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

199
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,...
199
Linear time-invariant Systems01:23

Linear time-invariant Systems

669
A system is linear if it displays the characteristics of homogeneity and additivity, together termed the superposition property. This principle is fundamental in all linear systems. Linear time-invariant (LTI) systems include systems with linear elements and constant parameters.
The input-output behavior of an LTI system can be fully defined by its response to an impulsive excitation at its input. Once this impulse response is known, the system's reaction to any other input can be...
669
Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

241
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
241
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

258
Cruise control systems in cars are designed as multi-input systems to maintain a driver's desired speed while compensating for external disturbances such as changes in terrain. The block diagram for a cruise control system typically includes two main inputs: the desired speed set by the driver and any external disturbances, such as the incline of the road. By adjusting the engine throttle, the system maintains the vehicle's speed as close to the desired value as possible.
In the absence of...
258
Piecewise-Defined Functions01:28

Piecewise-Defined Functions

76
Piecewise defined functions are mathematical models where different expressions define a function over distinct intervals of the domain. These functions are useful for representing systems with varying behaviors depending on input values.For example, the function:  uses a linear rule for inputs less than or equal to –1 and a quadratic rule for values greater than –1. Although it has two formulas, it still defines a single function.Another common type is the absolute value function, given...
76
Classification of Systems-I01:26

Classification of Systems-I

434
Linearity is a system property characterized by a direct input-output relationship, combining homogeneity and additivity.
Homogeneity dictates that if an input x(t) is multiplied by a constant c, the output y(t) is multiplied by the same constant. Mathematically, this is expressed as:
434

You might also read

Related Articles

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

Sort by
Same author

Integrating a Large Language Model Into a Socially Assistive Robot in a Hospital Geriatric Unit: Two-Wave Comparative Study on Performance, Engagement, and User Perceptions.

JMIR human factors·2025
Same author

Acceptability and Usability of a Socially Assistive Robot Integrated With a Large Language Model for Enhanced Human-Robot Interaction in a Geriatric Care Institution: Mixed Methods Evaluation.

JMIR human factors·2025
Same author

Robust Audio-Visual Contrastive Learning for Proposal-Based Self-Supervised Sound Source Localization in Videos.

IEEE transactions on pattern analysis and machine intelligence·2024
Same author

A multimodal dynamical variational autoencoder for audiovisual speech representation learning.

Neural networks : the official journal of the International Neural Network Society·2024
Same author

TransCenter: Transformers With Dense Representations for Multiple-Object Tracking.

IEEE transactions on pattern analysis and machine intelligence·2022
Same author

Uncertainty-Aware Contrastive Distillation for Incremental Semantic Segmentation.

IEEE transactions on pattern analysis and machine intelligence·2022

Related Experiment Video

Updated: Nov 17, 2025

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
10:44

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

Published on: December 7, 2021

2.5K

Variational Inference and Learning of Piecewise Linear Dynamical Systems.

Xavier Alameda-Pineda, Vincent Drouard, Radu Patrice Horaud

    IEEE Transactions on Neural Networks and Learning Systems
    |February 11, 2021
    PubMed
    Summary

    This study introduces a variational approximation for piecewise linear dynamical systems, enabling efficient modeling of complex temporal data. The new method improves accuracy in applications like head-pose tracking.

    More Related Videos

    Quantifying Learning in Young Infants: Tracking Leg Actions During a Discovery-learning Task
    11:18

    Quantifying Learning in Young Infants: Tracking Leg Actions During a Discovery-learning Task

    Published on: June 1, 2015

    10.9K

    Related Experiment Videos

    Last Updated: Nov 17, 2025

    Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
    10:44

    Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline

    Published on: December 7, 2021

    2.5K
    Quantifying Learning in Young Infants: Tracking Leg Actions During a Discovery-learning Task
    11:18

    Quantifying Learning in Young Infants: Tracking Leg Actions During a Discovery-learning Task

    Published on: June 1, 2015

    10.9K

    Area of Science:

    • Dynamical Systems Modeling
    • Machine Learning
    • Signal Processing

    Background:

    • Accurate modeling of temporal data is crucial across scientific and engineering disciplines.
    • Traditional linear-Gaussian models are insufficient for processes with multiple behavioral modes.
    • Switching dynamical systems offer flexibility but face computational intractability due to exponential complexity.

    Purpose of the Study:

    • To develop a computationally tractable variational approximation for piecewise linear dynamical systems.
    • To introduce efficient variational expectation-maximization (EM) algorithms for filtering and smoothing.
    • To enable offline estimation of static model parameters and the number of linear modes.

    Main Methods:

    • Proposed a variational approximation for piecewise linear dynamical systems.
    • Derived two variational EM algorithms: a filter and a smoother.
    • Demonstrated parameter splitting into static and dynamic sets for offline estimation.

    Main Results:

    • The proposed variational approximation effectively handles piecewise linear dynamics.
    • Static parameters and the number of modes can be estimated offline.
    • The method was successfully applied to head-pose tracking, showing competitive performance.

    Conclusions:

    • The variational approximation offers an efficient solution for modeling complex, multi-modal temporal data.
    • The developed algorithms provide a robust framework for parameter estimation and state inference.
    • This approach advances the state-of-the-art in dynamical systems modeling and tracking applications.