Null controllability of some degenerate wave equations

This paper is devoted to a study of the null controllability problems for one-dimensional linear degenerate wave equations through a boundary controller. First, the well-posedness of linear degenerate wave equations is discussed. Then the null controllability of some degenerate wave equations is established, when a control acts on the non-degenerate boundary. Different from the known controllability results in the case that a control acts on the degenerate boundary, any initial value in state space is controllable in this case. Also, an explicit expression for the controllability time is given. Furthermore, a counterexample on the controllability is given for some other degenerate wave equations.     

Performance comparison of distributed state estimation algorithms for power systems

A newly proposed distributed dynamic state estimation algorithm based on the maximum a posteriori (MAP) technique is generalised and studied for power systems. The system model involves linear time-varying load dynamics and nonlinear measurements. The main contribution of this paper is to compare the performance and feasibility of this distributed algorithm with several existing distributed state estimation algorithms in the literature. Simulations are tested on the IEEE 39-bus and 118-bus systems under various operating conditions. The results show that this distributed algorithm performs better than distributed quasi-steady state estimation algorithms which do not use the load dynamic model. The results also show that the performance of this distributed method is very close to that by the centralized state estimation method. The merits of this algorithm over the centralized method lie in its low computational complexity and low communication load. Hence, the analysis supports the efficiency and benefits of the distributed algorithm in applications to large-scale power systems.     

Maximum likelihood estimator of the parameter for a continuous one-parameter exponential family under the optimal ranked set sampling

This paper studies a maximum likelihood estimator (MLE) of the parameter for a continuous one-parameter exponential family under ranked set sampling (RSS). The authors first find the optimal RSS according to the character of the family, viz, arrange the RSS based on quasi complete and sufficient statistic of independent and identically distributed (iid) samples. Then under this RSS, some sufficient conditions for the existence and uniqueness of the MLE, which are easily used in practice, are obtained. Using these conditions, the existence and uniqueness of the MLEs of the parameters for some usual distributions in this family are proved. Numerical simulations for these distributions fully support the result from the above two step optimizations of the sampling and the estimation method.     

Robust output regulation problem for discrete-time linear systems with both input and communication delays

Recently, the robust output regulation problem for continuous-time linear systems with both input and communication time-delays was studied. This paper will further present the results on the robust output regulation problem for discrete-time linear systems with input and communication delays. The motivation of this paper comes from two aspects. First, it is known that the solvability of the output regulation problem for linear systems is dictated by two matrix equations. While, for delay-free systems, these two matrix equations are same for both continuous-time systems and discrete-time systems, they are different for continuous-time time-delay systems and discrete-time time-delay systems. Second, the stabilization methods for continuous-time timedelay systems and discrete-time time-delay systems are also somehow different. Thus, an independent treatment of the robust output regulation problem for discrete-time time-delay systems will be useful and necessary.     

Some open problems related to creative telescoping

Creative telescoping is the method of choice for obtaining information about definite sums or integrals. It has been intensively studied since the early 1990s, and can now be considered as a classical technique in computer algebra. At the same time, it is still a subject of ongoing research. This paper presents a selection of open problems in this context. The authors would be curious to hear about any substantial progress on any of these problems.     

Generating semi-algebraic invariants for non-autonomous polynomial hybrid systems

Hybrid systems are dynamical systems with interacting discrete computation and continuous physical processes, which have become more common, more indispensable, and more complicated in our modern life. Particularly, many of them are safety-critical, and therefore are required to meet a critical safety standard. Invariant generation plays a central role in the verification and synthesis of hybrid systems. In the previous work, the fourth author and his coauthors gave a necessary and sufficient condition for a semi-algebraic set being an invariant of a polynomial autonomous dynamical system, which gave a confirmative answer to the open problem. In addition, based on which a complete algorithm for generating all semi-algebraic invariants of a given polynomial autonomous hybrid system with the given shape was proposed. This paper considers how to extend their work to non-autonomous dynamical and hybrid systems. Non-autonomous dynamical and hybrid systems are with inputs, which are very common in practice; in contrast, autonomous ones are without inputs. Furthermore, the authors present a sound and complete algorithm to verify semi-algebraic invariants for non-autonomous polynomial hybrid systems. Based on which, the authors propose a sound and complete algorithm to generate all invariants with a pre-defined template.     

