# Optimal actuator design based on shape calculus

@article{Kalise2017OptimalAD, title={Optimal actuator design based on shape calculus}, author={Dante Kalise and Karl Kunisch and Kevin Sturm}, journal={Mathematical Models and Methods in Applied Sciences}, year={2017} }

An approach to optimal actuator design based on shape and topology optimization techniques is presented. For linear diffusion equations, two scenarios are considered. For the first one, best actuators are determined depending on a given initial condition. In the second scenario, optimal actuators are determined based on all initial conditions not exceeding a chosen norm. Shape and topological sensitivities of these cost functionals are determined. A numerical algorithm for optimal actuator…

## 20 Citations

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A method to aid the design of an actuator layout is developed that has a clear physical interpretation for the next-generation wafer scanners and numerical results seem to indicate that the designed actuator shapes might be unique.

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By using the Brunovsky normal form, this paper provides a reformulation of the problem consisting in finding the actuator design which minimizes the controllability cost for finite-dimensional linear systems with scalar controls and allows for an easy deduction of existence of solutions.

### A topological derivative-based algorithm to solve optimal control problems with $L^0(\Omega)$ control cost

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