Inverse Dynamic Games With Process Noise and Unknown Target States: A Linear Estimation Approach

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.