Optimal control of communication in energy constrained sensor networks through team theory and Extended RItz Method

The Extended RItz Method (ERIM) can be used to face optimal decision and control problems when finding the global solution is hard, because the problem is ill-conditioned or we can only compute the solution via numerical approximations. It consists in constraining the control functions to take on a fixed structure with a certain number of free parameters to be optimized. We will show the use of such method for the solution of a communication problem in a mixed (analog/digital) transmission environment. A noisy channel is used to convey information from a limited-energy analog device to a sink; in the presence of a binary link, how can we reduce the energy spent for transmission without renouncing reconstruction capability and real-time encoding?

[1]  Franco Davoli Team decision theory and the control of a communication channel , 1984 .

[2]  T. Başar,et al.  Stochastic Teams with Nonclassical Information Revisited: When is an Affine Law Optimal? , 1986, 1986 American Control Conference.

[3]  Michael Gastpar,et al.  To code, or not to code: lossy source-channel communication revisited , 2003, IEEE Trans. Inf. Theory.

[4]  Y. Ho,et al.  Teams, signaling, and information theory , 1977, 1977 IEEE Conference on Decision and Control including the 16th Symposium on Adaptive Processes and A Special Symposium on Fuzzy Set Theory and Applications.

[5]  Harold J. Kushner,et al.  Stochastic Approximation Algorithms and Applications , 1997, Applications of Mathematics.

[6]  Amos Lapidoth,et al.  Superimposed Coded and Uncoded Transmissions of a Gaussian Source over the Gaussian Channel , 2006, 2006 IEEE International Symposium on Information Theory.

[7]  Bernard Widrow,et al.  Improving the learning speed of 2-layer neural networks by choosing initial values of the adaptive weights , 1990, 1990 IJCNN International Joint Conference on Neural Networks.

[8]  R. J. Pilc The optimum linear modulator for a Gaussian source used with a Gaussian channel , 1969 .

[9]  R. Radner,et al.  Economic theory of teams , 1972 .

[10]  Carlos S. Kubrusly,et al.  Stochastic approximation algorithms and applications , 1973, CDC 1973.

[11]  H. Witsenhausen A Counterexample in Stochastic Optimum Control , 1968 .

[12]  Marcello Sanguineti,et al.  Error Estimates for Approximate Optimization by the Extended Ritz Method , 2005, SIAM J. Optim..

[13]  Shlomo Shamai,et al.  Systematic Lossy Source/Channel Coding , 1998, IEEE Trans. Inf. Theory.

[14]  J. Spall,et al.  Stochastic optimization with inequality constraints using simultaneous perturbations and penalty functions , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[15]  M. Sanguineti,et al.  Approximating Networks and Extended Ritz Method for the Solution of Functional Optimization Problems , 2002 .

[16]  Thomas Parisini,et al.  Numerical solutions to the Witsenhausen counterexample by approximating networks , 2001, IEEE Trans. Autom. Control..