2024/06/12 by Behzad Azmi, Karl Kunisch, Azmi, Behzad +3
Computer Science · Engineering · #35Q93 #49M05 #93C05 #93C20 #93D20 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2406.07997
openalex publication_date 2024/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is shown that a switching control involving a finite number of Dirac delta actuators is able to steer the state of a general class of nonautonomous parabolic equations to zero as time increases to infinity. The strategy is based on a recent feedback stabilizability result, which utilizes control forces given by linear combinations of appropriately located Dirac delta distribution actuators. Then, the existence of a stabilizing switching control with no more than one actuator active at each time instant is established. For the implementation in practice, the stabilization problem is formulated as an infinite horizon optimal control problem, with cardinality-type control constraints enforcing the switching property. Subsequently, this problem is tackled using a receding horizon framework. Its suboptimality and stabilizabilizing properties are analyzed. Numerical simulations validate the approach, illustrating its stabilizing and switching properties.