Realization using the FM model for implementations in distributed grid sensor networks

Based on the Fornasini-Marchesini and Roesser local state space models, a method for distributed information processing in grid sensor networks is presented in [1], [4]. The method can be employed to implement linear systems in grid sensor networks. For a system described by either state space model to be implementable in real-time on a sensor network, when information originating in a node cannot be conveyed over the entire sensor network in a single time slot, the system matrices of the state space model have to satisfy particular conditions. This constraint limits the type of systems implementable, in real-time on sensor networks, using the method proposed in [1], [4]. Realizability of transfer matrices in the constrained Roesser model is discussed in [5]. The analogous problem for FM model based implementations is addressed in this paper. A necessary and sufficient condition for a proper transfer matrix to be realizable in the constrained FM model is established. A realization algorithm to derive a FM model that satisfies the desired condition, given an admissible transfer matrix is also derived in this paper. The analogues problem for the realization of non-proper transfer matrices is also addressed.

[1]  Donald D. Givone,et al.  Multidimensional Linear Iterative Circuits - General Properties , 1972, IEEE Trans. Computers.

[2]  M. Vetterli,et al.  Lattice sensor networks: capacity limits, optimal routing and robustness to failures , 2004, Third International Symposium on Information Processing in Sensor Networks, 2004. IPSN 2004.

[3]  Lorenzo Ntogramatzidis,et al.  On the Partial Realization of Noncausal 2-D Linear Systems , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  Spyros G. Tzafestas,et al.  A canonical state-space model for three-dimensional systems , 1984 .

[5]  Zhiping Lin,et al.  A Constructive Procedure for Three-Dimensional Realization , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[6]  N. Bose.  Multidimensional systems theory and applications , 1995 .

[7]  Ettore Fornasini,et al.  Doubly-indexed dynamical systems: State-space models and structural properties , 1978, Mathematical systems theory.

[8]  G. Marchesini,et al.  Dynamic regulation of 2D systems: A state-space approach , 1989 .

[9]  Peter H. Bauer,et al.  Realization using the Roesser model for implementations in distributed grid sensor networks , 2010, 49th IEEE Conference on Decision and Control (CDC).

[10]  Zhiping Lin,et al.  A New Constructive Procedure for 2-D Coprime Realization in Fornasini–Marchesini Model , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[11]  S. Sitharama Iyengar,et al.  Computing reliability and message delay for Cooperative wireless distributed sensor networks subject to random failures , 2005, IEEE Transactions on Reliability.

[12]  P. Paraskevopoulos,et al.  On the canonical state-space realisation of 3-D discrete systems , 1989 .

[13]  J. Mendel,et al.  Modeling and recursive state estimation for two-dimensional noncausal filters with applications in image restoration , 1987 .

[14]  Krzysztof Galkowski,et al.  State-space realisations of linear 2-D systems with extensions to the general nD (n>2) case , 2001 .

[15]  Sanjay Jha,et al.  A Communication Paradigm for Hybrid Sensor/Actuator Networks* , 2004, 2004 IEEE 15th International Symposium on Personal, Indoor and Mobile Radio Communications (IEEE Cat. No.04TH8754).

[16]  Peter H. Bauer,et al.  A novel approach to grid sensor networks , 2008, 2008 15th IEEE International Conference on Electronics, Circuits and Systems.

[17]  Zhiping Lin,et al.  On Realization of 2D Discrete Systems by Fornasini-Marchesini Model , 2005 .

[18]  R. Srikant,et al.  Unreliable sensor grids: coverage, connectivity and diameter , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[19]  Hossam S. Hassanein,et al.  A flow-based reliability measure for wireless sensor networks , 2007, Int. J. Sens. Networks.

[20]  Ki-Hyung Kim,et al.  Node-link-failure resilient routing architecture for sensor grids , 2006, 2006 8th International Conference Advanced Communication Technology.

[21]  Buddika Sumanasena,et al.  A Roesser model based multidimensional systems approach for grid sensor networks , 2010, 2010 Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers.

[22]  Hossam S. Hassanein,et al.  On the robustness of grid-based deployment in wireless sensor networks , 2006, IWCMC '06.

[23]  Mauro Leoncini,et al.  Analysis of a wireless sensor dropping problem in wide-area environmental monitoring , 2005, IPSN 2005. Fourth International Symposium on Information Processing in Sensor Networks, 2005..

[24]  C. Manikopoulos,et al.  State-space realization of three-dimensional systems using the modified Cauer form , 1990 .

[25]  Zhiping Lin,et al.  A direct-construction approach to multidimensional realization and LFR uncertainty modeling , 2008, Multidimens. Syst. Signal Process..