Zhikun She

Bai Xue, Qiuye Wang, Naijun Zhan et al.

In this paper we propose a novel semi-definite programming based method to compute robust domains of attraction for state-constrained perturbed polynomial systems. A robust domain of attraction is a set of states such that every trajectory starting from it will approach an equilibrium while never violating a specified state constraint, regardless of the actual perturbation. The semi-definite program is constructed by relaxing a generalized Zubov's equation. The existence of solutions to the constructed semi-definite program is guaranteed and there exists a sequence of solutions such that their strict one sub-level sets inner-approximate the interior of the maximal robust domain of attraction in measure under appropriate assumptions. Some illustrative examples demonstrate the performance of our method.

Yongwei Zhang, Yuanzhe Xing, Quanyi Liang et al.

For safety-critical applications, model-free reinforcement learning (RL) faces numerous challenges, particularly the difficulty of establishing verifiable stability guarantees while maintaining high exploration efficiency. To address these challenges, we present Multi-Step Actor-Critic Learning with Lyapunov Certificates (MSACL), a novel approach that seamlessly integrates exponential stability with maximum entropy reinforcement learning (MERL). In contrast to existing methods that rely on complex reward engineering and single-step constraints, MSACL utilizes intuitive rewards and multi-step data for actor-critic learning. Specifically, we first introduce Exponential Stability Labels (ESLs) to categorize samples and propose a $λ$-weighted aggregation mechanism to learn Lyapunov certificates. Leveraging these certificates, we then develop a stability-aware advantage function to guide policy optimization, thereby ensuring rapid Lyapunov descent and robust state convergence. We evaluate MSACL across six benchmarks, comprising four stabilization and two high-dimensional tracking tasks. Experimental results demonstrate its consistent superiority over both standard RL baselines and state-of-the-art Lyapunov-based RL algorithms. Beyond rapid convergence, MSACL exhibits significant robustness against environmental uncertainties and remarkable generalization to unseen reference signals. The source code and benchmarking environments are available at \href{https://github.com/YuanZhe-Xing/MSACL}{https://github.com/YuanZhe-Xing/MSACL}.