A convex optimization approach to signal reconstruction over switching networks

In this paper we consider signal reconstruction over communication network channels that can be modeled as input switching systems. Such systems can be associated with a variety of applications including control and estimation over networks. In particular, we formulate the signal reconstruction problem as a prototypical model matching problem where the various mappings involved belong to a class of input switching systems. The design interest is placed on minimizing the worst case or stochastic average performance of this model matching system over all possible switchings with an H2H2 norm as the performance criterion. This minimization is performed over all stable receivers RR in the class of input switching systems. For the particular setup at hand, and in the case of matched switching, two convergent sequences to the optimal solution from above and below respectively are formulated in terms of quadratic programs. An approximate solution with any a priori   given precision is possible by finite truncation. Also, it is shown that in the cases of arbitrary, partially matched or unmatched switching, the optimal receiver RR need not depend on the switching sequence and that it can be obtained as a linear time-invariant solution to an associated H2H2 norm optimization.