Observability Matrices Research Articles

Neural network-based distributed consensus tracking control for uncertain Euler–Lagrange systems over directed topologies

This paper proposes a neural network-based robust control approach for driving disturbed Euler–Lagrange systems (e.g., robot manipulator) in a directed network to perform consensus tracking of a heterogeneous leader’s output signal. The parameter matrices and external disturbances in each follower’s Euler–Lagrange dynamics are unmeasurable, thus we unify them into one lumped uncertainty term. Neural networks are then employed to online estimate these uncertainties, with adaptive update laws ensuring the boundedness of the estimation errors. Subsequently, a set of distributed observers are developed to adaptively estimate the leader’s states as well as the unidentified parameter vector and output matrix in the leader’s model. With their help, the robust cooperative controller is designed. Its efficacy on directed networks is theoretically justified by designing a Lyapunov function with a special structure. This function produces symmetric positive definite matrices when its first derivative terms interact with the specified parameters in the observer and Laplacian matrices for directed graphs. Finally, numerical simulations based on two-link robot manipulators are carried out to verify that the tracking errors converge to zero when applying the neural network-based robust controller.

Being Attractive on a Dating App: Generational and Gender Differences in Tinder Bios and Profile Pictures

On dating apps, the image that users project of themselves, especially in terms of physical attributes, is important. This study explored how individuals of different generations and genders present their desirability through photos and self-descriptions—‘bios’—on their Tinder profiles. Through a virtual ethnographic study, 400 profiles of users aged 18–70 years were analysed and grouped into generation- and gender-based categories. The photographs were thematically analysed using observation matrices and descriptions. The results showed that, although all groups try to present themselves positively, generation- and gender-based differences exist in how individuals present their physicality through photographs (postures, angles, type of photo, place, facial expressions, body stereotypes, sexualisation) and bios. With respect to generations, these differences are attributable to the values and preferences of each group. Regarding gender differences, the influence of sociocultural stereotypes and ideals of femininity and masculinity is observed.

Синтез параметрически грубых систем управления с регуляторами и наблюдателями состояния на основе грамианных технологий

Automatic control systems based on regulators with state observers are effective means to control linear and linearized objects of a high degree of complexity. One of the key problems in the synthesis of modal systems is the development of parametrically rough (robust) systems that retain their performance, as well as the main quality indicators with possible variations of the parameters of both the control object and the controller itself. The synthesis of a robust system with a state observer is carried out by the modal control method based on the matrix model of the controlled object. To ensure the parametric robustness of the system, the authors have proposed a technique which based on the mathematical apparatus of Gramians of controllability and observability as well as on the similarity transformation of observer matrices. Computer simulation of the system with state controller and observer is carried out by means of the MatLab software. The authors have proposed a method to form an observer state structure that is optimal in the sense of parametric roughness of the system, which is based on the procedure of transforming the similarity of the object model. And the transformation matrix is formed by varying the singular numbers of the controllability and observability gramians. The proposed method allows us to obtain an observer structure with a certain ratio of controllability and observability that ensures the fulfillment of the condition of parametric roughness i.e., the absence of positive feedback in the control device. The results obtained make it possible to clearly demonstrate the high efficiency of using the Gramian method for the synthesis of control systems with state observers with low sensitivity to variations of the controller own parameters.

Embodiment of Symbolism and Meaning of Human Life Phases in the Characteristics of Topeng Tunggal Through the Creation of a Dance Film Titled Nindak Jirumklan

This research innovates dance creation by integrating Betawi dance, cinematography, music technology, visual arts, and scenography, aiming to broaden our understanding of dance in a cinematic format. It challenges the assumption that dance is confined to stages and advocates for a broader visual platform. Drawing inspiration from the Topeng Nindak Jirumklan, the dance film symbolizes life stages. The research problem formulation for creating a dance film involves exploring how to depict the different phases of life using the framework of a single-mask dance that features four mask characters. Betawi Mask Dance is an adaptation of the Cirebon Babakan mask, where each dance embodies aspects of human life. Using a qualitative approach, this study encompasses focus determination, data collection, observation, document use, interviews, and data collection matrices. Guided by Hawkins’ creation theory, it explores experiences, perceptions, feelings, imaginations, realizations, and formations. The anticipated outcomes of Betawi arts, including mask dances, Wayang, and Tanjidor music, extending across various regions with Malay influence, and the dance film Nindak Jirumklan, incorporating music, dance, comedy, and drama, inspired by the single mask dance, encompasses providing an imaginative journey, enriching artistic memories, exploring space through technology, and contributing to choreographic knowledge.
 Keywords: symbolization, character mask, Nindak Jirumklan, dance film

