Matrix Variables Research Articles

Block structure-based covariance tensor decomposition for group identification in matrix variables

In research fields such as financial market analysis and social network research, understanding variable grouping relationships is fundamental to effective data analysis. This study describes the concept of the covariance tensor and emphasizes its significant role in analyzing matrix variable groupings through block structures. We propose a novel tensor decomposition-based method to exploit these structures for group identification. In addition, we explore the asymptotic properties of our estimators, focusing on the precision of the estimation of the number of groups and the asymptotic convergence of classification error rates to zero. We validate the effectiveness of the method through extensive numerical simulations across diverse data volumes and complexities, affirming its capability in variable grouping.

An Aperiodic-Sampling-Dependent Event-Triggered Control Strategy for Interval Type-2 Fuzzy Systems: New Communication Scheme and Discontinuous Functional.

This article studies the event-triggered control problem of interval type-2 (IT2) fuzzy systems. It proposes a new aperiodic-sampling-dependent event-triggered communication scheme, and introduces an improved sampling-dependent discontinuous functional. First, taking into account that the system is with aperiodic sampling, the weighting matrices used for judgement in the event-triggered scheme are designed to be related to each sampling interval or its upper and lower bounds, according to the sampling interval being predictable or not. This design makes the scheme more flexible, thereby improving control effectiveness. Second, a sampling-dependent discontinuous functional is introduced into event-triggered control, which contains matrix variables depending on the aperiodic sampling, and incorporates an improved discontinuous term and a vector related to event-triggered condition. Thus, the functional reduces the conservativeness of stability and stabilization criteria. Based on the above aperiodic-sampling-dependent strategy, the derived results achieve better event-triggered control effects compared with the recent literature. At the end, two examples are given to validate the theoretical effectiveness and advantages of the results under various parameters.

Parameterization to fault detection filtering for Itô stochastic T‐S fuzzy systems

AbstractThis article focuses on the fault detection filtering problem for Itô stochastic Takagi–Sugeno (T‐S) fuzzy systems. In terms of line integral Lyapunov function, a sufficient condition of exponential stability in mean square and extended dissipativity for the systems under consideration is established which has less conservatism than the one based on quadratic Lyapunov function. The obtained sufficient condition is nonlinear, which makes the synthesis of fault detection filter being difficult and challenging. By choosing general matrix variables and constructing the appropriate orthogonal complement matrices, the nonlinear sufficient condition can be converted into linear one ingeniously via utilizing Finsler's lemma twice. Thus, the fault detection filter can be developed by virtue of parameterization. It should be pointed out that our filter determined by the parameterization approach includes the one obtained by the equivalent transformation method as a special case. Finally, we demonstrate the feasibility and superiority of our proposed approach through three numerical examples.

Distributed algorithms of solving linear matrix equations via double-layered networks

This paper focuses on designing distributed algorithms for solving the linear matrix equation in the form of AXB=F via a double-layered multi-agent network. Firstly, we equivalently transform the least squares (LS) problem of AXB=F into two subproblems. We introduce a double-layered multi-agent network, in which each agent only has access to partial information of matrices A, B and F, to solve these two subproblems in a distributed structure. Subsequently, we develop continuous-time and discrete-time distributed algorithms to obtain an LS solution of AXB=F. In particular, the sufficient and necessary conditions about the step-sizes are established, under which the discrete-time algorithm can linearly converge to an LS solution. Compared with the previous results in which each agent needs to communicate multiple matrix variables with the neighbors, the proposed algorithms effectively reduce communication burden for each agent since only one matrix variable is communicated in the upper-layer network and the communication variables in the lower-layered network are vectors with lower dimensions than matrices. Finally, an application example is provided to demonstrate the effectiveness of the proposed algorithms.

