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In practice, we rarely know the population standard deviation. In the past, when the sample size was large, this did not present a problem to statisticians. They used the sample standard deviation s as an estimate for σ and proceeded as before to calculate a confidence interval with close enough results. However, statisticians ran into problems when the sample size was small. A small sample size caused inaccuracies in the confidence interval.
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    Area of Science:

    • Control Theory
    • Game Theory
    • Robotics

    Background:

    • Modeling multi-agent interactions is crucial for understanding complex systems.
    • Identifying underlying cost functions from observed behavior is a key challenge in dynamic games.

    Purpose of the Study:

    • To develop a method for identifying unknown cost functions in discrete-time, finite-horizon linear-quadratic (LQ) dynamic games.
    • To address scenarios with unknown state and input weight matrices, process noise, observation noise, and player-specific linear cost terms.

    Main Methods:

    • Established sufficient conditions for the solvability of weight matrices.
    • Proved structural identifiability of the inverse dynamic games problem, unaffected by process noise.
    • Formulated cost function parameter estimation as a distributed homogeneous linear estimation problem based on Nash equilibrium conditions.

    Main Results:

    • The proposed estimator achieves statistical consistency under observation noise.
    • Demonstrated the effectiveness of the method in a multivehicle spring-coupled dynamic game.
    • Validated the approach in an interactive steering control scenario.

    Conclusions:

    • The study provides a robust framework for inverse dynamic games with complex cost functions.
    • The developed estimation method is effective and statistically consistent, even with noise.
    • The findings have implications for modeling and analyzing multi-agent systems in various applications.