Robust Estimators for Missing Observations in Linear Discrete-Time Stochastic Systems with Uncertainties

As a first approach to estimating the signal and the state, Theorem 1 proposes recursive least-squares (RLS) Wiener fixed-point smoothing and filtering algorithms that are robust to missing measurements in linear discrete-time stochastic systems with uncertainties. The degraded quantity is given by multiplying the Bernoulli random variable by the degraded signal caused by the uncertainties in the system and observation matrices. The degraded quantity is observed with additional white observation noise. The probability that the degraded signal is present in the observation equation is assumed to be known. The design feature of the proposed robust estimators is the fitting of the degraded signal to a finite-order autoregressive (AR) model. Theorem 1 is transformed into Corollary 1, which expresses the covariance information in a semi-degenerate kernel form. The autocovariance function of the degraded state and the cross-covariance function between the nominal state and the degraded state is expressed in semi-degenerate kernel forms. Theorem 2 shows the robust RLS Wiener fixed-point and filtering algorithms for estimating the signal and state from degraded observations in the second method. The robust estimation algorithm of Theorem 2 has the advantage that, unlike Theorem 1 and the usual studies, it does not use information on the existence probability of the degraded signal. This is a unique feature of Theorem 2.

Quasidifferentiability and Uniform Observability of Linear Time-Varying Singularly Perturbed Systems

For linear time-varying singularly perturbed systems (LTVSPS) with quasidifferentiable coefficients and a small parameter multiplying some derivatives, the problem of uniform observability is considered. Necessary and sufficient conditions for the quasidifferentiability of the set of output functions independent of the small parameter are proved, observability matrices independent of the small parameter for the slow subsystem and the family of fast subsystems associated with the LTVSPS are constructed, and a connection is established between them and the observability matrix of the original system. On the basis of the complete decomposition of the original LTVSPS with respect to the action of the group of linear nonsingular transformations, we prove rank sufficient conditions for the uniform observability of the LTVSPS that are independent of the small parameter and valid for all sufficiently small values of it. The conditions are expressed in terms of the observability matrices of the slow subsystem and the family of fast subsystems of smaller dimensions than the original LTVSPS.

The new Subspace-based poly-reference Complex Frequency (S-pCF) for robust frequency-domain modal parameter estimation

Subspace identification has been widely used in modal parameter estimation. The formulation of a parametric subspace-driven modal identification technique is achieved by using the Singular Value Decomposition (SVD) to remove most the uncertainties present in the null space of the system matrices used in the identification process, which leads to a more robust estimation of the modal properties. This idea has been used in the formulation of time domain modal identification techniques like the (time-domain) Eigensystem Realization Algorithm and the Stochastic Subspace identification techniques. In this paper, a subspace implementation of the new poly-reference Complex Frequency (pCF) formulated in Modal Model is proposed. The idea is to combine SVD with the new pCF to derive a new system identification technique that operates in the frequency domain by using either the Frequency Response Function or the Half Spectrum as primary data. Similarly to the ERA, the idea behind the subspace implementation of the pCF is to use different subspaces of the observability and frequency-domain controllability matrices, and carry out eigen-system realizations to estimate the modal properties corresponding to each chosen subspace. In order to illustrate its robustness, the subspace-driven pCF is applied to a simulated and two practical application examples.

