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Related Concept Videos

Second Order systems II01:18

Second Order systems II

In an underdamped second-order system, where the damping ratio ζ is between 0 and 1, a unit-step input results in a transfer function that, when transformed using the inverse Laplace method, reveals the output response. The output exhibits a damped sinusoidal oscillation, and the difference between the input and output is termed the error signal. This error signal also demonstrates damped oscillatory behavior. Eventually, as the system reaches a steady state, the error diminishes to zero.
If  ζ...
Second Order systems I01:20

Second Order systems I

A servo system exemplifies a second-order system, featuring a proportional controller and load elements that ensure the output position aligns with the input position. The relationship between these components is described by a second-order differential equation. Applying the Laplace transform under zero initial conditions yields the transfer function, showing how inputs are converted to outputs in the system.
By reinterpreting the system, one can derive the closed-loop transfer function, which...
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...
First Order Systems01:21

First Order Systems

First-order systems, such as RC circuits, are foundational in understanding dynamic systems due to their straightforward input-output relationship. Analyzing their responses to different input functions under zero initial conditions reveals significant insights into system behavior.
When a first-order system is subjected to a unit-step input, its response is characterized by its transfer function. By applying the Laplace transform of the unit-step input to the transfer function, expanding the...
Masking and Demasking Agents01:19

Masking and Demasking Agents

EDTA titrations may necessitate masking and demasking agents to temporarily protect a particular metal ion in a mixture from the EDTA reaction. These agents facilitate the sequential analysis of the metal ions by forming stable complexes with some—but not all—metal ions during certain steps.
There are many masking agents, such as cyanide, fluoride, triethanolamine, thiourea, and 2,3-bis(sulfanyl)propan-1-ol (formerly 2,3-dimercapto-1-propanol), with the masking agent chosen based on the metal...
Conservation of Energy in Control Volume01:14

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:

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Related Experiment Videos

Scaled containment control for first/second-order multi-agent systems in a noisy environment.

Chongyang Wang1, Shuzhi Sam Ge2, Dongjie Zhao1

  • 1Institute for Future, School of Automation, Qingdao University, Qingdao 266071, China; Shandong Key Laboratory of Industrial Control Technology, Qingdao University, Qingdao 266071, China; Qingdao Key Laboratory of Embodied Intelligence and Robot Control, Qingdao University, Qingdao 266071, China.

ISA Transactions
|June 12, 2026
PubMed
Summary
This summary is machine-generated.

This study tackles scaled containment control for stochastic multi-agent systems (SMASs) in noisy conditions. It shows followers converge to a scaled constant determined by leaders, even with noise.

Keywords:
Multi-agent systemsNoisy environmentScaled containmentStochastic approximation

Related Experiment Videos

Area of Science:

  • Control Theory
  • Distributed Systems
  • Stochastic Systems

Background:

  • Multi-agent systems (MASs) are crucial for distributed tasks.
  • Scalability and noise are significant challenges in MAS control.
  • Containment control aims for followers to stay within a region defined by leaders.

Purpose of the Study:

  • To investigate the scaled containment control problem (SCCP) for first/second-order stochastic multi-agent systems (SMASs).
  • To develop a control protocol robust to noise and scaling factors.
  • To establish conditions for follower convergence in a noisy environment.

Main Methods:

  • Design of a stochastic approximation protocol with time-varying gains.
  • Application of a state decomposition method for analysis.
  • Analysis of two interaction modes for second-order systems (constant velocities and zero velocity).

Main Results:

  • Sufficient and necessary conditions for SCCP derived under a directed spanning forest topology.
  • For first-order SMASs, followers converge to a scaled deterministic constant formed by leaders.
  • For second-order SMASs, convergence depends on interaction modes, with positions and velocities converging to scaled constants or zero.

Conclusions:

  • The proposed protocol effectively addresses the SCCP for both first and second-order SMASs.
  • The findings provide theoretical guarantees for follower convergence in scaled containment scenarios.
  • Numerical examples validate the effectiveness of the developed control strategy.