Controllability of Flow-Conservation Transportation Networks with Fractional-Order Dynamics

In this paper, we adapt the fractional derivative approach to formulate the flow-conservation transportation networks, which consider the propagation dynamics and the users’ behaviors in terms of route choices. We then investigate the controllability of the fractional-order transportation networks by employing the Popov-Belevitch-Hautus rank condition and the QR decomposition algorithm. Furthermore, we provide the exact solutions for the full controllability pricing controller location problem, which includes where to locate the controllers and how many controllers are required at the location positions. Finally, we illustrate two numerical examples to validate the theoretical analysis.

Control sets for bilinear and affine systems

For homogeneous bilinear control systems, the control sets are characterized using a Lie algebra rank condition for the induced systems on projective space. This is based on a classical Diophantine approximation result. For affine control systems, the control sets around the equilibria for constant controls are characterized with particular attention to the question when the control sets are unbounded.

Sparse nonnegative tensor decomposition using proximal algorithm and inexact block coordinate descent scheme

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.

Structure-Activity Relationships of the Imidazolium Compounds as Antibacterials of Staphylococcus aureus and Pseudomonas aeruginosa

This paper presents the results of structure–activity relationship (SAR) studies of 140 3,3’-(α,ω-dioxaalkan)bis(1-alkylimidazolium) chlorides. In the SAR analysis, the dominance-based rough set approach (DRSA) was used. For analyzed compounds, minimum inhibitory concentration (MIC) against strains of Staphylococcus aureus and Pseudomonas aeruginosa was determined. In order to perform the SAR analysis, a tabular information system was formed, in which tested compounds were described by means of condition attributes, characterizing the structure (substructure parameters and molecular descriptors) and their surface properties, and a decision attribute, classifying compounds with respect to values of MIC. DRSA allows to induce decision rules from data describing the compounds in terms of condition and decision attributes, and to rank condition attributes with respect to relevance using a Bayesian confirmation measure. Decision rules present the most important relationships between structure and surface properties of the compounds on one hand, and their antibacterial activity on the other hand. They also indicate directions of synthesizing more efficient antibacterial compounds. Moreover, the analysis showed differences in the application of various parameters for Gram-positive and Gram-negative strains, respectively.

Graphical Minimax Game and Off-Policy Reinforcement Learning for Heterogeneous MASs with Spanning Tree Condition

In this paper, the optimal consensus control problem is investigated for heterogeneous linear multi-agent systems (MASs) with spanning tree condition based on game theory and reinforcement learning. First, the graphical minimax game algebraic Riccati equation (ARE) is derived by converting the consensus problem into a zero-sum game problem between each agent and its neighbors. The asymptotic stability and minimax validation of the closed-loop systems are proved theoretically. Then, a data-driven off-policy reinforcement learning algorithm is proposed to online learn the optimal control policy without the information of the system dynamics. A certain rank condition is established to guarantee the convergence of the proposed algorithm to the unique solution of the ARE. Finally, the effectiveness of the proposed method is demonstrated through a numerical simulation.

Construction of LDPC convolutional codes via difference triangle sets

In this paper, a construction of $$(n,k,\delta )$$ ( n , k , δ ) LDPC convolutional codes over arbitrary finite fields, which generalizes the work of Robinson and Bernstein and the later work of Tong is provided. The sets of integers forming a (k, w)-(weak) difference triangle set are used as supports of some columns of the sliding parity-check matrix of an $$(n,k,\delta )$$ ( n , k , δ ) convolutional code, where $$n\in {\mathbb {N}}$$ n ∈ N , $$n>k$$ n > k . The parameters of the convolutional code are related to the parameters of the underlying difference triangle set. In particular, a relation between the free distance of the code and w is established as well as a relation between the degree of the code and the scope of the difference triangle set. Moreover, we show that some conditions on the weak difference triangle set ensure that the Tanner graph associated to the sliding parity-check matrix of the convolutional code is free from $$2\ell $$ 2 ℓ -cycles not satisfying the full rank condition over any finite field. Finally, we relax these conditions and provide a lower bound on the field size, depending on the parity of $$\ell $$ ℓ , that is sufficient to still avoid $$2\ell $$ 2 ℓ -cycles. This is important for improving the performance of a code and avoiding the presence of low-weight codewords and absorbing sets.

Global Structure of Determining Matrices for a Class of Differential Control Systems

This paper developed and established unprecedented global results on the structure of determining matrices of generic double time-delay linear autonomous functional differential control systems, with a view to obtaining the controllability matrix associated with the rank condition for the Euclidean controllability of the system. The computational process and implementation of the controllability matrix were demonstrated on the MATLAB platform to determine the controllability disposition of a small-problem instance. Finally, the work examined the computing complexity of the determining matrices.

Fundamental Results on Determining Matrices for a Certain Class of Hereditary Systems

Three major tools are required to investigate the controllability of control systems, namely, determining matrices, index of control systems and controllability Grammian. Determining matrices are the preferred choice for autonomous control systems due to the fact that they are devoid of integral operators in their computations. This article developed the structure of certain parameter-ordered determining matrices of generic double time-delay linear autonomous functional differential control systems, with a view to obtaining the controllability matrix associated with the rank condition for Euclidean controllability of the system. Expressions for the relevant determining matrices were formulated and it was established that the determining matrices for double time-delay linear autonomous functional differential control systems do not exist if one of the time-delays is not an integer multiple of the other paving the way for the investigation of the Euclidean controllability of generic double time-delay control systems.