Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Control Systems

Control Systems

Control systems are everywhere in contemporary society, influencing diverse applications from aerospace to automated manufacturing. These systems can be found naturally within biological processes, such as blood sugar regulation and heart rate adjustment in response to stress, as well as in man-made systems like elevators and automated vehicles. A control system is essentially a network of subsystems and processes that collaboratively convert specific inputs into desired outputs.
At the heart...

Open and closed-loop control systems

Open and closed-loop control systems

Control systems are foundational elements in automation and engineering. They are broadly categorized into open-loop and closed-loop systems. These classifications hinge on the presence or absence of feedback mechanisms, significantly influencing the system's performance, complexity, and application.
An open-loop control system operates without feedback from the output. It consists of two primary elements: the controller and the controlled process. The controller receives an input signal...

Time-Domain Interpretation of PD Control

Time-Domain Interpretation of PD Control

Proportional-Derivative (PD) control is a widely used control method in various engineering systems to enhance stability and performance. In a system with only proportional control, common issues include high maximum overshoot and oscillation, observed in both the error signal and its rate of change. This behavior can be divided into three distinct phases: initial overshoot, subsequent undershoot, and gradual stabilization.
Consider the example of control of motor torque. Initially, a positive...

Feedback control systems

Feedback control systems

Feedback control systems are categorized in various ways based on their design, analysis, and signal types.
Linear feedback systems are theoretical models that simplify analysis and design. These systems operate under the principle that their output is directly proportional to their input within certain ranges. For instance, an amplifier in a control system behaves linearly as long as the input signal remains within a specific range. However, most physical systems exhibit inherent nonlinearity...

Conservation of Energy in Control Volume

Conservation of Energy in Control Volume

Consider a turbine operating under steady-flow conditions. The control volume is drawn around the turbine, with fluid entering at one point and exiting at another. The turbine extracts energy from the fluid, which performs mechanical work (shaft work).
For steady flow systems, the time derivative of the stored energy becomes zero since there is no energy accumulation within the control volume. This simplifies the energy equation to:

Conservation of Mass in Fixed, Nondeforming Control Volume

Conservation of Mass in Fixed, Nondeforming Control Volume

The principle of conservation of mass is fundamental in fluid dynamics and is crucial for analyzing flow within fixed control volumes, such as pipes or ducts. This principle states that the total mass within a control volume remains constant unless altered by the inflow or outflow of mass through the control surfaces. This results in a vital relationship for steady, incompressible flow where the mass entering a system equals the mass leaving it.
In the case of a sewer pipe, which can be modeled...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Mean Field Games and Ideal Free Distribution.

Journal of mathematical biology·2025

Same author

Minimization of peak stresses with the shape derivative.

Philosophical transactions. Series A, Mathematical, physical, and engineering sciences·2024

Same author

Fully and semi-automated shape differentiation in <b>NGSolve</b>.

Structural and multidisciplinary optimization : journal of the International Society for Structural and Multidisciplinary Optimization·2021

Same journal

Quadratic Sparse Domination and Weighted Estimates for Non-integral Square Functions.

Journal of geometric analysis·2026

Same journal

A Schwarz Lemma for the Pentablock.

Journal of geometric analysis·2026

Same journal

Flows of Conformally Coclosed <math><msub><mi>G</mi> <mn>2</mn></msub></math> -Structures with Dilaton.

Journal of geometric analysis·2026

Same journal

Kähler-Einstein Metrics.

Journal of geometric analysis·2026

Same journal

On Shape Optimization with Large Magnetic Fields in Two Dimensions.

Journal of geometric analysis·2026

Same journal

Families of proper holomorphic maps.

Journal of geometric analysis·2026

See all related articles

Search research articles

Related Experiment Video

Updated: Jul 29, 2025

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

The Topological State Derivative: An Optimal Control Perspective on Topology Optimisation.

Phillip Baumann¹, Idriss Mazari-Fouquer², Kevin Sturm¹

¹TU Wien, Wiedner Hauptstr. 8-10, 1040 Vienna, Austria.

Journal of Geometric Analysis

|May 19, 2023

Summary

This summary is machine-generated.

We introduce the topological state derivative for shape optimization, linking it to optimal control theory. This method offers a flexible approach for calculating topological derivatives for various shape changes.

Keywords:

Optimal control Shape optimisation Topological derivative Topology optimisation

More Related Videos

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

Published on: December 9, 2012

Generic Protocol for Optimization of Heterologous Protein Production Using Automated Microbioreactor Technology

Generic Protocol for Optimization of Heterologous Protein Production Using Automated Microbioreactor Technology

Published on: December 15, 2017

Related Experiment Videos

Last Updated: Jul 29, 2025

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control

Published on: August 15, 2020

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

Spatial Multiobjective Optimization of Agricultural Conservation Practices using a SWAT Model and an Evolutionary Algorithm

Published on: December 9, 2012

Generic Protocol for Optimization of Heterologous Protein Production Using Automated Microbioreactor Technology

Generic Protocol for Optimization of Heterologous Protein Production Using Automated Microbioreactor Technology

Published on: December 15, 2017

Area of Science:

Computational Mathematics
Optimal Control Theory
Shape Optimization

Background:

Standard optimal control theory often deals with fixed domains.
Topological derivatives are crucial for shape optimization problems.
Existing methods for topological derivatives can be limited in scope.

Purpose of the Study:

Introduce the topological state derivative for general topological dilatations.
Explore its connection to standard optimal control theory.
Provide a flexible framework for shape optimization.

Main Methods:

Differentiating shape-dependent state variables with respect to topology.
Linearizing systems similar to those in optimal control.
Utilizing Stampacchia-type regularity estimates and asymptotic expansions.
Handling general dilatations of shapes (curves, surfaces, hypersurfaces).

Main Results:

Established a link between topological state derivatives and optimal control.
Demonstrated that the topological state derivative can be computed using a linearized system.
Showed the flexibility of the approach for various shape perturbations.
Provided a method to compute first-order topological derivatives of shape functionals.

Conclusions:

The topological state derivative offers a unified and flexible approach to shape optimization.
It connects domain variations with optimal control principles.
The method accommodates complex shape changes beyond simple point perturbations.