Control Of Linear Dynamical Systems Using Sparse Inputs

In this work, we consider control of linear dynamical systems using sparse inputs. We provide an algorithm for determining a sequence of sparse inputs that will take the system from any given initial state to a desired final state, and stay in that state thereafter. We formulate this as a sparse vector recovery problem and obtain conditions on the sparse recovery algorithm that will enable the state of the system to be within an $\epsilon$ ball of the desired state. Further, we also give a computationally efficient test that checks whether it is possible to remain in a given desired state using only sparse inputs.