Localization and Estimation of Unknown Forced Inputs: A Group LASSO Approach

This paper studies the problem of locating the sparse set of sources of forcing inputs driving linear systems from noisy measurements when the initial state is unknown. This problem is particularly relevant to detecting forced oscillations in electric power networks. We express measurements as an additive model comprising the initial state and inputs grouped over time, both expanded in terms of the basis functions (i.e., impulse response coefficients). Using this model, with probabilistic guarantees, we recover the locations and simultaneously estimate the initial state and forcing inputs using a variant of the group LASSO (linear absolute shrinkage and selection operator) method. Specifically, we provide upper bounds on: (i) the probability that the group LASSO estimator incorrectly identifies the locations and (ii) the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{2}$</tex-math></inline-formula> -norm of the estimation error. Our bounds depend on the number of measurements, inputs, and sensors; the sensor noise variance; and the minimum singular value of the observability and impulse response matrices. Our theoretical analysis is one of the first to provide a complete treatment for the group LASSO estimator for the left invertible linear systems with delay. Finally, we validate the performance of the estimator on synthetic models and the IEEE 68-bus, 16-machine power system.

An Improved Orthogonal Matching Pursuit Algorithm for CS-Based Channel Estimation

Wireless broadband transmission channels usually have time-domain-sparse properties, and the reconstruction of these channels using a greedy search-based orthogonal matching pursuit (OMP) algorithm can effectively improve channel estimation performance while decreasing the length of the reference signal. In this research, the improved OMP and SOMP algorithms for compressed-sensing (CS)-based channel estimation are proposed for single-carrier frequency domain equalization (SC-FDE) systems, which, in comparison with conventional algorithms, calculate the path gain after obtaining the path delay and updating the observation matrices. The reliability of the communication system is further enhanced because the channel path gain is calculated using longer observation vectors, which lowers the Cramér–Rao lower bound (CRLB) and results in better channel estimation performance. The developed method can also be applied to time-domain-synchronous OFDM (TDS-OFDM) systems, and it is applicable to the improvement of other matching pursuit algorithms.

An Investigation of Stability, Controllability and Observability of a Three Degree of Freedom Translational Mechanical System using State Space Approach

State-space modelling approach which is essentially time-domain developed in the late 1960s is a new approach to the analysis and design of complex control systems. Several researches have carried out modelling and analysis of mechanical systems with a number of degrees of freedom of movement using state space approach among which is the work of Sivak and Darina (2012) who modelled a system with two degrees of freedom. In this paper, therefore, we provide an extension of the work of Sivak and Darina to model and analyse a three degree of freedom translational mechanical system using state-space approach. The system was first presented in equivalent free body diagrams, then Newton's second law of motion was used to derive its equations of motion. The State-space formulation in the controllable canonical form obtained from the time-domain differential equations is adopted and the Laplace transform method was used in the analysis to determine the poles (natural frequencies) of the system using two numerical examples in MATLAB software. The software was also used to determine the controllability and observability matrices of the system. The stability, controllability and observability of the system were then discussed from the poles, controllability matrix and observability matrix respectively. Tables of numerical values and line graphs were used to present the results obtained from the analysis. Finally, in these results, the system was found to be stable, controllable and observable suggesting that a state feedback ( pole placement ) control design for the system is possible.

Observer-Based Security Fuzzy Control for Nonlinear Networked Systems Under Weighted Try-Once-Discard Protocol

This paper is concerned with the observer-based security fuzzy control problem for a class of nonlinear networked systems with imperfectly matched membership functions (MFs) under weighted try-once-discard (WTOD) protocol. The nonlinear networked system is constructed based on interval type-2 (IT2) Takagi-Sugeno (T-S) model, which can properly handle parameter uncertainties via lower and upper MFs. To mitigate the communication load, WTOD protocol is exploited to schedule the transmission order of the signals, in which those signals may be subjected to randomly occurring deception attacks. The observer is constructed under unmeasurable premise variables, and then the controller with imperfect matching MFs is designed according to the estimated states. Moreover, the observer-based controller is derived with Lyapunov stability theory such that the stochastic stability of the augmented closed-loop system with predefined disturbance attenuation performance can be guaranteed. Subsequently, sufficient conditions are provided for the desired observer and controller gain matrices based on linear matrix inequalities (LMIs) technique. Numerical simulation example demonstrates the validity of the proposed observer-based security fuzzy control design scheme.