On stability and H∞ control synthesis of sampled‐data systems: A multiple convex function approximation approach

AbstractThis article deals with the stability and control synthesis for a class of linear sampled‐data systems. First, a novel integral inequality with the cubic term of integral interval length instead of reciprocal one of integral interval length is constructed by non‐orthogonal polynomials. This can make full use of slack matrix variables and additional information about sawtooth structural sampling pattern. Then, on the basis of the constructed integral inequality, a cubic‐term‐dependent discontinuous exponent Lyapunov–Krasovskii Functional (LKF) is developed containing additional information about system states to design an sampled‐data state feedback controller. To better estimate the upper bound of the derivative of LKF, a kind of multiple convex function approximation approach is developed, which can be used to deal with the two‐variable polynomial negative definite issue by dividing the variable interval into multiple subintervals. By the constructed integral inequality and multiple convex function approximation approach, sufficient conditions with less conservatism are deduced for the feasibility of sampled‐data state feedback controller. Moreover, by the inner convex approximation solution technique and proposed iterative algorithm, the bilinear matrix inequalities can be transformed into linear matrix ones, which can be easily tackled, to obtain the desired sampled‐data controller gain. Finally, by comparing with existing results, the advantages and superiority of our proposed approaches can be confirmed via two numerical examples.

Admissibility LMI criteria for descriptor fractional-order systems with a changeable number of decision variables

This paper studies the admissibility problem of descriptor fractional-order systems (DFOSs) with order in (0,1). Firstly, an approach to stability for FOSs is derived which is effective for the case of at least two complex matrix variables. Secondly, based on the generalized linear matrix inequality (GLMI) region, a new admissibility criterion for DFOSs with multiple choices for the number of decision variables is presented, which does not involve complex variables and equality constraints. Moreover, all the theorems are necessary and sufficient conditions, and can be described by strict linear matrix inequalities (LMIs). Finally, two numerical examples are provided to verify the validity of theoretical conclusions.

Refined Dynamic Event-Triggering Cluster Consensus of Multiagent Systems With Fixed/Switching Topology.

This article is concerned with cluster consensus control of multiagent systems (MASs) with the fixed/switching topology under a dynamic event-trigger (DET) mechanism. A refined sampled-data-based DET scheme is proposed by introducing two dynamically adjusting threshold parameters to distinguish the different transmission requirements for neighboring agents intra and outer cluster. Faced with the difficulties of acquiring full state information among spatially distributed agents, output feedback is employed to construct cooperative control protocols. Both fixed and switching topologies are considered to execute the designed DET-based cooperative cluster consensus control protocols. By constructing appropriate Lyapunov-Krasovskii functionals (LKFs), some sufficient criteria in terms of matrix inequalities for the cluster consensus of MASs are derived, which can ensure that the error system with the proposed DET-based control strategy is asymptotically stable. Facing the nonconvex issue induced by output feedback, a particle swarm optimization (PSO)-based control design algorithm is novelly developed to calculate the control gains and event-triggering parameters jointly based on the derived stability criteria. The elements of the matrix variables are valued stochastically in certain ranges and the fitness function is designed as the accumulation of the weighting value of each matrix inequality. Finally, an application of multiple satellites formation flying is applied to numerically illustrate the effectiveness of the cluster consensus control strategy with the designed DET mechanism.

Event-triggered interval type-2 fuzzy control of networked systems with extended dissipative under Markovian switching

In this technical note, the problem of the extended dissipative control for interval type-2 fuzzy model with nonlinear network systems in the event-triggered framework is investigated. A novel dynamic event-triggered strategy is developed to ascertain the instants of activation. It has the advantage of reducing data transmission and optimising the utilisation of communication resources. On the basis of the proposed mechanism, the stochastic Lyapunov function including internal dynamic variables is constructed. Based on this function, coupled with the inequality scaling technique and the application of Dynkin's formula, we derive a sufficient condition for the system's stochastic asymptotic stability and extended dissipativity. The design of the dynamic event-triggered extended dissipative controller becomes challenging because the new sufficient condition is nonlinear for some matrix variables. However, utilising the Projection Lemma and the co-design approach, such a controller can be developed based on the obtained analysis result. The methodology is demonstrated through a rigorous numerical simulation case study.

