2017/10/03 by Drew Steeves, Steeves, Drew, Bahman Gharesifard +3
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1710.01397
openalex publication_date 2017/10/03 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
This work studies the null controllability of a system of coupled parabolic\nPDEs. In particular, our work specializes to an important subclass of these\ncontrol problems which are coupled by first and zero-order couplings and are,\nadditionally, underactuated. We pose our control problem in a fairly new\nframework which divides the problem into interconnected parts: we refer to the\nfirst part as the analytic control problem, where we use slightly non-classical\ntechniques to prove null controllability by means of internal controls\nappearing on every equation; we refer to the second part as the algebraic\ncontrol problem, where we use an algebraic method to invert a linear partial\ndifferential operator that describes our system; this allows us to recover null\ncontrollability by means of internal controls which appear on only a few of the\nequations. We establish a null controllability result for the original problem\nby solving these control problems concurrently.\n