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Controller configurations are crucial in a car's cruise control system because they manage speed over time to maintain a consistent pace regardless of road conditions, thereby meeting design goals. In traditional control systems, fixed-configuration design involves predetermined controller placement. System performance modifications are known as compensation.
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    Area of Science:

    • Control Theory
    • Nonlinear Systems
    • Robotics

    Background:

    • Stabilizing control of nonholonomic systems often involves independent steps, leading to discontinuous switching control issues.
    • Certain initial system states can exacerbate these discontinuous control problems.

    Purpose of the Study:

    • To investigate continuous and smooth stabilization control for nonlinear systems.
    • To develop methods for handling systems with piecewise continuous or smooth stabilization controllers.
    • To address the challenge of discontinuous switching control in nonholonomic systems.

    Main Methods:

    • Sufficient conditions for controller existence were established.
    • A controller extension method was employed to create intermediate auxiliary controllers.
    • Model transformation (cascade, fully actuated) and extended state observers were utilized.

    Main Results:

    • The controller extension method successfully linked piecewise controllers continuously or smoothly.
    • The proposed method effectively solved the stabilization control problem for an underactuated surface ship.
    • External disturbances were successfully managed in the stabilization control of the ship.

    Conclusions:

    • Continuous and smooth stabilization control is achievable for nonlinear systems with piecewise controllers.
    • The controller extension method offers a viable approach to overcoming discontinuous control issues.
    • The developed techniques are applicable to complex systems like underactuated ships facing external disturbances.