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    This study introduces heteroclinic networks as a hybrid control system for robotics and artificial neural networks. These networks offer a novel approach to analyzing complex, high-dimensional systems, bridging continuous and discrete dynamics.

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    Area of Science:

    • Robotics
    • Artificial Neural Networks
    • Dynamical Systems Theory

    Background:

    • Designing controllers for complex, high-dimensional systems in AI and robotics is challenging due to difficulties in dynamical analysis.
    • Existing systems often involve intricate nonlinearities and high dimensionality, hindering thorough understanding.

    Purpose of the Study:

    • To propose a restricted controller architecture incorporating heteroclinic networks for improved dynamical analysis.
    • To explore heteroclinic networks as a hybrid system bridging continuous and discrete dynamics.
    • To investigate this architecture in a minimal categorical perception task.

    Main Methods:

    • Introducing heteroclinic networks into the dynamical systems underlying controllers.
    • Analyzing systems with continuous variables that exhibit properties similar to finite-state machines (FSMs).
    • Testing the controller architecture in a categorical perception task.

    Main Results:

    • Demonstrated that systems with heteroclinic networks can be analyzed more effectively than traditional high-dimensional systems.
    • Showcased the hybrid nature of heteroclinic networks, combining continuous dynamics with discrete-like state transitions.
    • Observed behaviors that elude simple FSM descriptions, highlighting ongoing controller-environment interactions.

    Conclusions:

    • Heteroclinic networks offer a promising framework for creating more analyzable controllers in AI and robotics.
    • These networks provide a novel hybrid between continuous and discrete systems, enabling new insights into complex dynamics.
    • Further research into controller-environment interactions within these systems is warranted.