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    Area of Science:

    • Control Theory
    • Optimization
    • Systems Engineering

    Background:

    • Discounted optimal regulation design is sensitive to the discount factor.
    • Inappropriate discount factors can lead to unstabilizing control policies.

    Purpose of the Study:

    • To investigate the effect of the discount factor on control strategy stabilization.
    • To develop criteria for selecting discount factors in linear quadratic regulator problems.

    Main Methods:

    • Developed a system stability criterion and discount factor selection rules.
    • Utilized the general discounted value iteration algorithm.
    • Established a method to judge system stability during iteration based on value function monotonicity.

    Main Results:

    • A method to judge controlled system stability during the iteration process was established.
    • Control policies become stabilizing once specific stability conditions are met.
    • A practical rule for selecting appropriate discount factors was constructed.

    Conclusions:

    • The discount factor is critical for ensuring stability in optimal control.
    • The developed criteria and rules provide a practical approach for selecting discount factors.
    • Simulation examples validate the theoretical results for physical systems.