When a mathematical model is not available for a dynamical system, it is reasonable to use a data-driven approach for analysis and control of the system. With this motivation, the authors have recently developed a data-driven solution to Lyapunov equations, which uses not the model but the data of several state trajectories of the system. However, the number of state trajectories to uniquely determine the solution is O(n2) for the dimension n of the system. This prevents us from applying the method to a case with a large n. Thus, this paper proposes a novel class of data-driven Lyapunov equations, which requires a smaller amount of data. Although the previous method constructs one scalar equation from one state trajectory, the proposed method constructs three scalar equations from any combination of two state trajectories. Based on this idea, we derive data-driven Lyapunov equations such that the number of state trajectories to uniquely determine the solution is O(n).

This review provides a current overview of the fabrication processes for superconducting digital circuits at CRAVITY (clean room for analog and digital superconductivity) at the National Institute of Advanced Industrial Science and Technology (AIST), Japan. CRAVITY routinely fabricates superconducting digital circuits using three types of fabrication processes and supplies several thousand chips to its collaborators each year. Researchers at CRAVITY have focused on improving the controllability and uniformity of device parameters and the reliability, which means reducing defects. These three aspects are important for the correct operation of large-scale digital circuits. The current technologies used at CRAVITY permit ±10% controllability over the critical current density (Jc) of Josephson junctions (JJs) with respect to the design values, while the critical current (Ic) uniformity is within 1σ=2% for JJs with areas exceeding 1.0 µm2 and the defect density is on the order of one defect for every 100,000 JJs.

Recently, the controllability of complex networks has become a hot topic in the field of network science, where the driver nodes play a key and central role. Therefore, studying their structural characteristics is of great significance to understand the underlying mechanism of network controllability. In this paper, we systematically investigate the nodal centrality of driver nodes in controlling complex networks, we find that the driver nodes tend to be low in-degree but high out-degree nodes, and most of driver nodes tend to have low betweenness centrality but relatively high closeness centrality. We also find that the tendencies of driver nodes towards eigenvector centrality and Katz centrality show very similar behaviors, both high eigenvector centrality and high Katz centrality are avoided by driver nodes. Finally, we find that the driver nodes towards PageRank centrality demonstrate a polarized distribution, i.e., the vast majority of driver nodes tend to be low PageRank nodes whereas only few driver nodes tend to be high PageRank nodes.

We address analysis and design problems of aggregate demand response systems composed of various consumers based on controllability to facilitate to design automated demand response machines that are installed into consumers to automatically respond to electricity price changes. To this end, we introduce a controllability index that expresses the worst-case error between the expected total electricity consumption and the electricity supply when the best electricity price is chosen. The analysis problem using the index considers how to maximize the controllability of the whole consumer group when the consumption characteristic of each consumer is not fixed. In contrast, the design problem considers the whole consumer group when the consumption characteristics of a part of the group are fixed. By solving the analysis problem, we first clarify how the controllability, average consumption characteristics of all consumers, and the number of selectable electricity prices are related. In particular, the minimum value of the controllability index is determined by the number of selectable electricity prices. Next, we prove that the design problem can be solved by a simple linear optimization. Numerical experiments demonstrate that our results are able to increase the controllability of the overall consumer group.

The paper studies controllability of an aggregate demand response system, i.e., the amount of the change of the total electric consumption in response to the change of the electric price, for real-time pricing (RTP). In order to quantify the controllability, this paper defines the controllability index as the lowest occurrence probability of the total electric consumption when the best possible the electric price is chosen. Then the paper formulates the problem which finds the consumer group maximizing the controllability index. The controllability problem becomes hard to solve as the number of consumers increases. To give a solution of the controllability problem, the article approximates the controllability index by the generalized central limit theorem. Using the approximated controllability index, the controllability problem can be reduced to a problem for solving nonlinear equations. Since the number of variables of the equations is independent of the number of consumers, an approximate solution of the controllability problem is obtained by numerically solving the equations.

