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This article investigates observability/controllability of a networked dynamic system (NDS) in which system matrices of its subsystems are expressed through linear fractional transformations (LFTs). Some relations have been obtained between this NDS and descriptor systems about their observability/controllability. A necessary and sufficient condition is established with the associated matrices depending affinely on subsystem parameters/connections. An attractive property of this condition is that all the required calculations are performed independently on each individual subsystem. Except well posedness, not any other conditions are asked for subsystem parameters/connections. This is in sharp contrast to recent results on structural observability/controllability, which is proven to be NP-hard. Some characteristics are established for a subsystem that are helpful in constructing an observable/controllable NDS. It has been made clear that subsystems with an input matrix of full column rank are helpful in constructing an observable NDS while subsystems with an output matrix of full row rank are helpful in constructing a controllable NDS. These results are extended to an NDS with descriptor form subsystems. As a byproduct, the full normal rank condition of previous works on network observability/controllability has been completely removed. On the other hand, satisfaction of this condition is shown to be appreciative in building an observable/controllability NDS.

In this article, the controllability and observability of a general networked dynamic system (NDS) are reinvestigated. While some computationally efficient conditions have been established in previous works, difficulties arise when a full normal rank condition is not satisfied for some subsystems. To address this problem, the subsystem connection topology of the NDS is utilized and a sufficient and necessary condition is derived for its controllability and observability in this article. It is observed that the effects of the transmission zeros and the uncontrollable/unobservable modes of subsystems should be eliminated by subsystem connections to guarantee the controllability/observability of an NDS. Moreover, a sufficient condition and a necessary condition are provided for constructing controllable/observable NDSs in the view of subsystem connection topology and subsystem internal input/output signal, respectively. Finally, the sensor placement of a mechanical system is discussed, which shows the effectiveness of our results.

This paper investigates the problem of fault estimation and fault tolerant control for a class of T-S fuzzy stochastic singular systems. An integral-type sliding surface based augmented singular sliding mode observer, which is applicable to both dual normalized and non-dual normalized singular systems, is constructed. It is shown that the restrictive rank condition and the equality constraint can be removed. Then a sufficient condition in terms of linear matrix inequalities is developed to guarantee the asymptotically mean square admissibility of the closed-loop systems such that the fault can be estimated and the open-loop system can be stabilized. Moreover, a new adaptive sliding mode controller is designed such that the reachability condition can be guaranteed. Finally, two examples are presented to verify the effectiveness of the proposed method.

This article studies the controllability degree via analyzing the condition number of Gramian matrix. Our aim is to explore how the network characteristics affect the controllability degree. Specifically, we prove that a large time parameter would worsen the controllability degree. The time parameter could be understood as the network coupling strength. For directed path networks, we derive how edge weights and time parameter jointly determine the best controllability degree. Furthermore, we prove that either adding a new edge or enhancing an existing edge weight appropriately would worsen the controllability degree. Moreover, through the numerical simulation of external inputs deployment, we find a significant statistical relationship between the controllability index and the controllability degree. In this article, the Gramian matrix reveals the importance of network characteristics that cannot be captured by classic Kalman rank condition or Popov–Belevitch–Hautus (PBH) test.

Nonnegative tensor decomposition is a versatile tool for multiway data analysis, by which the extracted components are nonnegative and usually sparse. Nevertheless, the sparsity is only a side effect and cannot be explicitly controlled without additional regularization. In this paper, we investigated the nonnegative CANDECOMP/PARAFAC (NCP) decomposition with the sparse regularization item using $$l_1$$ l 1 -norm (sparse NCP). When high sparsity is imposed, the factor matrices will contain more zero components and will not be of full column rank. Thus, the sparse NCP is prone to rank deficiency, and the algorithms of sparse NCP may not converge. In this paper, we proposed a novel model of sparse NCP with the proximal algorithm. The subproblems in the new model are strongly convex in the block coordinate descent (BCD) framework. Therefore, the new sparse NCP provides a full column rank condition and guarantees to converge to a stationary point. In addition, we proposed an inexact BCD scheme for sparse NCP, where each subproblem is updated multiple times to speed up the computation. In order to prove the effectiveness and efficiency of the sparse NCP with the proximal algorithm, we employed two optimization algorithms to solve the model, including inexact alternating nonnegative quadratic programming and inexact hierarchical alternating least squares. We evaluated the proposed sparse NCP methods by experiments on synthetic, real-world, small-scale, and large-scale tensor data. The experimental results demonstrate that our proposed algorithms can efficiently impose sparsity on factor matrices, extract meaningful sparse components, and outperform state-of-the-art methods.

