New Distributed Positioning Algorithm Based on Centroid of Circular Belt for Wireless Sensor Networks

This paper presents a new distributed positioning algorithm for unknown nodes in a wireless sensor network. The algorithm is based exclusively on connectivity. First, assuming that the positions of the anchor nodes are already known, a circular belt containing an unknown node is obtained using information about the anchor nodes that are in radio range of the unknown node, based on the geometric relationships and communication constraints among the unknown node and the anchor nodes. Then, the centroid of the circular belt is taken to be the estimated position of the unknown node. Since the algorithm is very simple and since the only communication needed is between the anchor nodes and the unknown node, the communication and computational loads are very small. Furthermore, the algorithm is robust because neither the failure of old unknown nodes nor the addition of new unknown nodes influences the positioning of unknown nodes to be located. A theoretical analysis and simulation results show that the algorithm does not produce any cumulative error and is insensitive to range error, and that a change in the number of sensor nodes does not affect the communication or computational load. These features make this algorithm suitable for all sizes of low-power wireless sensor networks.

A Fast LDL-factorization Approach for Large Sparse Positive Definite System and Its Application to One-to-one Marketing Optimization Computation

LDL-factorization is an efficient way of solving Ax = b for a large symmetric positive definite sparse matrix A. This paper presents a new method that further improves the efficiency of LDL-factorization. It is based on the theory of elimination trees for the factorization factor. It breaks the computations involved in LDL-factorization down into two stages： 1） the pattern of nonzero entries of the factor is predicted, and 2） the numerical values of the nonzero entries of the factor are computed. The factor is stored using the form of an elimination tree so as to reduce memory usage and avoid unnecessary numerical operations. The calculation results for some typical numerical examples demonstrate that this method provides a significantly higher calculation efficiency for the one-to-one marketing optimization algorithm.

Adaptive Equivalent-input-disturbance Approach to Improving Disturbance-rejection Performance

This paper presents an adaptive equivalent-input-disturbance(AEID)approach that contains a new adjustable gain to improve disturbance-rejection performance.A linear matrix inequality is derived to design the parameters of a control system.An adaptive law for the adjustable gain is presented based on the combination of the root locus method and Lyapunov stability theory to guarantee the stability of the AEID-based system.The adjustable gain is limited in an allowable range and the information for adjusting is obtained from the state of the system.Simulation results show that the method is effective and robust.A comparison with the conventional EID approach demonstrates the validity and superiority of the method.

Design of a Discrete-time Output-feedback Based Repetitive-control System

This paper deals with the problem of designing a robust discrete output-feedback based repetitive-control system for a class of linear plants with periodic uncertainties. The periodicity of the repetitive-control system is exploited to establish a two-dimensional （2D） model that converts the design problem into a robust stabilization problem for a discrete 2D system. By employing Lyapunov stability theory and the singular-value decomposition of the output matrix, a linear-matrix-inequality （LMI） based stability condition is derived. The condition can be used directly to design the gains of the repetitive controller. Two tuning parameters in the LMI enable the preferential adjustment of control and learning. A numerical example illustrates the design procedure and demonstrates the validity of the method.