Robust Recursive Least-Squares Wiener Filter for Linear Continuous-Time Uncertain Stochastic Systems

For linear continuous-time systems with uncertainties in the system and observation matrices, an original robust RLS Wiener filter is designed in this study. The robust RLS Wiener filter does not assume norm-bounded uncertainty for the system and observation matrices, in contrast to the robust Kalman filter. In the design of the robust RLS Wiener filter, the degraded signal, affected by the uncertainties in the system and observation matrices, is modeled by an autoregressive (AR) model. The system and observation matrices for the degraded signal are formulated from the relationship between the AR model of the degraded signal and the state-space model. Estimation formulas for the system and observation matrices are proposed in Section 2. The robust filtering problem is introduced based on the minimization of the mean-square value of the filtering errors for the system states. The robust filtering estimate is given as an integral transformation of the degraded observations using the impulse response function. The integral equation that an optimal impulse response function satisfies is given in Section 3. Theorem 1 presents a robust RLS Wiener filtering algorithm starting from this integral equation. The proposed robust RLS Wiener filter outperforms the existing robust Kalman filter regarding estimate accuracy, as shown by a numerical simulation example.

Codesign for Resilience and Performance

We present two optimization approaches to minimize the impact of sensor falsification attacks in linear time invariant systems controlled by estimate-based feedback. We accomplish this by finding observer and controller gain matrices that minimize outer ellipsoidal bounds that contain the reachable set of attack-induced states. To avoid trivial solutions, we involve a covariance-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Vert H\Vert _{2}$</tex-math></inline-formula> closed-loop performance constraint. This exposes a trade-off between system security and closed-loop performance and demonstrates that only small concessions in performance can lead to large gains in our reachability-based security metric. We provide both a nonlinear optimization based on geometric sums and a fully convexified approach formulated with linear matrix inequalities. We demonstrate the effectiveness of these tools on two numerical case studies.

Large sample covariance matrices of Gaussian observations with uniform correlation decay

We derive the Marchenko–Pastur (MP) law for sample covariance matrices of the form Vn=1nXXT, where X is a p×n data matrix and p/n→y∈(0,∞) as n,p→∞. We assume the data in X stems from a correlated joint normal distribution. In particular, the correlation acts both across rows and across columns of X, and we do not assume a specific correlation structure, such as separable dependencies. Instead, we assume that correlations converge uniformly to zero at a speed of an/n, where an may grow mildly to infinity. We employ the method of moments tightly: We identify the exact condition on the growth of an which will guarantee that the moments of the empirical spectral distributions (ESDs) converge to the MP moments. If the condition is not met, we can construct an ensemble for which all but finitely many moments of the ESDs diverge. We also investigate the operator norm of Vn under a uniform correlation bound of C/nδ, where C,δ>0 are fixed, and observe a phase transition at δ=1. In particular, convergence of the operator norm to the maximum of the support of the MP distribution can only be guaranteed if δ>1. The analysis leads to an example for which the MP law holds almost surely, but the operator norm remains stochastic in the limit, and we provide its exact limiting distribution.

Observability Analysis for Orbit Determination Using Spaceborne Gradiometer

The application of a spaceborne gradiometer to satellite orbit determination has been proposed in recent years. The advantages lie in its full autonomy and its immunity against spoofing attacks. The objective of this paper is to study the observability of the spaceborne gradiometer-based orbit determination (SGOD) system. To address the problem of unknown biases in spaceborne gradiometer measurements, the joint estimation of satellite orbital states and gradiometer biases is adopted. Then, the system observability matrices are formulated based on the theory of nonlinear observability. The local weak observability is assessed numerically by singular values and condition numbers of the observability matrices. A special unobservable case is demonstrated, which is the circular orbit in the Keplerian two-body model. Different orbital parameters, attitude control modes, and gravity models are furtherly employed to analyze their effects on system observability. The observability analysis shows that low altitudes, large eccentricities, large inclinations, attitude maneuverings, and the J2 perturbation can improve the system observability. Furthermore, a numerical simulation using the extended Kalman filter (EKF) is developed to obtain accuracies and convergence rates of the SGOD system. Effects of orbital parameters, attitude control modes, and the J2 perturbation on orbit determination results are also studied. It is shown that the simulation results agree with the observability analysis. Using a spaceborne gradiometer with 0.1 E (1 E=10−9 s−2) accuracy, position accuracy of tens of meters is achieved for a low Earth orbit.