Pollinator assemblages in grasslands along river valleys depend on the urban matrix and local habitat scale variables

Riverside urban grasslands (distinctive riparian ecosystems situated alongside rivers within cities) can provide several benefits for pollinators, which are crucial for the health and sustainability of ecosystems. Maintaining these habitats not only promotes the diversity of pollinators but also helps mitigate the negative impacts of human activities on the urban landscape. However, it is still unclear how local environmental and vegetation factors affect pollinators' functional and taxonomic distribution along riverside grasslands in cities and how to use these results to preserve and conserve urban wildlife. In this study, we examined how the taxonomic and functional diversity of wild bees, butterflies, and hoverflies and their traits in urban riverside grasslands are related to the environmental and vegetation factors. We studied bee, butterfly, and hoverfly assemblages in 30(200 long and 1 m wide) transects along riverside grassland sites in Poznań, Poland. We found that higher cover of impervious surface area leads to lower butterfly abundance and species richness and taxonomical diversity of butterflies and hoverflies. Butterfly taxonomical and functional diversity increased with increasing distance to human settlements. Furthermore, the higher cover of plants and tall vegetation positively correlated with butterfly abundance, species richness, and diversity, as well as hoverfly species richness. Cover of water bodies was positively related to bee diversity and hoverfly taxonomical and functional diversity. As a result, specialized pollinators are more likely to decline than generalist pollinators adapted to urban environment. By creating and maintaining riverside urban grasslands that prioritize the needs of pollinators, cities policymaker and local communities can contribute to the conservation of these vital insects and promote a healthier, more sustainable urban environment.

Inhibitory Components in Muscle Synergies Factorized by The Rectified Latent Variable Model from Electromyographic Data.

Non-negative matrix factorization (NMF), widely used in motor neuroscience for identifying muscle synergies from electromyographical signals (EMGs), extracts non-negative synergies and is yet unable to identify potential negative components (NegCps) in synergies underpinned by inhibitory spinal interneurons. To overcome this constraint, we propose to utilize rectified latent variable model (RLVM) to extract muscle synergies. RLVM uses an autoencoder neural network, and the weight matrix of its neural network could be negative, while latent variables must remain non-negative. If inputs to the model are EMGs, the weight matrix and latent variables represent muscle synergies and their temporal activation coefficients, respectively. We compared performances of NMF and RLVM in identifying muscle synergies in simulated and experimental datasets. Our simulated results showed that RLVM performed better in identifying muscle-synergy subspace and NMF had a good correlation with ground truth. Finally, we applied RLVM to a previously published experimental dataset comprising EMGs from upper-limb muscles and spike recordings of spinal premotor interneurons (PreM-INs) collected from two macaque monkeys during grasping tasks. RLVM and NMF synergies were highly similar, but a few small negative muscle components were observed in RLVM synergies. The muscles with NegCps identified by RLVM exhibited near-zero values in their corresponding synergies identified by NMF. Importantly, NegCps of RLVM synergies showed correspondence with the muscle connectivity of PreM-INs with inhibitory muscle fields, as identified by spike-triggered averaging of EMGs. Our results demonstrate the feasibility of RLVM in extracting potential inhibitory muscle-synergy components from EMGs.

FLOOD MAPPING IN MOUNTAINOUS AREAS USING SENTINEL-1 & 2 DATA AND GLCM FEATURES

Abstract. Flooding events have been frequently observed throughout the world and may have devastating effects on the environment. Mapping of flood extent is important for taking the necessary mitigation measures for future. The freely available Sentinel-1 radar and Sentinel-2 optical images allow analysis of flood extent with adequate spatial resolution. However, temporal resolution may be insufficient, and currently only events with the suitable satellite orbital passes can be analyzed with Sentinel sensors. In addition, clouds are often in scene during and shortly after a flood event, which hinders the use of optical imagery. Here, we investigated the complementary use of Sentinel-1 and Sentinel-2 data with a land cover classification approach based on random forest over a part of northern Türkiye, which frequently confronts floods and landslides. We expanded the feature set with principal components (PC) of gray-level co-occurrence matrix (GLCM) variables obtained from Sentinel-1 polarization and Sentinel-2 spectral bands, and also the normalized difference vegetation index (NDVI) and modified normalized difference water index (MNDWI) images produced from the optical data. The training and test data were manually extracted from pre- and post-event optical data. The findings demonstrated that using GLCM PCs significantly increased the overall accuracy (OA = 99% with GLCM and OA = 93% without GLCM) of the classification. Furthermore, the flooded vegetation differs in textural features when compared with the other inundated surfaces, and also permanent water. Therefore, by allowing the separation of flooded vegetation and the other flooded areas, the GLCM data considerably increased the map quality.

