标题： 基于HJB的在线安全嵌入批评者学习方法，用于具有自触发机制的不确定系统 显示英文标题

标题： HJB-based online safety-embedded critic learning for uncertain systems with self-triggered mechanism

摘要： 本文提出了一种基于学习的最优控制框架，用于具有参数不确定性的安全关键系统，同时解决了时间触发和自触发控制器实现的问题。 首先，我们开发了一种鲁棒控制屏障函数（RCBF），结合基于李雅普诺夫的补偿项，以严格保证在参数不确定性下的安全性。 在此安全保证的基础上，我们将约束最优控制问题表述为一种新型安全嵌入价值函数的最小化问题，其中通过拉格朗日乘子涉及RCBF，该乘子自适应地平衡安全约束与最优稳定化目标。 为了提高计算效率，我们提出了一种自触发实现机制，减少了控制更新次数，同时保持双重稳定性-安全性保证。 所得的自触发约束哈密顿-雅可比-贝尔曼（HJB）方程通过一种在线安全嵌入评论家学习框架求解，其中拉格朗日乘子实时计算以确保安全性。 数值仿真证明了所提出方法在实现安全性和控制性能方面的有效性。 显示英文摘要

摘要： This paper presents a learning-based optimal control framework for safety-critical systems with parametric uncertainties, addressing both time-triggered and self-triggered controller implementations. First, we develop a robust control barrier function (RCBF) incorporating Lyapunov-based compensation terms to rigorously guarantee safety despite parametric uncertainties. Building on this safety guarantee, we formulate the constrained optimal control problem as the minimization of a novel safety-embedded value function, where the RCBF is involved via a Lagrange multiplier that adaptively balances safety constraints against optimal stabilization objectives. To enhance computational efficiency, we propose a self-triggered implementation mechanism that reduces control updates while maintaining dual stability-safety guarantees. The resulting self-triggered constrained Hamilton-Jacobi-Bellman (HJB) equation is solved through an online safety-embedded critic learning framework, with the Lagrange multiplier computed in real time to ensure safety. Numerical simulations demonstrate the effectiveness of the proposed approach in achieving both safety and control performance.