Elliptic optimal control problems with L1-control cost and applications for the placement of control devices

Elliptic Optimal Control Problems with L-control Cost and Applications for the Placement of Control Devices

Elliptic optimal control problems with L-control cost are analyzed. Due to the nonsmooth objective functional the optimal controls are identically zero on large parts of the control domain. For applications, in which one cannot put control devices (or actuators) all over the control domain, this provides information about where it is most efficient to put them. We analyze structural properties ...

Shape-Measure Method for Solving Elliptic Optimal Shape Problems (Fixed Control Case)

Optimal Placement of Remote Control Switches in Radial Distribution Network for Reliability Improvement using Particle Swarm Optimization with Sine Cosine Acceleration Coefficients

Abstract: One of the equipment that can help improve distribution system status today and reduce the cost of fault time is remote control switches (RCS). Finding the optimal location and number of these switches in the distribution system can be modeled with various objective functions as a nonlinear optimization problem to improve system reliability and cost. In this article, a particle swarm ...

A Computational Method for Solving Optimal Control Problems and Their Applications

In order to obtain a solution to an optimal control problem‎, ‎a numerical technique based on state-control parameterization method is presented‎. ‎This method can be facilitated by the computation of performance index and state equation via approximating the control and state variable as a function of time‎. ‎Several numerical examples are presented to confirm the analytical findings and illus...

Optimality Conditions and Error Analysis of Semilinear Elliptic Control Problems with L Cost Functional∗

Abstract. Semilinear elliptic optimal control problems involving the L1 norm of the control in the objective are considered. Necessary and sufficient second-order optimality conditions are derived. A priori finite element error estimates for piecewise constant discretizations for the control and piecewise linear discretizations of the state are shown. Error estimates for the variational discret...