In this paper, we consider families of linear systems (linear ensembles) defined by matrix pairs ( A ( θ ) , B ( θ ) ) depending on a parameter θ ∈ P that is varying over a compact subset P of the complex plane. In particular, we investigate the existence of open-loop controls which are independent of the parameter θ ∈ P and steer a given family of initial states x 0 ( θ ) arbitrarily close to a desired family of terminal states f ( θ ) in finite time. Here, the maps θ ↦ x 0 ( θ ) and θ ↦ f ( θ ) are assumed to lie in a common appropriately chosen Banach space X n ( P ) of C n -valued functions. If this task is solvable for all initial and terminal states, the pair ( A ( θ ) , B ( θ ) ) is called (completely) ensemble controllable with respect to X n ( P ) . Using a well-known infinite-dimensional version of the Kalman rank condition for systems on Banach spaces, we derive sufficient conditions for cascade and parallel connections of linear ensembles. Moreover, we prove an abstract decomposition theorem which results from a spectral splitting of the matrix family A ( θ ) . Based on these findings as well as on cyclicity conditions for multiplication operators and approximation theory, we obtain necessary and sufficient conditions for ensemble controllability (reachability) with respect to the space of continuous functions and the space of L q -functions. In the last section, results on averaged controllability (reachability) for linear families ( A ( θ ) , B ( θ ) , C ( θ ) ) are presented.

This paper focuses on fault detection and isolation (FDI) for a network of discrete-time multi-agent systems (MASs) with disturbances, in which a bank of finite-frequency H − / H ∞ unknown input observers (UIOs) are constructed. To detect the fault in one agent, the unknown input consisting of faults in the other agents and disturbances in the whole system can be partitioned into two parts, the decoupled part and the non-decoupled part, which avoids the constraint of the strict rank condition of UIO. To make the generated residual sensitive to the corresponding fault while robust against the non-decoupled unknown input, a finite-frequency H − / H ∞ UIO is proposed, of which the design conditions are transformed into a set of linear matrix inequalities (LMIs). A numerical simulation is conducted to illustrate the effectiveness of the proposed method.

Among the existing estimators of factor-augmented regressions, the CCE approach is the most popular. A major reason for this popularity is the simplicity and good small-sample performance of the approach, making it very attractive from an empirical point of view. The main drawback is that most of the available asymptotic theory is based on quite restrictive assumptions, such as that the common factor component should be independent of the regressors. The present paper can be seen as a reaction to this. The purpose is to study the asymptotic properties of the pooled CCE estimator under more realistic conditions. In particular, the common factor component may be correlated with the regressors, and the true number of common factors, r , can be larger than the number of estimated factors, which in CCE is given by k + 1 , where k is the number of regressors. The main conclusion is that while the estimator is generally consistent, asymptotic normality can fail when r > k + 1 .

This article proposes various sufficient controllability criteria for a class of networked higher dimensional systems under the influence of impulses exhibited by their state functions. The conditions obtained are characterised in terms of impulse matrices, inner coupling matrix, network topology and the system matrices. It is demonstrated that Kalman’s rank condition and Popov–Belevitch–Hautus (PBH)-rank condition are just sufficient conditions for the controllability of these systems, but not necessary unlike as that of the networked systems without impulses. Various numerical examples are provided to validate the theoretical results. Further, the control function and controlled trajectory are plotted for the systems considered, that helps to estimate the cost of controller.

The Liquid Composite Molding is a processing technique has the capability of manufacturing polymer composites with large size and complex shapes. A good control of process leads to improve the process performance hence the productivity and quality of manufactured parts and that requires knowing all or some process states, but it is often difficult to access these states. However, in many cases, due to cost considerations and physical constraints, the use of sensors is still very limited. In this paper, we overcame the need to use of mechanical sensors by using an observer. This paper proposes an observer for determine the observability for liquid composite molding process. The system observability is analysed by the rank condition, then a nonlinear state observer is designed using a Lyapunov theory and a linear matrix inequalities technique. The observer is formally shown that all variables converge to their true values. The effectiveness of the proposed scheme is demonstrated through computer simulations in the MATLAB/SIMULINK environment.

Lightweight materials in industrial applications have been mostly made of polymer matrix composites. Manufacturing process of composites still requires development to increase quality. Good control of the manufacturing process is very important for reducing injection time and ensuring product quality. Design of a control system is necessary to direct the flow of resin in the desired manner and to prevent the formation of voids during impregnation of resin. So, this paper proposes a derivative controller to achieve real-time and high stabilization precision of the resin transfer molding process. The manufacturing process controllability is analysed by the rank condition and the effectiveness of the proposed control scheme gives best performance to the system controllability.

