2018/05/01 by Milad Siami, Alex Olshevsky, Siami, Milad +3 · 3 citations
Decision Sciences · Engineering · Physics and Astronomy · #Advanced Bandit Algorithms Research #Control Systems and Identification #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Model Reduction and Neural Networks #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1805.00606
openalex publication_date 2018/05/01 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
In this paper, we investigate the problem of actuator selection for linear\ndynamical systems. We develop a framework to design a sparse actuator schedule\nfor a given large-scale linear system with guaranteed performance bounds using\ndeterministic polynomial-time and randomized approximately linear-time\nalgorithms. First, we introduce systemic controllability metrics for linear\ndynamical systems that are monotone and homogeneous with respect to the\ncontrollability Gramian. We show that several popular and widely used\noptimization criteria in the literature belong to this class of controllability\nmetrics. Our main result is to provide a polynomial-time actuator schedule that\non average selects only a constant number of actuators at each time step,\nindependent of the dimension, to furnish a guaranteed approximation of the\ncontrollability metrics in comparison to when all actuators are in use. Our\nresults naturally apply to the dual problem of sensor selection, in which we\nprovide a guaranteed approximation to the observability Gramian. We illustrate\nthe effectiveness of our theoretical findings via several numerical simulations\nusing benchmark examples.\n