Volumen 30 (2020): Heft 4 (December 2020)

This work develops a technique for constructing a reduced-order system that not only has low computational complexity, but also maintains the stability of the original nonlinear dynamical system. The proposed framework is designed to preserve the contractivity of the vector field in the original system, which can further guarantee stability preservation, as well as provide an error bound for the approximated equilibrium solution of the resulting reduced system. This technique employs a low-dimensional basis from proper orthogonal decomposition to optimally capture the dominant dynamics of the original system, and modifies the discrete empirical interpolation method by enforcing certain structure for the nonlinear approximation. The efficiency and accuracy of the proposed method are illustrated through numerical tests on a nonlinear reaction diffusion problem.

This paper presents an abstraction-based technique to solve the problem of distributed controller design enforcing persistency specifications for interconnected systems. For each subsystem, controller synthesis is based on local distributed sensor information from other subsystems. An effective method is presented for quantification of such partial information in an abstraction in terms of level sets of Lyapunov-like ranking functions. The results are illustrated on a laboratory hydraulic system.

Descriptor and standard linear continuous-time systems with different fractional orders are investigated. Descriptor systems are analyzed making use of the Drazin matrix inverse. Necessary and sufficient conditions for the pointwise completeness and pointwise degeneracy of descriptor continuous-time linear systems with different fractional orders are derived. It is shown that (i) the descriptor linear continuous-time system with different fractional orders is pointwise complete if and only if the initial and final states belong to the same subspace, (ii) the descriptor linear continuous-time system with different fractional orders is not pointwise degenerated in any nonzero direction for all nonzero initial conditions. Results are reported for the case of two different fractional orders and can be extended to any number of orders.

In this paper, a stability analysis of interconnected discrete-time fractional-order (FO) linear time-invariant (LTI) state-space systems is presented. A new system is formed by interconnecting given FO systems using cascade, feedback, parallel interconnections. The stability requirement for such a system is that all zeros of a non-polynomial characteristic equation must be within the unit circle on the complex z-plane. The obtained theoretical results lead to a numerical test for stability evaluation of interconnected FO systems. It is based on modern root-finding techniques on the complex plane employing triangulation of the unit circle and Cauchy’s argument principle. The developed numerical test is simple, intuitive and can be applied to a variety of systems. Furthermore, because it evaluates the function related to the characteristic equation on the complex plane, it does not require computation of state-matrix eigenvalues. The obtained numerical results confirm the efficiency of the developed test for the stability analysis of interconnected discrete-time FO LTI state-space systems.

A simple computational algorithm is proposed for minimizing sums of largest eigenvalues of the matrix inverse over the set of all convex combinations of a finite number of nonnegative definite matrices subject to additional box constraints on the weights of those combinations. Such problems arise when experimental designs aiming at minimizing sums of largest asymptotic variances of the least-squares estimators are sought and the design region consists of finitely many support points, subject to the additional constraints that the corresponding design weights are to remain within certain limits. The underlying idea is to apply the method of outer approximations for solving the associated convex semi-infinite programming problem, which reduces to solving a sequence of finite min-max problems. A key novelty here is that solutions to the latter are found using generalized simplicial decomposition, which is a recent extension of the classical simplicial decomposition to nondifferentiable optimization. Thereby, the dimensionality of the design problem is drastically reduced. The use of the algorithm is illustrated by an example involving optimal sensor node activation in a large sensor network collecting measurements for parameter estimation of a spatiotemporal process.

The paper is devoted to the problem of increasing the efficiency of underwater vehicles by using a fault diagnosis system for their thrusters which provides detection, isolation, and identification of minor faults. To address the problem, a two-stage method is proposed. At the first stage, a bank of diagnostic observers is designed to detect and isolate the emerging faults. Each observer in this bank is constructed to be sensitive to some set of faults and insensitive to others. At the second stage, additional observers working in sliding mode are synthesized in order to accurately estimate the error value in the signal obtained from the angular velocity sensor and to estimate deviations of the thruster parameters from their nominal values due to the faults. In contrast to the existing solutions, reduced-order (i.e., lower-dimensional) models of the original system are proposed as a basis to construct sliding mode observers. This approach permits reduction of the complexity of the obtained observers in comparison with the known methods, where full-order observers are constructed. The simulation results show the efficiency and high quality of all synthesized observers. In all cases considered, it was possible to detect typical faults, as well as estimate their values.

The topologies of protein-protein interaction networks are uncertain and noisy. The network topology determines the reliability of computational knowledge acquired from noisy networks and can impose the deterministic and non-deterministic character of the resulting data. In this study, we analyze the effect of the network topology on Lyapunov exponents and its relationship with network stability. We define the methodology to convert the network data into signal data and obtain the Lyapunov exponents for a variety of networks. We then compare the Lyapunov exponent response and the stability results. Our technique can be applied to all types of network topologies as demonstrated with our experiments, conducted on both synthetic and real networks from public databases. For the first time, this article presents findings where Lyapunov exponents are evaluated under topological mutations and used for network analysis. Experimental results show that Lyapunov exponents have a strong correlation with network stability and both are correlatively affected by the network model. Hence we develop a novel coefficient, termed LEC, to measure the robustness of biological networks. LEC can be applied to real or synthetic biological networks rapidly. Results are a striking indication that the Lyapunov exponent is a potential candidate measure for network analysis.

