2024/01/20 by Reis, Timo, Schaller, Manuel · 2 citations
#49J20 #49K27 #49N10 #93C25 #FOS: Mathematics #Functional Analysis (math.FA) #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2401.11302
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value is prescribed, we are minimizing over all inputs within a specified convex subset of square integrable controls with values in a Hilbert space. The considered class of infinite-dimensional systems is based on the system node formulation. Thus, our developed approach includes optimal control of a wide variety of linear partial differential equations with boundary control and observation that are not well-posed in the sense that the output continuously depends on the input and the initial value. We provide an application of particular optimal control problems arising in energy-optimal control of port-Hamiltonian systems. Last, we illustrate the our abstract theory by two examples including a non-well-posed heat equation with Dirichlet boundary control and a wave equation on an L-shaped domain with boundary control of the stress in normal direction.