MS Thesis Defense: Ada Yildirim

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MS Thesis Defense: Ada Yildirim

Abstract

Predictive control requires the controller to possess an embedded prediction model. In multi-agent control, this prediction model must consider the behavior that emerges from other agents' strategic decisions. Game theory offers a natural model for the emergent collective behavior of self-interested agents. Model predictive games (MPGs) are a class of controllers in which an agent iteratively solves a finite-horizon game to predict the behavior of a multi-agent system and synthesize their own control action. When all agents use the same game model to select their control action, conditions have been found that guarantee the stability of the multi-agent system. However, when multiple agents implement their own MPG controllers, their respective game models may be misspecified due to inaccurate estimates or conjectures about other agents' objectives, resulting in heterogeneous MPG controllers. This thesis analyzes the consequences of these prediction misalignments on the system's behavior. Using a two-agent example, we show that existing stability conditions for homogeneous MPG controllers do not extend to the heterogeneous setting, even when they hold for each agent's individual game. The closed-loop system is defined as the linear system dynamics in feedback with the agents' Nash equilibrium maps obtained from their heterogeneous MPG controllers, and analyzed with the tools of dissipativity and monotone operator theory. Sufficient conditions for the stability of multi-agent dynamical systems with heterogeneous MPG controllers adopting strongly monotone linear-quadratic game models are provided in a linear matrix inequality (LMI) form. The sensitivity of the closed-loop equilibrium to individual agents' game parameters is quantified via parametric variational inequality theory. In a financial duopoly simulation, the closed-loop stability is analyzed for increasing levels of misspecification and prediction horizons via the derived stability certificate. The results show that heterogeneous game models alone can destabilize a multi-agent system, and that the LMI offers a verifiable stability certificate.

Thesis Committee

• Bryce L. Ferguson (Chair)
• Richard Granger
• Wesley Marrero

Contact

For more information, contact Thayer Registrar at thayer.registrar@dartmouth.edu .