对于具有模型错误和外部干扰的非线性系统进行强大的近似动态编程
IEEE transactions on neural networks and learning systems
|November 28, 2023
概括
本研究引入了一种新的方法,用于同时管理非线性控制系统中的模型错误和外部干扰. 该方法使用增强的汉密尔顿 - 雅各比 - 艾萨克斯方程和批评在线学习以实现强大的性能.
科学领域:
- 控制理论 控制理论
- 非线性系统是非线性系统.
- 优化优化 优化优化
背景情况:
- 传统的控制方法单独处理模型误差和外部干扰,这对于复杂的非线性问题是不够的.
- 同时处理这些不确定性引入了重大挑战,比如性能优化中的非凸度.
- 现有的方法在与模型不确定性和外部干扰在非线性稳定控制的同时管理方面扎.
研究的目的:
- 开发一个统一的框架,同时解决非线性稳健性能问题的模型错误和外部干扰.
- 在增强的Hamilton-Jacobi-Isaacs (HJI) 方程中引入一个额外的成本函数,以管理并发的不确定性.
- 揭示额外成本函数与满足汉密尔顿-雅各比不等式的模型不确定性之间的关系.
主要方法:
- 增强的汉密尔顿 - 雅各比 - 艾萨克斯 (HJI) 方程,包含一个额外的成本函数.
- 一个批评在线学习算法,利用Lyapunov稳定术语和历史状态.
- 构建稳定性和收性分析的联合Lyapunov候选项.
主要成果:
- 拟议的方法有效地管理非线性系统中的模型误差和外部干扰.
- 批评者在线学习算法将解决方案与增强的HJI方程相近.
- 使用莱普诺夫的第二种方法证明了稳定性和收性,历史数据减少了系统和批评错误.
结论:
- 在增强的HJI方程中引入的额外成本函数为非线性稳健性能提供了可行的解决方案.
- 批评者在线学习算法确保稳定性和趋同性,同时处理不确定性.
- 该方法通过数值示例证明了有效性,提供了改进的系统性能界限.
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