tighter ellipsoid to contain the state with lower computation complexity. Finally, the performance of each method is evaluated by several typical numerical examples in information fusion and filtering.

Event-triggered set-membership filtering for discrete-time memristive neural networks subject to measurement saturation and fadings

In this paper, the set-membership (SM) filtering problem is investigated for a class of discrete time-delayed memristive neural networks (MNNs) with unknown-but-bounded disturbances. The output measurements are subject to saturation, whose transmission is governed by a predetermined event-triggered strategy. In addition, the communication channel is usually fading, which is described by a set of stochastic variables taking different values in the interval [0,1]. The nonlinear activation function and the saturation function are assumed to satisfy the Lipschitz-like and sector conditions, respectively. The purpose of this paper is to design an event-triggered (ET) filter to estimate the certain region which includes the real states while guaranteeing the benefits of resource conservations. Via recursive linear matrix inequalities, some sufficient conditions are derived to optimize the estimation elliptic sets. Furthermore, the design of the optimal SM filter for MNNs is recast as solving a convex optimization problem via the semidefinite programming method. Finally, a persuasive simulation example is provided to verify the effectiveness of the designed filtering algorithm.

Methods for Multiple-Attribute Group Decision Making with q-Rung Interval-Valued Orthopair Fuzzy Information and Their Applications to the Selection of Green Suppliers

In the practical world, there commonly exist different types of multiple-attribute group decision making (MAGDM) problems with uncertain information. Symmetry among some attributes’ information that is already known and unknown, and symmetry between the pure attribute sets and fuzzy attribute membership sets, can be an effective way to solve this type of MAGDM problem. In this paper, we investigate four forms of information aggregation operators, including the Hamy mean (HM) operator, weighted HM (WHM) operator, dual HM (DHM) operator, and the dual-weighted HM (WDHM) operator with the q-rung interval-valued orthopair fuzzy numbers (q-RIVOFNs). Then, some extended aggregation operators, such as the q-rung interval-valued orthopair fuzzy Hamy mean (q-RIVOFHM) operator; q-rung interval-valued orthopairfuzzy weighted Hamy mean (q-RIVOFWHM) operator; q-rung interval-valued orthopair fuzzy dual Hamy mean (q-RIVOFDHM) operator; and q-rung interval-valued orthopair fuzzy weighted dual Hamy mean (q-RIVOFWDHM) operator are presented, and some of their precious properties are studied in detail. Finally, a real example for green supplier selection in green supply chain management is provided, to demonstrate the proposed approach and to verify its rationality and scientific nature.

Security-Constrained Unit Commitment in Presence of Lithium-Ion Battery Storage Units Using Information-Gap Decision Theory

This paper proposes a robust framework for the security-constrained unit commitment (SCUC) of generating units, in the presence of lithium-ion battery energy storage units, using the information-gap decision theory (IGDT) technique. In the suggested model, the degradation cost of the battery storage units has been considered in the objective function as a highly influencing factor in the operation of such storage units. The framework is independent of probability density functions or membership of sets and enables the system operator to adjust the conservatism of the operating strategy (between overconservative and reckless) against the load demand uncertainty. In this respect, the SCUC model has been presented within a day-ahead scheduling problem on the hourly basis using mixed-integer linear programming. Finally, the proposed framework has been simulated on a typical 6-bus test system as well as IEEE 24-bus and IEEE 118-bus systems to verify the efficiency and the effectiveness of the model using the IGDT technique.

Novel Generalized Distance Measure of Pythagorean Fuzzy Sets and a Compromise Approach for Multiple Criteria Decision Analysis Under Uncertainty

This paper aims at developing a novel generalized distance measure of Pythagorean fuzzy (PF) sets and constructing a distance-based compromise approach for multiple criteria decision analysis (MCDA) within PF environments. The theory of Pythagorean fuzziness provides a representative model of nonstandard fuzzy sets; it is valuable for representing complex vague or imprecise information in many practical applications. The distance measure for Pythagorean membership grades is important because it can effectively quantify the separation between PF information. Based on the essential characteristics of PF sets (membership, non-membership, strength, and direction), this paper proposes several distance measures, namely, new Hamming and Euclidean distances and a generalized distance measure that is based on them for Pythagorean membership grades and for PF sets. Moreover, the useful and desirable properties of the proposed PF distance measures are investigated to evaluate their advantages and form a solid theoretical basis. In addition, to evaluate the performance of the proposed distance measures in practice, this paper establishes a PF-distance-based compromise approach for addressing MCDA problems that involve PF information. The effectiveness and practicability of the developed approach are further evaluated through a case study on bridge-superstructure construction methods. According to the application results and comparative analysis, the proposed PF distance measures are accurate and outperform other methods in handling the inherent uncertainties of evaluation information. Furthermore, the PF-distance-based compromise approach can accommodate the much higher degrees of uncertainty in real-life decision scenarios and effectively determine the priority ranking among candidate alternatives for managing complicated MCDA problems.