Sparsity based feedback design: A new paradigm in opportunistic sensing

We introduce the concept of using compressive sensing techniques to provide feedback in order to control dynamical systems. Compressive sensing algorithms use l₁-regularization for reconstructing data from a few measurement samples. These algorithms provide highly efficient reconstruction for sparse data. For data that is not sparse enough, the reconstruction technique produces a bounded error in the estimate. In a dynamical system, such erroneous state-estimation can lead to undesirable effects in the output of the plant. In this work, we present some techniques to overcome the aforementioned restriction. Our efforts fall into two main categories. First, we present some techniques to design feedback systems that sparsify the state in order to perfectly reconstruct it using compressive sensing algorithms. We study the effect of such sparsification schemes on the stability and regulation of the plant. Second, we study the characteristics of dynamical systems that produce sparse states so that compressive sensing techniques can be used for feedback in such scenarios without any additional modification in the feedback loop.