Do Wan Kim

Donghwan Lee, Do Wan Kim

Temporal difference (TD) learning is a cornerstone reinforcement learning (RL) method for policy evaluation, where the goal is to estimate the value function of a Markov decision process under a fixed policy. While a substantial body of work has established its convergence and stability properties, more recent efforts have focused on its statistical efficiency through finite-time error bounds. In this paper, we advance this line of research by developing a new finite-time error analysis for tabular TD learning that directly exploits a discrete-time stochastic linear system representation and leverages Schur stability of the associated matrices. Beyond the specific bounds obtained, the proposed framework provides a reusable template for analyzing TD learning and related RL algorithms, and it offers control-theoretic insights that may guide future developments in finite-sample RL theory.

Donghwan Lee, Do Wan Kim

The main goal of this paper is to introduce new local stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems. These stability conditions are based on linear matrix inequalities (LMIs) in combination with quadratic Lyapunov functions. Moreover, they integrate information on the membership functions at the origin and effectively leverage the linear structure of the underlying nonlinear system in the vicinity of the origin. As a result, the proposed conditions are proved to be less conservative compared to existing methods using fuzzy Lyapunov functions in the literature. Moreover, we establish that the proposed methods offer necessary and sufficient conditions for the local exponential stability of T-S fuzzy systems. The paper also includes discussions on the inherent limitations associated with fuzzy Lyapunov approaches. To demonstrate the theoretical results, we provide comprehensive examples that elucidate the core concepts and validate the efficacy of the proposed conditions.