A Game Theoretic Lens for Robustness in Control

Abstract

The control of dynamical systems is a fundamental problem with a vast array of applications, from robotics to biological engineering. Recently, the game-theoretic primitive of regret minimization has been applied to control, yielding novel instance-optimal performance guarantees in more challenging non-stochastic control settings. This thesis further explores the benefits of a multi-agent perspective of control. Concretely, we begin with a new algorithm for generating disturbances for controller verification, which relies on recasting the players in the nonstochastic control game. Next, we provide a cooperative multi-agent extension of the nonstochastic control setting, involving a reduction from our multi-agent game to single agent regret minimization. Furthermore, we show new notions of robustness to failure can be attained through this perspective, even in a single-agent setting. While control is a powerful tool, it relies heavily on knowledge of the dynamics. The final chapters provide two very different approaches to robustness without such a model. The first approach extends the nonstochastic control methodology to model-free reinforcement learning. In an alternative approach, we consider unknown systems with dynamics that are approximately linear using tools from classical control theory.