On the Generalization of Data-Assisted Control in port-Hamiltonian Systems (DAC-pH)

Abstract: This paper introduces a hypothetical hybrid control framework for port-Hamiltonian (p$\mathcal{H}$) systems, employing a dynamic decomposition based on Data-Assisted Control (DAC). The system's evolution is split into two parts with fixed topology: Right-Hand Side (RHS)- an intrinsic Hamiltonian flow handling worst-case parametric uncertainties, and Left-Hand Side (LHS)- a dissipative/input flow addressing both structural and parametric uncertainties. A virtual port variable $\Pi$ serves as the interface between these two components. A nonlinear controller manages the intrinsic Hamiltonian flow, determining a desired port control value $\Pi_c$. Concurrently, Reinforcement Learning (RL) is applied to the dissipative/input flow to learn an agent for providing optimal policy in mapping $\Pi_c$ to the actual system input. This hybrid approach effectively manages RHS uncertainties while preserving the system's inherent structure. Key advantages include adjustable performance via LHS controller parameters, enhanced AI explainability and interpretability through the port variable $\Pi$, the ability to guarantee safety and state attainability with hard/soft constraints, reduced complexity in learning hypothesis classes compared to end-to-end solutions, and improved state/parameter estimation using LHS prior knowledge and system Hamiltonian to address partial observability. The paper details the p$\mathcal{H}$ formulation, derives the decomposition, and presents the modular controller architecture. Beyond design, crucial aspects of stability and robustness analysis and synthesis are investigated, paving the way for deeper theoretical investigations. An application example, a pendulum with nonlinear dynamics, is simulated to demonstrate the approach's empirical and phenomenological benefits for future research.