The controllability of complex networks has attracted increasing attention within various scientific fields. Many power grids are complex networks with some common topological characteristics such as small-world and scale-free features. This Letter investigate the controllability of some real power grids in comparison with classical complex network models with the same number of nodes. Several conclusions are drawn after detailed analyses using several real power grids together with Erdös-Rényi (ER) random networks, Wattz-Strogatz (WS) small-world networks, Barabási-Albert (BA) scale-free networks and configuration model (CM) networks. The main conclusion is that most driver nodes of power grids are hub-free nodes with low nodal degree values of 1 or 2. The controllability of power grids is determined by degree distribution and heterogeneity, and power grids are harder to control than WS networks and CM networks while easier than BA networks. Some power grids are relatively difficult to control because they require a far higher ratio of driver nodes than ER networks, while other power grids are easier to control for they require a driver node ratio less than or equal to ER random networks.

We propose a scalable parallel interface that provides an ideal aggregated bandwidth link for an application. The scalable parallel interface uses time information to align packets and allows dynamic lane and/or path change, a large difference in transmission delays among lanes, and so on. The basic performance of the scalable parallel interface in 10 Gb/s 2 lanes is verified using an estimation board that is newly developed to evaluate the basic functions used in a Terabit LAN. The evaluation shows that the scalable parallel interface achieves a very low delay variation that is almost the same as that under back-to-back conditions. The difference in the delay variation between the scalable parallel interface and the back-to-back condition is approximately 10 ns when the transmission delay time varies from 10 µs to 1 s.

This paper proposes the Gramian-preserving frequency transformation for linear discrete-time state-space systems. In this frequency transformation, we replace each delay element of a discrete-time system with an allpass system that has a balanced realization. This approach can generate transformed systems that have the same controllability/observability Gramians as those of the original system. From this result, we show that the Gramian-preserving frequency transformation gives us transformed systems with different magnitude characteristics, but with the same structural property with respect to the Gramians as that of the original system. This paper also presents a simple method for realization of the Gramian-preserving frequency transformation. This method makes use of the cascaded normalized lattice structure of allpass systems.

This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under variable transformations with positive-real functions. That is, given a transfer function H(s) and its second-order modes, we analyze the second-order modes of transformed systems H(F(s)), where 1/F(s) is an arbitrary positive-real function. We first discuss the case of lossless positive-real transformations, and show that the second-order modes are invariant under any lossless positive-real transformation. We next consider the case of general positive-real transformations, and reveal that the values of the second-order modes are decreased under any general positive-real transformation. We achieve the derivation of these results by describing the controllability/observability Gramians of transformed systems, with the help of the lossless positive-real lemma, the positive-real lemma, and state-space formulation of transformed systems.

This paper proposes a notion of a controllability measure of discrete-time piecewise affine systems, which is a natural extension of the controllability gramian of linear systems. Although this measure is calculated in a probabilistic way, it may be applied to control of biological systems for providing a policy to experiments for pharmaceutical developments. Thus an application to gene regulatory control of luminescence in the marine bacterium modeled by the piecewise affine system is discussed in this paper.

This paper discusses the behavior of the second-order modes (Hankel singular values) of linear discrete-time systems under bounded-real transformations, where the transformations are given by arbitrary transfer functions with magnitude bounded by unity. Our main result reveals that the values of the second-order modes are decreased under any of the above-mentioned transformations. This result is the generalization of the theory of Mullis and Roberts, who proved that the second-order modes are invariant under any allpass transformation, i.e. any lossless bounded-real transformation. We derive our main result by describing the controllability/observability Gramians of transformed systems with the help of the discrete-time bounded-real lemma.

