A Control-Theoretic Foundation for Agentic Systems

This paper develops a control-theoretic framework for analyzing agentic systems embedded within feedback control loops, where an AI agent may adapt controller parameters, select among control strategies, invoke external tools, reconfigure decision architectures, and modify control objectives during operation. These capabilities are formalized by interpreting agency as hierarchical runtime decision authority over elements of the control architecture, leading to an augmented closed-loop representation in which physical states, internal memory, tool outputs, interaction signals, and design variables evolve as a coupled dynamical system. A five-level hierarchy of agency is defined, ranging from fixed control laws to runtime synthesis of control architectures and objectives. The analysis shows that increasing agency introduces interacting dynamical mechanisms such as time-varying adaptation, endogenous switching, decision-induced delays, and structural reconfiguration. The framework is developed in both nonlinear and linear settings, providing explicit design constraints for AI-enabled control systems in safety-critical applications.