Recovery of Sparse Inputs to Over-actuated Linear Systems
Year: 2014
Type: preprint
Abstract: This paper considers the recovery of sparse control inputs to an overactuated linear system, i.e., one in which the number of inputs greatly outnumbers the number of states. Such a system is relevant for certain models of biological systems such as neuronal networks. In general, the overactuated formulation leads to an underdetermined recovery problem, such that it is impossible to exactly infer the system inputs based on state observation alone. We show, however, that under assumptions of input sparsity, it is possible to perform exact and stable recovery over a finite time-horizon and develop an error bound for the reconstructed control input. The solution methodology involves l1-based regularization, commonplace is sparse recovery problems, but here extended to the case of a linear dynamical system evolving over a time horizon. Simulation results are presented to verify the solution and performance bounds.
Source: arXiv (Cornell University)
Language: English
Subfield: Computational Mechanics
Field: Engineering
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2216607366