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

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Set-based corral control in stochastic dynamical systems: making almost invariant sets more invariant.

Eric Forgoston¹, Lora Billings, Philip Yecko

¹Department of Mathematical Sciences, Montclair State University, Montclair, New Jersey 07043, USA. eric.forgoston@montclair.edu

Chaos (Woodbury, N.Y.)

|April 5, 2011

Summary

This study introduces a method for controlling systems in unpredictable environments, like the ocean. By using geometric and probabilistic approaches, we can significantly increase system loitering time with minimal control effort.

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Real-Time Proxy-Control of Re-Parameterized Peripheral Signals using a Close-Loop Interface

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Published on: May 8, 2021

Area of Science:

Fluid dynamics
Stochastic systems
Control theory

Background:

Complex systems, such as the ocean, are subject to random fluctuations causing unpredictable behavior.
Understanding and controlling escape from almost invariant regions is crucial for prediction and management.

Purpose of the Study:

To develop a method for stochastic prediction and control in time-dependent stochastic environments.
To design high-probability control-actuation sets that enhance loitering time while minimizing control effort.

Main Methods:

Utilizing geometric and probabilistic methods.
Computing regions of uncertainty, almost invariant sets, and Lagrangian coherent structures.
Combining these to design effective control regions.

Main Results:

Demonstrated an increase in loitering time within almost invariant sets.
Showcased an exponential scaling of loitering time with control actuation.
Achieved more invariant sets through minimal control actuation.

Conclusions:

The developed methods provide an effective strategy for stochastic control in dynamic environments.
Small changes in actuation force can lead to significant increases in loitering times.
This approach enhances the stability and predictability of systems within almost invariant sets.