Game theoretic and data-driven methods for dynamic decisions - from full to partial information

Abstract

Modern systems are increasingly complex, interconnected, and influenced by various decision makers. This introduces new challenges for designing dynamic decision laws which ensure such systems behave as expected, respond appropriately to inputs, or operate safely autonomously - particularly if decision makers have incomplete information regarding the system dynamics or performance criteria. The objective of this thesis is to develop game theoretic and data-driven methods for dynamic decisions towards tackling such challenges. Dynamic game theory concerns the dynamic interaction of strategic decision makers called players. As games involve multi-objective optimisation problems, the “best” strategy for each player is typically not obvious, and various solution concepts exist. In this thesis, feedback Nash equilibrium solutions of linear quadratic discrete-time dynamic games are considered. Computing such solutions is generally challenging, and multiple solutions with different outcomes may exist. To build intuition, conditions characterising the number of solutions and certain properties are derived for games involving scalar dynamics. To address the challenges associated with obtaining solutions in the general case, a notion of approximate Nash equilibrium is introduced, and iterative Nash equilibrium finding methods are proposed. Data-driven control exploits measured data to recover or replace missing information for designing dynamic decision laws. In this thesis, a framework to design control laws directly using data, while providing performance guarantees, is extended to the class of linear time-varying systems, and methods are developed to represent control objectives using data. Combining the above, methods are proposed to overcome incomplete information in multi-player dynamic decisions. First, games in which one player lacks system and cost information are considered, before iterative data-driven methods are designed to determine a solution if all players have incomplete information. The results are illustrated and motivated via numerical examples and practically relevant case studies, including macroeconomic policy design, power systems, snake-like robots, and human-robot interaction.