动态规划
贝尔曼方程
数学优化
最优控制
计算机科学
单调函数
国家(计算机科学)
功能(生物学)
非线性系统
控制器(灌溉)
人工神经网络
控制理论(社会学)
理论(学习稳定性)
非线性规划
序列(生物学)
控制(管理)
数学
算法
人工智能
机器学习
物理
生物
数学分析
进化生物学
量子力学
遗传学
农学
作者
Jiahui Xu,Jingcheng Wang,Jun Rao,Yanjiu Zhong,Hongyuan Wang
摘要
Abstract Adaptive dynamic programming (ADP) methods have demonstrated their efficiency. However, many of the applications for which ADP offers great potential, are also safety‐critical and need to meet safety specifications in the presence of physical constraints. In this article, an optimal controller for solving discrete‐time nonlinear systems with state constraints is proposed. By introducing the control barrier function into the utility function, the problem with state constraints is transformed into an unconstrained optimal control problem, addressing state constraints which are difficult to handle by traditional ADP methods. The constructed sequence of value function is shown to be monotonically non‐increasing and converges to the optimal value. Besides, this article gives the stability proof of the developed algorithm, as well as the conditions for satisfying the state constraints. To implement and approximate the control barrier function based adaptive dynamic programming algorithm, an actor‐critic network structure is built. During the training process, two neural networks are used for approximation separately. The performance of the proposed method is validated by testing it on a simulation example.
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