This paper presents a new analysis of power complementary filters using the state-space representation. Our analysis is based on the bounded-real Riccati equations that were developed in the field of control theory. Through this new state-space analysis of power complementary filters, we prove that the sum of the controllability/observability Gramians of a pair of power complementary filters is represented by a constant matrix, which is given as a solution to the bounded-real Riccati equations. This result shows that power complementary filters possess complementary properties with respect to the Gramians, as well as the magnitude responses of systems. Furthermore, we derive new theorems on a specific family of power complementary filters that are generated by a pair of invertible solutions to the bounded-real Riccati equations. These theorems show some interesting relationships of this family with respect to the Gramians, zeros, and coefficients of systems. Finally, we give a numerical example to demonstrate our results.

This paper discusses the behavior of the second-order modes (Hankel singular values) of linear continuous-time systems under typical frequency transformations, such as lowpass-lowpass, lowpass-highpass, lowpass-bandpass, and lowpass-bandstop transformations. Our main result establishes the fact that the second-order modes are invariant under any of these typical frequency transformations. This means that any transformed system that is generated from a prototype system has the same second-order modes as those of the prototype system. We achieve the derivation of this result by describing the state-space equations and the controllability/observability Gramians of transformed systems.

We study computation of a controllable sublanguage of a given non-prefix-closed regular specification language for an unbounded Petri net. We approximate the generated language of the unbounded Petri net by a regular language, and compute the supremal controllable sublanguage of the specification language with respect to the regular language approximation. This computed language is a controllable sublanguage with respect to the original generated language of the unbounded Petri net, but is not necessarily the supremal one. We then present a sufficient condition under which the computed sublanguage is the supremal controllable sublanguage with respect to the original generated language of the unbounded Petri net.

In this paper, we study supervisory control of a class of discrete event systems with simultaneous event occurrences, which we call concurrent discrete event systems. The behavior of the system is described by a language over the simultaneous event set. We introduce a notion of concurrent well-posedness of languages. We then prove that Lm(G)-closure, controllability, and concurrent well-posedness of a specification language are necessary and sufficient conditions for the existence of a nonblocking supervisor. We address the computational complexity for verifying the existence conditions.

The purpose of a testability analysis program is to estimate the difficulty of testing a fault. A good measurement can give an early warning about the testing problem so as to provide guidance in improving the testability of a circuit. There have been researches attempting to efficiently compute the testability analysis. Among those, the Controllability and Observability Procedure COP can calculate the testability value of a stuck-at fault efficiently in a tree-structured circuit but may be very inaccurate for a general circuit. The inaccuracy in COP is due to the ignorance of signal correlations. Recently, the algorithm of TAIR in [5] proposes a testability analysis algorithm, which starts from the result of COP and then gradually improves the result by applying a set of rules. The set of rules in TAIR can capture some signal correlations and therefore the results of TAIR are more accurate than COP. In this paper, we first prove that the rules in TAIR can be replaced by a closed-form formulation. Then, based on the closed-form formulation, we proposed two novel techniques to further improve the testability analysis results. Our experimental results have shown improvement over the results of TAIR.

The controllability and the stability of the blood clotting system are examined with the linear system analysis. The dynamic behavior of the clotting system consisting of a cascade of ten proteolytic reactions of the clotting factors with multiple positive feed back and feed forward loops is represented by the rate equations in a system of non linear ordinary differential equations with 35 variables. The time courses of concentration change in every factor are revealed by numerical integration of the rate equations. Linearization of the rate equations based on the dynamic behavior of the chemical species relevant to the nonlinear terms leads to the linear systems analysis of the clotting system to clarify the essential features of blood coagulation. It follows from the analysis that the clotting system is uncontrollable regardless of changes in any system parameters and control input and that all the chemical species of the system are uncontrollable so that the sequential reactions in the cascade proceed irreversibly, once they are activated. More over by the analysis of the eigen values, the clotting reaction as a total system was shown to be unstable which was insensitive to changes in the system parameters. These characteristic natures of clotting system must be derived in the sequential cascade reaction pattern and the inherent multiple positive feed back and feed forward regulation.