This paper poses the question of whether or not the usage of the kernel trick is justified. We investigate it for the special case of its usage in the kernel k-means algorithm. Kernel-k-means is a clustering algorithm, allowing clustering data in a similar way to k-means when an embedding of data points into Euclidean space is not provided and instead a matrix of “distances” (dissimilarities) or similarities is available. The kernel trick allows us to by-pass the need of finding an embedding into Euclidean space. We show that the algorithm returns wrong results if the embedding actually does not exist. This means that the embedding must be found prior to the usage of the algorithm. If it is found, then the kernel trick is pointless. If it is not found, the distance matrix needs to be repaired. But the reparation methods require the construction of an embedding, which first makes the kernel trick pointless, because it is not needed, and second, the kernel-k-means may return different clusterings prior to repairing and after repairing so that the value of the clustering is questioned. In the paper, we identify a distance repairing method that produces the same clustering prior to its application and afterwards and does not need to be performed explicitly, so that the embedding does not need to be constructed explicitly. This renders the kernel trick applicable for kernel-k-means.

Fast discovering of various relationships in data is an important feature of modern data mining, cognitive, knowledge-based, and explainable AI systems, including deep neural networks. The ability to represent a rich set of relationships between stored data and objects is essential for fast inferences, finding associations, representing knowledge, and extracting useful patterns or other pieces of information. This paper introduces self-balancing, aggregating, and sorting ASA-graphs for efficient data representation in various data structures, databases, and data mining systems. These graphs are smaller and use more efficient algorithms for searching, inserting, and removing data than the most commonly used self-balancing trees. ASA-graphs also automatically aggregate and count all duplicates of values and represent them by the same nodes, connecting them in order, and simultaneously providing very fast data access based on a binary search tree approach. The proposed ASA-graph structure combines the advantages of sorted lists, binary search trees, B-trees, and B+trees, eliminating their weaknesses. Our experiments proved that the ASA-graphs outperform many commonly used self-balancing trees.

We discuss a quantum circuit construction designed for classification. The circuit is built of regularly placed elementary quantum gates, which implies the simplicity of the presented solution. The realization of the classification task is possible after the procedure of supervised learning which constitutes parameter optimization of Pauli gates. The process of learning can be performed by a physical quantum machine but also by simulation of quantum computation on a classical computer. The parameters of Pauli gates are selected by calculating changes in the gradient for different sets of these parameters. The proposed solution was successfully tested in binary classification and estimation of basic non-linear function values, e.g., the sine, the cosine, and the tangent. In both the cases, the circuit construction uses one or more identical unitary operations, and contains only two qubits and three quantum gates. This simplicity is a great advantage because it enables the practical implementation on quantum machines easily accessible in the nearest future.

Practically, any digital system includes sequential blocks represented using a model of finite state machine (FSM). It is very important to improve such FSM characteristics as the number of logic elements used, operating frequency and consumed energy. The paper proposes a novel technology-dependent design method targeting a decrease in the number of look-up table (LUT) elements and their levels in logic circuits of FPGA-based Mealy FSMs. It produces FSM circuits having three levels of logic blocks. Also, it produces circuits with regular systems of interconnections between the levels of logic. The method is based on dividing the set of internal states into two subsets. Each subset corresponds to a unique part of an FSM circuit. Only a single LUT is required for implementing each function generated by the first part of the circuit. The second part is represented by a multi-level circuit. The proposed method belongs to the group of two-fold state assignment methods. Each internal state is encoded as an element of the set of states and as an element of some of its subsets. A binary state assignment is used for states corresponding to the first part of the FSM circuit. The one-hot assignment is used for states corresponding to the second part. An example of FSM synthesis with the proposed method is shown. The experiments with standard benchmarks are conducted to analyze the efficiency of the proposed method. The results of experiments show that the proposed approach leads to diminishing the number of LUTs in the circuits of rather complex Mealy FSMs having more than 15 internal states. The positive property of this method is a reduction in energy consumption (without any overhead cost) and an increase in operating frequency compared with other investigated methods.

Regularity in musical structure is experienced as a strongly structured texture with repeated and periodic patterns, with the musical ideas presented in an appreciable shape to the human mind. We recently showed that manipulation of musical content (i.e., deviation of musical structure) affects the perception of music. These deviations were detected by musical experts, and the musical pieces containing them were labelled as irregular. In this study, we replace the human expert involved in detection of (ir)regularity with artificial intelligence algorithms. We evaluated eight variables measuring entropy and information content, which can be analysed for each musical piece using the computational model called Information Dynamics of Music and different viewpoints. The algorithm was tested using 160 musical excerpts. A preliminary statistical analysis indicated that three of the eight variables were significant predictors of regularity (E cpitch, IC cpintfref, and E cpintfref). Additionally, we observed linear separation between regular and irregular excerpts; therefore, we employed support vector machine and artificial neural network (ANN) algorithms with a linear kernel and a linear activation function, respectively, to predict regularity. The final algorithms were capable of predicting regularity with an accuracy ranging from 89% for the ANN algorithm using only the most significant predictor to 100% for the ANN algorithm using all eight prediction variables.