Optimal control of fractional semilinear PDEs

Optimal Feedback Control of Fractional Semilinear Integro-differential Equations in The Banach Spaces

Recently, there has been significant development in the existence of mild solutions for fractional semilinear integro-differential equations but optimal control is not provided. The aim of this paper is studying optimal feedback control for fractional semilinear integro-differential equations in an arbitrary Banach space associated with operators ...

Distributed event-triggered control of diffusion semilinear PDEs

We introduce distributed event-triggered networked control of parabolic systems governed by semilinear diffusion PDEs. Sampled in time spatially distributed (either point or averaged) measurements are transmitted through a communication network to the controller only if a triggering condition is violated. We take into account quantization of the transmittedmeasurements and network-induced delay...

Optimal Control of Nonsmooth, Semilinear Parabolic Equations

This paper is concerned with an optimal control problem governed by a semilinear, nonsmooth operator differential equation. The nonlinearity is locally Lipschitz-continuous and directionally differentiable, but not Gâteaux-differentiable. Two types of necessary optimality conditions are derived, the first one by means of regularization, the second one by using the directional differentiability ...

Optimal Control of Semilinear Elliptic Obstacle Problems

Submodularity in Binary Optimal Control of PDEs

We show that in a large class of semilinear elliptic binary optimal control problems, the point-wise states are submodular functions in the control variables almost everywhere. Moreover, we discuss how to use this result in order to design global optimization algorithms for such problems. To our knowledge, this is the rst time submodularity is investigated in the context of optimal control.