Dual hesitant fuzzy information aggregation with Einstein t-conorm and t-norm

Dual hesitant fuzzy set (DHFS) is a new generalization of fuzzy set (FS) consisting of two parts (i.e., the membership hesitancy function and the non-membership hesitancy function), which confronts several different possible values indicating the epistemic degrees whether certainty or uncertainty. It encompasses fuzzy set (FS), intuitionistic fuzzy set (IFS), and hesitant fuzzy set (HFS) so that it can handle uncertain information more flexibly in the process of decision making. In this paper, we propose some new operations on dual hesitant fuzzy sets based on Einstein t-conorm and t-norm, study their properties and relationships and then give some dual hesitant fuzzy aggregation operators, which can be considered as the generalizations of some existing ones under fuzzy, intuitionistic fuzzy and hesitant fuzzy environments. Finally, a decision making algorithm under dual hesitant fuzzy environment is given based on the proposed aggregation operators and a numerical example is used to demonstrate the effectiveness of the method.     

Adaptive Event-Based Consensus of Multi-Agent Systems with General Linear Dynamics

In this paper, adaptive event-based consensus of multi-agent systems with general linear dynamics is considered. A novel adaptive event-based controller and a state-dependent triggering function are proposed for each agent. The consensus can be achieved without the assumption that (A,B) is stabilizable. Furthermore, the Zeno-behavior of the concerned closed-loop system is also excluded under certain conditions. Finally, a numerical simulation example is presented to show the effectiveness of the theoretical results.     

An Economic Model-Based Matching Approach Between Buyers and Sellers Through a Broker in an Open E-Marketplace

A broker in an open e-marketplace enables buyers and sellers to do business with each other. Although a broker plays an important role in e-marketplaces, theory and guidelines for matching between buyers and sellers in multi-attribute exchanges are limited. Therefore, a challenge for a broker’s responsibility is how to maximize a buyer’s total satisfaction degree as its goals under the consideration of trade-off between a buyer’s buying quantity and price paid to a seller, and other attributes. To solve this challenge, this paper proposes an economic model-based matching approach between a buyer’s requirements and a seller’s offers. The major contributions of this paper are that (i) a broker can model a seller’s price policy as per a buyer’s buying quantity through communication between a broker and a seller; (ii) due to each buyer’s different quantity demand, a broker models a buyer’s satisfaction degree as per a buyer’s buying quantity based on communication between a broker and a buyer; and (iii) to carry out a broker’s matching processes, an objective function and a set of constraints are generated to help a broker to maximize a buyer’s total satisfaction degree. Experimental results demonstrate the good performance of the proposed approach.     

Film Use to Promote Understanding in Change and Diffusion of Innovation

The paper explores cinematic films as a pedagogical tool to promote critical thinking and student discussions in a doctoral-level learning, design, and technology seminar course at a major U.S. research university. These discussions focused on systemic change and systemic thinking concepts. The authors offer evidence from the literature that supports films’ power as a visual metaphor and neurocognitive stimulator to promote development of new perspectives in graduate students on case studies through articulation, reflection, and explanation of their thought processes on change and diffusion of innovation. There are theoretical, political, social, and technological issues that create tensions during any systemic change effort. The goal of using film in this seminar is to equip students with the requisite skills, theoretical frameworks, and interpersonal experiences needed to address these issues within organizations and communities. The change expected from systemic thinking is for students to think more deeply about the interconnectedness of systems and the importance of bottom-up change efforts that consider the perspective of all stakeholders.