2017/11/21 by Darío Pighín, Enrique Zuazua, Pighin, Dario +1 · 1 citation
Engineering · #35k51 #35k58 #49J99 #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1711.07678
openalex publication_date 2017/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In many practical applications of control theory some constraints on the\nstate and/or on the control need to be imposed.\n In this paper, we prove controllability results for semilinear parabolic\nequations under positivity constraints on the control, when the time horizon is\nlong enough. As we shall see, in fact, the minimal controllability time turns\nout to be strictly positive.\n More precisely, we prove a global steady state constrained controllability\nresult for a semilinear parabolic equation with C1 nonlinearity, without\nsign or globally Lipschitz assumptions on the nonlinear term. Then, under\nsuitable dissipativity assumptions on the system, we extend the result to any\ninitial datum and any target trajectory.\n We conclude with some numerical simulations that confirm the theoretical\nresults that provide further information of the sparse structure of constrained\ncontrols in minimal time.\n