Event-triggered finite-time state estimation for discrete singular Markovian systems with quantization

The problem of finite-time state estimation is discussed for discrete singular Markov jump network systems (DSMNSs) based on event-triggered (ET) quantization control strategy. According to the ET network communication and quantization control schemes, an augmented DSMNS model with time-delays is first constructed. Employing stochastic Lyapunov functional and introducing relaxation matrix variables, sufficient conditions are established for the DSMNS to be singularly stochastic finite-time bounded. Besides, the ET gain matrices and ET quantized feedback controllers are co-designed by decoupling matrix variable parameters so that the augmented DSMNS is singularly stochastic finite-time bounded with a specified performance index. Eventually, the effectiveness of the proposed scheme is verified and evaluated by a numerical simulation.

Additive autoregressive models for matrix valued time series

In this article, we develop additive autoregressive models (Add‐ARM) for the time series data with matrix valued predictors. The proposed models assume separable row, column and lag effects of the matrix variables, attaining stronger interpretability when compared with existing bilinear matrix autoregressive models. We utilize the Gershgorin's circle theorem to impose some certain conditions on the parameter matrices, which make the underlying process strictly stationary. We also introduce the alternating least squares estimation method to solve the involved equality constrained optimization problems. Asymptotic distributions of the parameter estimators are derived. In addition, we employ hypothesis tests to run diagnostics on the parameter matrices. The performance of the proposed models and methods is further demonstrated through simulations and real data analysis.

SMC for Discrete Fuzzy Semi-Markov Jump Models With Partly Known Semi-Markov Kernel

This article investigates the sliding mode control (SMC) for discrete-time nonlinear semi-Markov jump models with a partly known semi-Markov kernel (SMK). The nonlinear system is characterized by the Takagi–Sugeno (T–S) fuzzy model, where the membership functions for fuzzy rules are designed to be related to the system mode. In view of the fact that the statistical characteristic of the SMK is difficult to fully obtain in practical engineering, the SMK is recognized to be partly known with less conservativeness than both semi-Markov jump models with completely known SMK and Markov jump models with partly known transition probabilities. On the basis of classical Lyapunov stability and fuzzy-model-based approach, novel convex mean-square stability is proposed for the underlying system by eliminating the nonlinear coupling terms with the aid of additional matrix variables. Afterward, a fuzzy SMC law strategy is constructed to guarantee the reachability of the discrete quasi-sliding mode. Finally, a robot arm model is simulated to verify the proposed fuzzy SMC strategy.

Bee movement between natural fragments is rare despite differences in species, patch, and matrix variables

Bee movement between natural fragments is rare despite differences in species, patch, and matrix variables

An asymmetric Lyapunov–Krasovskii functional and its application to stochastic admissibility analysis of time-delay singular Markovian jump systems

This paper investigates the stochastic admissibility of time-delay singular Markovian jump systems (SMJSs). A new asymmetric Lyapunov–Krasovskii functional (LKF) is built to obtain new sufficient conditions for ensuring stochastic admissibility. The merits of our method are that we remove the positive definite constraint of some matrix variables to reduce the conservativeness. Finally, a numerical example is provided to verify the less conservativeness of our result.