Observer-Based PID Control Protocol of Positive Multi-Agent Systems

This paper proposes the observer-based proportional-integral-derivative control of positive multi-agent systems. First, a positive observer is constructed for the considered multi-agent systems in terms of a matrix decomposition approach. Then, a novel proportional-integral-derivative protocol framework is proposed based on an improved observer. By using copositive Lyapunov function, the positivity and consensus of the multi-agent systems are achieved. The corresponding observer and control protocol gain matrices are designed in terms of linear programming. Moreover, the proposed design is developed for heterogeneous positive multi-agent systems. The main contributions of this paper include the following: (i) A positive observer is constructed to estimate the states of positive multi-agent systems; (ii) A novel observer-based proportional-integral-derivative protocol is designed to handle the consensus problem of positive multi-agent systems; and (iii) The presented conditions are solvable in terms of linear programming and the gain matrices can be constructed based on a matrix decomposition technology. Finally, two illustrative examples are provided to verify the effectiveness of the design.

Guaranteed root mean square estimates of linear matrix equations solutions under conditions of uncertainty

The article focuses on the linear estimation problems of unknown rectangular matrices, which are solutions of linear matrix equations with the right-hand sides belonging to bounded sets. The random errors of the observation vector have zero mathematical expectation, and the correlation matrix is unknown and belongs to one of two bounded sets. Explicit expressions of the guaranteed root mean square errors of estimates for linear operators acting from the space of rectangular matrices into some vector space are given. Guaranteed quasi-minimax root mean square errors of linear estimates are obtained. As the test examples, two options for solving the problem are considered, taking into account small perturbations of known observation matrices.

On Resolution Matrices

Solution appraisal, which has been realized on the basis of projections from the true medium to the solution, is an essential procedure in practical studies, especially in computer tomography. The projection operator in a linear problem or its linear approximation in a nonlinear problem is the resolution matrix for the solution (or model). Practical applications of a resolution matrix can be used to quantitatively retrieve the resolvability of the medium, the constrainability of the solution parameters, and the relationship between the solution and the factors in the study system. A given row vector of the matrix for a solution parameter can be used to quantify the resolvability, deviation from expectation, and difference between that solution parameter and its neighbor from the main-diagonal element, row-vector sum, and difference between neighboring elements in the row vector, respectively. The resolution length of a solution parameter should be estimated from the row vector, although it may be unreliable when the vector is unstable (e.g., due to errors). Comparatively, the resolution lengths that are estimated from the column vectors of the observation-constrained parameters are reliable in this instance. Previous studies have generally employed either the direct resolution matrix or the hybrid resolution matrix as the model resolution matrix. The direct resolution matrix and hybrid resolution matrix in an inversion with damping (or general Tikhonov regularization) are Gramian (e.g., symmetric). The hybrid resolution matrix in an inversion using zero-row-sum regularization matrices (e.g., higher-order Tikhonov regularizations) is one-row-sum but is not a stochastic matrix. When the two resolution matrices appear in iterative nonlinear inversions, they are not a projection of the solution, but rather the gradient of the projection or a projection of the solution improvement immediately after a given iteration. Regardless, their resultant resolution lengths in iterative nonlinear inversions of surface-wave dispersion remain similar to those from the projection of the solution. The solution is influenced by various factors in the study, but the direct resolution matrix is derived only from the observation matrix, whereas the hybrid resolution matrix is derived from the observation and regularization matrices. The limitations imply that the appropriateness using the two resolution matrices may be questionable in practical applications. Here we propose a new complete resolution matrix to overcome the limitations, in which all of the factors (e.g., errors) in linear or nonlinear (inverse or non-inverse) studies can be incorporated. Insights on all of the above are essential for ensuring a reliable and appropriate application of the resolution matrix to appraise the model/solution and understand the relationship between the solution and all of the factors in the study system, which is also important for improving the system.

