Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

387
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
387
Differential Equations: Problem Solving01:21

Differential Equations: Problem Solving

102
When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...
102
Linear Differential Equations01:27

Linear Differential Equations

129
The integrating factor method provides a systematic way to solve first-order linear differential equations, especially those that cannot be handled by separation of variables. This method is particularly useful in modeling time-dependent physical systems influenced by both constant inputs and resistive forces. A common example is the motion of a car subjected to a constant engine force while experiencing air resistance proportional to its velocity.In such scenarios, Newton’s second law...
129
Area Problem01:26

Area Problem

150
Determining the area of a region with straight edges is straightforward, as geometric formulas for rectangles, triangles, and polygons can be applied directly. However, traditional geometric methods are insufficient when a region has a curved boundary, such as the area under a function.fromThe area problem involves finding a systematic way to measure such regions. One approach to solving this problem is through approximation. Instead of attempting to compute the area exactly at the outset, the...
150
Separable Differential Equations01:20

Separable Differential Equations

173
A separable differential equation is a type of first-order differential equation where the derivative dy/dx can be expressed as a product of two functions: one that depends only on x and another that depends only on y. This allows for the rearrangement of the equation so that all terms involving y are on one side, and all terms involving x are on the other. This process, known as the separation of variables, simplifies the process of solving the equation by enabling the integration of both...
173
Time-Domain Interpretation of PD Control01:07

Time-Domain Interpretation of PD Control

426
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...
426

You might also read

Related Articles

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

Sort by
Same author

Safe Optimal Control Framework for Cooperative Manipulation of Objects in Human-Robot Teams.

IEEE transactions on cybernetics·2026
Same author

Lifelong Learning-Based Optimal Trajectory Tracking Control of Constrained Nonlinear Affine Systems Using Deep Neural Networks.

IEEE transactions on cybernetics·2024
Same author

Optimal Adaptive Tracking Control of Partially Uncertain Nonlinear Discrete-Time Systems Using Lifelong Hybrid Learning.

IEEE transactions on neural networks and learning systems·2023
Same author

Cooperative Deep Q-Learning Framework for Environments Providing Image Feedback.

IEEE transactions on neural networks and learning systems·2023
Same author

QC_SANE: Robust Control in DRL Using Quantile Critic With Spiking Actor and Normalized Ensemble.

IEEE transactions on neural networks and learning systems·2021
Same author

Optimal Adaptive Control of Uncertain Nonlinear Continuous-Time Systems With Input and State Delays.

IEEE transactions on neural networks and learning systems·2021

Related Experiment Video

Updated: Mar 6, 2026

WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
08:18

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

Published on: August 15, 2020

5.5K

Boundary Control of Linear Uncertain 1-D Parabolic PDE Using Approximate Dynamic Programming.

Behzad Talaei, Sarangapani Jagannathan, John Singler

    IEEE Transactions on Neural Networks and Learning Systems
    |March 10, 2017
    PubMed
    Summary

    This study introduces a near-optimal boundary control for uncertain parabolic partial differential equations (PDEs) using approximate dynamic programming. The method ensures system stability and performance for complex diffusion-reaction processes.

    More Related Videos

    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
    06:45

    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

    Published on: October 28, 2022

    2.2K

    Related Experiment Videos

    Last Updated: Mar 6, 2026

    WheelCon: A Wheel Control-Based Gaming Platform for Studying Human Sensorimotor Control
    08:18

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

    Published on: August 15, 2020

    5.5K
    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
    06:45

    Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator

    Published on: October 28, 2022

    2.2K

    Area of Science:

    • Control Theory
    • Applied Mathematics
    • Dynamical Systems

    Background:

    • Distributed parameter systems governed by partial differential equations (PDEs) present significant control challenges.
    • Uncertainty in system dynamics complicates the design of effective control strategies.
    • Approximate dynamic programming offers a framework for optimal control in complex systems.

    Purpose of the Study:

    • To develop a near-optimal boundary control method for uncertain linear 1-D parabolic PDEs.
    • To formulate and solve the Hamilton-Jacobi-Bellman (HJB) equation in an infinite-dimensional space without model reduction.
    • To ensure the stability and performance of the closed-loop system.

    Main Methods:

    • Utilized approximate dynamic programming for control design.
    • Formulated an infinite-dimensional HJB equation using a quadratic surface integral cost functional.
    • Employed a neural network identifier and a radial basis network (RBN) for online estimation and control.
    • Developed novel tuning laws for identifier approximation error and RBN weights.
    • Verified closed-loop system ultimate boundedness using Lyapunov theory.

    Main Results:

    • A near-optimal boundary control strategy was developed for uncertain parabolic PDEs.
    • The neural network identifier effectively estimated unknown spatially varying coefficients.
    • The RBN provided an online approximation for the optimal surface kernel function.
    • The proposed control method ensured the stability of the closed-loop system.
    • Simulations demonstrated successful performance on an unstable diffusion-reaction process.

    Conclusions:

    • The developed approximate dynamic programming approach provides an effective near-optimal boundary control for uncertain distributed parameter systems.
    • The combination of neural network identification and RBN approximation enables online control design and stability guarantees.
    • The method is validated for complex systems, including unstable diffusion-reaction processes.