Li Qiu

Keyou You, Roberto Tempo, Li Qiu

This paper is concerned with distributed computation of several commonly used centrality measures in complex networks. In particular, we propose deterministic algorithms, which converge in finite time, for the distributed computation of the degree, closeness and betweenness centrality measures in directed graphs. Regarding eigenvector centrality, we consider the PageRank problem as its typical variant, and design distributed randomized algorithms to compute PageRank for both fixed and time-varying graphs. A key feature of the proposed algorithms is that they do not require to know the network size, which can be simultaneously estimated at every node, and that they are clock-free. To address the PageRank problem of time-varying graphs, we introduce the novel concept of persistent graph, which eliminates the effect of spamming nodes. Moreover, we prove that these algorithms converge almost surely and in the sense of $L^p$. Finally, the effectiveness of the proposed algorithms is illustrated via extensive simulations using a classical benchmark.

Wei Chen, Songbai Wang, Li Qiu

In this paper, we initiate the study of networked stabilization via a MIMO communication scheme between the controller and the plant. Specifically, the communication system is modeled as a MIMO transceiver, which consists of three parts: an encoder, a MIMO channel, and a decoder. In the spirit of MIMO communication, the number of SISO subchannels in the transceiver is often greater than the number of data streams to be transmitted. Moreover, the subchannel capacities are assumed to be fixed a priori. In this case, the encoder/decoder pair gives an additional design freedom on top of the controller, leading to a stabilization problem via coding/control co-design. It turns out that how to take the best advantage of the coding mechanism is quite crucial. From a demand/supply perspective, the design of the coding mechanism boils down to reshaping the demands for communication resource from different control inputs to match the given supplies. We study the problem for the case of AWGN subchannels and fading subchannels, respectively. In both cases, we arrive at a unified necessary and sufficient condition on the capacities of the subchannels under which the coding/control co-design problem is solvable. The condition is given in terms of a majorization type relation. As we go along, systematic procedures are also put forward to implement the coding/control co-design. A numerical example is presented to illustrate our results.

Di Zhao, Sei Zhen Khong, Li Qiu

A networked control system (NCS) consisting of cascaded two-port communication channels between the plant and controller is modeled and analyzed. Towards this end, the robust stability of a standard closed-loop system in the presence of conelike perturbations on the system graphs is investigated. The underlying geometric insights are then exploited to analyze the two-port NCS. It is shown that the robust stability of the two-port NCS can be guaranteed when the nonlinear uncertainties in the transmission matrices are sufficiently small in norm. The stability condition, given in the form of "arcsin" of the uncertainty bounds, is both necessary and sufficient.

Yanfang Mo, Wei Chen, Sei Zhen Khong et al.

Efficient resource allocation is one of the main driving forces of human civilizations. Of the many existing approaches to resource allocation, matrix completion is one that is frequently applied. In this paper, we investigate a special type of matrix completion problem concerning the class of $(0,1)$-matrices with given row/column sums and certain zeros prespecified. We provide a necessary and sufficient condition under which such a class is nonempty. The condition is stated in the form of the nonnegativity of a structure tensor constructed from the information regarding the given row/column sums and fixed zeros. Moreover, we show that a more general matrix completion problem can be studied in a similar manner, namely that involving the class of nonnegative integer matrices with prescribed row/column sums, predetermined zeros, and different bounds across the rows. To illustrate the utility of our results, we apply them to demand response applications in smart grids. Specifically, we address two adequacy problems in differentiated energy services, namely, the problems of supply/demand matching and minimum purchase profile.

Wei Chen, Dan Wang, Sei Zhen Khong et al.

In this paper, we introduce a definition of phase response for a class of multi-input multi-output (MIMO) linear time-invariant (LTI) systems, the frequency responses of which are cramped at all frequencies. This phase concept generalizes the notions of positive realness and negative imaginariness. We also define the half-cramped systems and provide a time-domain interpretation. As a starting point in an endeavour to develop a comprehensive phase theory for MIMO systems, we establish a small phase theorem for feedback stability, which complements the well-known small gain theorem. In addition, we derive a sectored real lemma for phase-bounded systems as a natural counterpart of the bounded real lemma.