Real-time robust generalized dynamic inversion based optimization control for coupled twin rotor MIMO system

This work is used to design a novel robust optimization control law augmented with Robust Generalized Dynamic Inversion (RGDI) for continuous varying perturbations in the Twin Rotor MIMO System (TRMS). The perturbations like coupling effect, un-known states, gyroscopic disturbance torque, parametric uncertainties and parametric disturbances are considered as unwanted signal which should be optimized by an efficient controller. The variable structured systems like the TRMS (prototype) have great focus due to its high computational cost with a higher order non-linear behavior. The RGDI based controller designed to remove nonlinear dynamics as well as to avoid singularity issue with the augmentation of stability based mathematical operations (lyapunov stability analysis, controllability and observability matrices ) in the presence of considered perturbations during implementation. In this paper, we develop estimation of state deviation calculation between control angles and desired angles known as Euclidean error norm. The next step was to design RGDI based controller [Sliding Mode Control (SMC) and {H_infty } optimization] to minimize considered perturbations as well as the computational cost. The sharp (rapid) chattering phenomena in RGDI based SMC reduce the actuators performance that goes towards the failure of actuators. While the RGDI based {H_infty } optimization overcome the computational cost and minimizes {H_infty } norm that’s guaranteeing the robust stability as well as robust performance. The robustness of the optimization control technique validated by taking its worst case via MATLAB-Simulation. A real-time implementation applied to evaluate the worth of novel dynamic approach.

TaxonWorks as a Tool for Managing Large Biodiversity Projects

Large systematic revisionary projects incorporating data for hundreds or thousands of taxa require an integrative approach, with a strong biodiversity-informatics core for efficient data management to facilitate research on the group. Our original biodiversity informatics platform, 3i (Internet-accessible Interactive Identification) combined a customized MS Access database backend with ASP-based web interfaces to support revisionary syntheses of several large genera of leafhopers (Hemiptera: Auchenorrhyncha: Cicadellidae). More recently, for our National Science Foundation sponsored project, “GoLife: Collaborative Research: Integrative genealogy, ecology and phenomics of deltocephaline leafhoppers (Hemiptera: Cicadellidae), and their microbial associates”, we selected the new open-source platform TaxonWorks as the cyberinfrastructure. In the scope of the project, the original “3i World Auchenorrhyncha Database” was imported into TaxonWorks. At the present time, TaxonWorks has many tools to automatically import nomenclature, citations, and specimen based collection data. At the time of the initial migration of the 3i database, many of those tools were still under development, and complexity of the data in the database required a custom migration script, which is still probably the most efficient solution for importing datasets with long development history. At the moment, the World Auchenorrhyncha Database comprehensively covers nomenclature of the group and includes data on 70 valid families, 6,816 valid genera, 47,064 valid species as well as synonymy and subsequent combinations (Fig. 1). In addition, many taxon records include the original citation, bibliography, type information, etymology, etc. The bibliography of the group includes 37,579 sources, about 1/3 of which are associated with PDF files. Species have distribution records, either derived from individual specimens or as country and state level asserted distribution, as well as biological associations indicating host plants, predators, and parasitoids. Observation matrices in TaxonWorks are designed to handle morphological data associated with taxa or specimens. The matrices may be used to automatically generate interactive identification keys and taxon descriptions. They can also be downloaded to be imported, for example, into Lucid builder, or to perform phylogenetic analysis using an external application. At the moment there are 36 matrices associated with the project. The observation matrix from GoLife project covers 798 taxa by 210 descriptors (most of which are qualitative multi-state morphological descriptors) (Fig. 2). Illustrations are provided for 9,886 taxa and organized in the specialized image matrix and could be used as a pictorial key for determination of species and taxa of a higher rank. For the phylogenetic analysis, a dataset was constructed for 730 terminal taxa and &amp;gt;160,000 nucleotide positions obtained using anchored hybrid enrichment of genomic DNA for a sample of leafhoppers from the subfamily Deltocephalinae and outgroups. The probe kit targets leafhopper genes, as well as some bacterial genes (endosymbionts and plant pathogens transmitted by leafhoppers). The maximum likelihood analyses of concatenated nucleotide and amino acid sequences as well as coalescent gene tree analysis yielded well-resolved phylogenetic trees (Cao et al. 2022). Raw sequence data have been uploaded to the Sequence Read Archive on GenBank. Occurrence and morphological data, as well as diagnostic images, for voucher specimens have been incorporated into TaxonWorks. Data in TaxonWorks could be exported in raw format, get accessed via Application Programming Interface (API), or be shared with external data aggregators like Catalogue of Life, GBIF, iDigBio.