We study joint nonlinear state estimation with multi-period measurement vectors that are potentially corrupted by sparse gross errors. We consider a nonlinear sparse optimization formulation for joint sparse error correction and robust state estimation in a nonlinear sensing system wherein we exploit the sparsity and short-term invariance properties of gross error locations. We introduce a sequential convex approximation approach that can be used to solve the nonlinear sparse optimization problem with a convergence guarantee. We derive a necessary rank condition that identifiable gross error matrix should satisfy. Then, we present an identifiability-aware version of the proposed algorithm wherein we exploit the aforementioned identifiability condition to improve the accuracy of gross error localization. We demonstrate the efficacy of the proposed approach by applying it to power system nonlinear state estimation of IEEE 14-bus and 118-bus networks.

This paper introduces a version of the interdependent value model of Milgrom and Weber (1982), where the signals are given by an index gathering signal shifters observed by the econometrician and private ones specific to each bidders. The model primitives are shown to be nonparametrically identified from first-price auction bids under a testable mild rank condition. Identification holds for all possible signal values. This allows to consider a wide range of counterfactuals where this is important, as expected revenue in second-price auction. An estimation procedure is briefly discussed.

Controllability of a complex network system is related to finding a set of minimum number of nodes, known as drivers, controlling which allows having a full control on the dynamics of the network. For some applications, only a portion of the network is required to be controlled, for which target control has been proposed. Often, along the controlling route from driver nodes to target nodes, some mediators (intermediate nodes) are also unwillingly controlled, which might cause various side effects. In controlling cancerous cells, unwillingly controlling healthy cells, might result in weakening them, thus affecting the immune system against cancer. This manuscript proposes a suitable candidate solution to the problem of finding minimum number of driver nodes under minimal mediators. Although many others have attempted to develop algorithms to find minimum number of drivers for target control, the newly proposed algorithm is the first one that is capable of achieving this goal and at the same time, keeping the number of the mediators to a minimum. The proposed controllability condition, based on path lengths between node pairs, meets Kalman's controllability rank condition and can be applied on directed networks. Our results show that the path length is a major determinant of in properties of the target control under minimal mediators. As the average path length becomes larger, the ratio of drivers to target nodes decreases and the ratio of mediators to targets increases. The proposed methodology has potential applications in biological networks. The source code of the algorithm and the networks that have been used are available from the following link: https://github.com/LBBSoft/Target-Control-with-Minimal-Mediators.git

We study the stabilizability of a class of abstract parabolic equations of the form $$\begin{aligned} u'(t)+Au(t)+p(t)Bu(t)=0,\qquad t\ge 0 \end{aligned}$$ u ′ ( t ) + A u ( t ) + p ( t ) B u ( t ) = 0 , t ≥ 0 where the control $$p(\cdot )$$ p ( · ) is a scalar function, A is a self-adjoint operator on a Hilbert space X that satisfies $$A\ge -\sigma I$$ A ≥ - σ I , with $$\sigma >0$$ σ > 0 , and B is a bounded linear operator on X. Denoting by $$\{\lambda _k\}_{k\in {\mathbb {N}}^*}$$ { λ k } k ∈ N ∗ and $$\{\varphi _k\}_{j\in {\mathbb {N}}^*}$$ { φ k } j ∈ N ∗ the eigenvalues and the eigenfunctions of A, we show that the above system is locally stabilizable to the eigensolutions $$\psi _j={\mathrm{e}}^{-\lambda _j t}\varphi _j$$ ψ j = e - λ j t φ j with doubly exponential rate of convergence, provided that the associated linearized system is null controllable. Moreover, we give sufficient conditions for the pair $$\{A,B\}$$ { A , B } to satisfy such a property, namely a gap condition for A and a rank condition for B in the direction $$\varphi _j$$ φ j . We give several applications of our result to different kinds of parabolic equations.

This paper proposes a new strategy for the identification of the marginal effects of an endogenous multivalued variable (which can be continuous, or a vector) in a model with an Instrumental Variable (IV) of lower dimension, which may even be a single binary variable, and multiple controls. Despite the failure of the classical order condition, we show that identification may be achieved by exploiting heterogeneity of the “first stage” in the controls through a new rank condition that we term covariance completeness. The identification strategy justifies the use of interactions between instruments and controls as additional exogenous variables and can be straightforwardly implemented by parametric, semiparametric, and nonparametric two-stage least squares estimators, following the same generic algorithm. Monte Carlo simulations show that the estimators have excellent performance in moderate sample sizes. Finally, we apply our methods to the problem of estimating the effect of air quality on house prices, based on Chay and Greenstone (2005, Journal of Political Economy 113, 376–424). All methods are implemented in a companion Stata software package.

