On the Stability of Datatic Control Systems

TL;DR

This paper introduces a novel stability verification algorithm for datatic control systems that relies on minimal assumptions, extending stability analysis to general nonlinear systems using data-driven Lipschitz continuity.

Contribution

The paper presents the η-testing algorithm, a new method for verifying stability in datatic control systems without requiring explicit models, applicable to nonlinear systems.

Findings

Successfully verifies stability, instability, and critical stability in tested systems.

Extends stability analysis to general nonlinear datatic systems.

Uses a quadratically constrained linear program for worst-case derivative estimation.

Abstract

The development of feedback controllers is undergoing a paradigm shift from $\textit{modelic}$ (model-driven) control to $\textit{datatic}$ (data-driven) control. Stability, as a fundamental property in control, is less well studied in datatic control paradigm. The difficulty is that traditional stability criteria rely on explicit system models, which are not available in those systems with datatic description. Some pioneering works explore stability criteria for datatic systems with special forms such as linear systems, homogeneous systems, and polynomial systems. However, these systems imply too strong assumptions on the inherent connection among data points, which do not hold in general nonlinear systems. This paper proposes a stability verification algorithm for general datatic control systems called $\eta$-testing. Our stability criterion only relies on a weak assumption of Lipschitz continuity so as to extend information from known data points to unmeasured regions. This information restricts the time derivative of any unknown state to the intersection of a set of closed balls. Inside the intersection, the worst-case time derivative of Lyapunov function is estimated by solving a quadratically constrained linear program (QCLP). By comparing the optimal values of QCLPs to zero in the whole state space, a sufficient condition of system stability can be checked. We test our algorithm on three datatic control systems, including both linear and nonlinear ones. Results show that our algorithm successfully verifies the stability, instability, and critical stability of tested systems.