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Related Concept Videos

State Space Representation01:27

State Space Representation

The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
Consider an RLC circuit, a...
Multi-input and Multi-variable systems01:22

Multi-input and Multi-variable systems

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...
BIBO stability of continuous and discrete -time systems01:24

BIBO stability of continuous and discrete -time systems

System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
To determine the BIBO stability, the convolution integral is utilized when a bounded continuous-time input is applied to a Linear Time-Invariant (LTI) system.
Collisions in Multiple Dimensions: Problem Solving01:06

Collisions in Multiple Dimensions: Problem Solving

In multiple dimensions, the conservation of momentum applies in each direction independently. Hence, to solve collisions in multiple dimensions, we should write down the momentum conservation in each direction separately. To help understand collisions in multiple dimensions, consider an example.
A small car of mass 1,200 kg traveling east at 60 km/h collides at an intersection with a truck of mass 3,000 kg traveling due north at 40 km/h. The two vehicles are locked together. What is the...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Propagation of Uncertainty from Random Error00:59

Propagation of Uncertainty from Random Error

An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements occur in successive steps, the uncertainty in one step necessarily contributes to that in the subsequent step. As we perform statistical analysis on these types of experiments, we must learn to account for the propagation of uncertainty from one step to the next. The propagation of uncertainty depends on the type of arithmetic operation performed on...

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Related Experiment Video

Updated: May 18, 2026

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

Containment control for stochastic multiagent systems with multiple dynamic leaders and compound noises.

Yingxue Du1, Jinxin Shang1, Zhi Liu1

  • 1School of Automation and Electrical Engineering, Linyi University, Shandong 276000, China.

ISA Transactions
|May 16, 2026
PubMed
Summary

This study introduces a new method for controlling stochastic multi-agent systems (SMASs) with compound noise and dynamic leaders. The novel approach ensures system stability and follower convergence despite unpredictable oscillations from additive and multiplicative noise.

Keywords:
Compound noiseContainment controlMulti-agent systemsMultiple dynamic leadersStochastic approximation

Related Experiment Videos

Last Updated: May 18, 2026

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior
10:07

Generating Controlled, Dynamic Chemical Landscapes to Study Microbial Behavior

Published on: January 31, 2020

Area of Science:

  • Control Theory
  • Systems Engineering
  • Applied Mathematics

Background:

  • Stochastic multi-agent systems (SMASs) are susceptible to compound noise (additive and multiplicative), degrading stability, especially in containment control with dynamic leaders.
  • Existing error analysis methods fail with multiplicative noise in dynamic SMASs, necessitating new approaches for robust control.
  • Containment control aims for followers to converge within the convex hull of leaders, a challenge amplified by dynamic leader behaviors and noise.

Purpose of the Study:

  • To develop a novel containment control protocol for SMASs under compound noise with multiple dynamic leaders.
  • To address the limitations of existing error analysis methods caused by multiplicative noise.
  • To establish a weaker control gain condition for achieving containment control.

Main Methods:

  • A novel model incorporating compound noises and dynamic leaders was developed.
  • A containment control protocol based on the stochastic approximation (SA) technique was designed.
  • A novel semi-decomposition technique was proposed to handle the challenges posed by multiplicative noise.

Main Results:

  • The proposed method achieves containment control, ensuring followers converge to the convex hull of dynamic leaders.
  • A weaker control gain condition (∫₀^∞σ^τ(t)dt<∞, τ=min{2,ρ}>1) was adopted, improving upon existing results.
  • Numerical simulations confirmed the feasibility, showing faster leader convergence than followers enhances control.
  • Multiplicative noise intensity significantly impacts convergence more than additive noise intensity.

Conclusions:

  • The developed containment control protocol effectively manages SMASs with compound noise and multiple dynamic leaders.
  • The novel semi-decomposition technique provides a robust framework for analyzing systems with multiplicative noise.
  • The findings offer a more flexible control gain condition and practical insights into noise impact for SMASs.