For a given technique, the wage-rate of profit curve is linear in one-sector models. In multisector models, Wicksell effects appear and some paradoxes in capital theory are linked to the complex shape of the wage curve. We study the conditions ensuring the linearity of the curve for a bisector model and for models satisfying a specific rank condition.

Made available in DSpace on 2021-06-25T11:06:21Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-09-01 Necessary optimality conditions for optimal control problems with mixed state-control equality constraints are obtained. The necessary conditions are given in the form of a weak maximum principle and are obtained under (i) a new regularity condition for problems with mixed linear equality constraints and (ii) a constant rank type condition for the general non-linear case. Some instances of problems with equality and inequality constraints are also covered. Illustrative examples are presented. Department of Applied Mathematics State University of Campinas (Unicamp), Rua Sérgio Buarque de Holanda, N. 651 Department of Applied Mathematics São Paulo State University (Unesp), Rua Cristóvão Colombo, N. 2265 Department of Applied Mathematics São Paulo State University (Unesp), Rua Cristóvão Colombo, N. 2265

We study linear groups G for which for every g in G there exists a subgroup E of G satisfying some sort of rank condition and such that for every x in G there is a positive integer m such that for all n ≥ m the repeated commutator [x, ng] lies in E. If E can always be chosen to be a Chernikov group (resp. a polycyclic-by-finite group) such G can be completely described (Wehrfritz in Adv Group Theory Appl 7:143–157, 2019; Wehrfritz in Boll Unione Mat Ital, to appear). For more general rank conditions our analyses below are complete for positive characteristics but are less so for characteristic zero.

For a discrete-time linear system, we use data from an open-loop experiment to design directly a linear feedback controller enforcing that a given (polyhedral) set of the state is invariant and given (polyhedral) constraints on the control are satisfied. By building on classical results from model-based set invariance and a fundamental result from Willems et al., the controller designed from data has the following desirable features. The satisfaction of the above properties is guaranteed only from data, it can be assessed by solving a numerically-efficient linear program, and, under a certain rank condition, a data-based solution is feasible if and only if a model-based solution is feasible.

In this paper we study the null controllability of some non diagonalizable degenerate parabolic systems of PDEs, we assume that the diffusion, coupling and controls matrices are constant and we characterize the null controllability by an algebraic condition so called \textit{Kalman's rank} condition.

This paper investigates the assessment of Granger causality (GC) between jointly Gaussian signals based on noisy or filtered measurements. To do so, a recent rank condition for inferring GC between jointly Gaussian stochastic processes is exploited. Sufficient conditions are derived under which GC can be reliably inferred from the second order moments of the noisy or filtered measurements. This approach does not require a model of the underlying Gaussian system to be identified. The noise signals are not required to be Gaussian or independent, and the filters may be noncausal or nonminimum-phase, as long as they are stable.

A structure preserving QR algorithm is developed for a set of symplectic matrices with a certain rank condition. The algorithm is constructed based on a factorization presentation of a symplectic H...

This paper proposes a binary classifier to evaluate the rank condition (RC) thatis required for consistency of the Common Correlated Effects (CCE) estimator. The RC postulates that the number of unobserved factors, m, is not larger than the rank of the unobserved matrix of average factor loadings, r. The key insight in this paper is that r can be consistently estimated with existing techniques through the matrix of cross-sectional averages of the data. Similarly, m can be estimated consistently from the data using existing methods. A binary classifier, constructed by comparing estimates of m and r, correctly determines whether the RC is satisfied or not as N and T grow large. We illustrate the practical relevance of testing the RC by studying the effect of the Dodd-Frank Act on bank profitability.

This paper proposes a binary classifier to evaluate the rank condition (RC) thatis required for consistency of the Common Correlated Effects (CCE) estimator. The RC postulates that the number of unobserved factors, m, is not larger than the rank of the unobserved matrix of average factor loadings, r. The key insight in this paper is that r can be consistently estimated with existing techniques through the matrix of cross-sectional averages of the data. Similarly, m can be estimated consistently from the data using existing methods. A binary classifier, constructed by comparing estimates of m and r, correctly determines whether the RC is satisfied or not as N and T grow large. We illustrate the practical relevance of testing the RC by studying the effect of the Dodd-Frank Act on bank profitability.