Optimal linear array orientation design for 3D direct position determination via semi-Definite relaxation

This paper presents an optimization strategy for array orientations in a three-dimensional (3D) direct position determination (DPD) system. Specifically, we consider a scenario in which uniform linear arrays (ULAs) are used to locate emitters, and we seek to optimize the array orientations in terms of localization accuracy. The E-optimality criterion, which minimizes the spectral norm of the Cramér-Rao lower bound (CRLB), is exploited to formulate this problem. As the objective function is non-convex with bilinear structures, we leverage semi-definite relaxation (SDR) to transform it into a convex semi-definite programming (SDP) problem by substituting the bilinear terms with a matrix variable. In addition, we tackle the array orientation configuration problem in the context of multi-emitter scenarios and develop an SDR solution for large-scale antenna array systems. Simulation results validate that the ULAs with array orientations designed by the proposed SDR-based method have near-optimal localization performance.

Dissipativity-based conditions for the feedback stabilization of systems with time-varying input delays

This note is concerned with presenting new dissipativity-based conditions for the stabilizability of discrete-time systems with time-varying delays by linear static output feedback (SOF). We demonstrate that the feasibility of nonlinear matrix inequalities for the design of feedback stabilizing gains derived from the literature is equivalent to the feasibility of a linear matrix inequality establishing dissipativity of the system plus one matrix inequality constraint. An iterative strategy allowing the computation of stabilizing SOF gains is then developed based on a new relaxed sufficient condition. Compared with other popular approaches in the literature, such as the celebrated cone complementarity linearization (CCL) method, the strategy avoids providing initial “guesses” for the matrix variables, which is especially complicated when dealing with a large number of matrices. Due to being a particular case of SOF with an identity output matrix, static state feedback (SSF) gains can also trivially be computed by exploiting the developed conditions.

LC-MS Metabolomic Profiling of Five Types of Unrefined, Cold-Pressed Seed Oils to Identify Markers to Determine Oil Authenticity and to Test for Oil Adulteration.

The authenticity of food products marketed as health-promoting foods-especially unrefined, cold-pressed seed oils-should be controlled to ensure their quality and safeguard consumers and patients. Metabolomic profiling using liquid chromatography coupled to quadrupole time-of-flight mass spectrometry (LC-QTOF) was employed to identify authenticity markers for five types of unrefined, cold-pressed seed oils: black seed oil (Nigella sativa L.), pumpkin seed oil (Cucurbita pepo L.), evening primrose oil (Oenothera biennis L.), hemp oil (Cannabis sativa L.) and milk thistle oil (Silybum marianum). Of the 36 oil-specific markers detected, 10 were established for black seed oil, 8 for evening primrose seed oil, 7 for hemp seed oil, 4 for milk thistle seed oil and 7 for pumpkin seed oil. In addition, the influence of matrix variability on the oil-specific metabolic markers was examined by studying binary oil mixtures containing varying volume percentages of each tested oil and each of three potential adulterants: sunflower, rapeseed and sesame oil. The presence of oil-specific markers was confirmed in 7 commercial oil mix products. The identified 36 oil-specific metabolic markers proved useful for confirming the authenticity of the five target seed oils. The ability to detect adulterations of these oils with sunflower, rapeseed and sesame oil was demonstrated.

The noncommutative geometry of matrix polynomial algebras

This work investigates the noncommutative affine geometry of matrix polynomial algebra extensions of a coefficient algebra by (elementary) matrix variables. A precise description of the spectrum (of maximal one-sided or bilateral ideals) of general matrix algebras is required. It results that the Zariski space of the irreducible representations of a matrix algebra is obtained by a natural gluing of the Zariski spaces of the irreducible representations of its diagonal components. An important step for the geometry of matrix polynomial algebras in commuting variables is achieved by a generalization of the Amitsur–Small Nullstellensatz, from which follows a precise description of their primitive quotients. We also characterize which of them are geometric algebras (in the sense of noncommutative deformation theory), reconstructible as algebras of observables from the scheme of irreducible representations. We then prove that each diagonal component of a matrix polynomial algebra in commuting variables is a Jacobson ring, whose non-Noetherian commutative geometry is efficiently described by the geometry of an affine essential subextension. And in the spirit of nonlocal algebraic geometry and addressing an open question by Charlie Beil, we obtain a class of non-Noetherian commutative monoid rings admitting closed points with positive geometric dimension.