Dimension reduction based adaptive dynamic programming for optimal control of discrete-time nonlinear control-affine systems
Dimension reduction based adaptive dynamic programming for optimal control of discrete-time nonlinear control-affine systems
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DOI：
10.1080/00207179.2022.2113438
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发表时间：
2022-08
影响因子：
2.1
通讯作者：
Qiang Li;Yun-Hong Xu
中科院分区：
文献类型：
--
作者：
Qiang Li;Yun-Hong Xu
基于动态规划的方法已广泛应用于求解离散时间非线性约束最优控制问题。然而，实时应用这些方法是具有挑战性的，因为需要大量的存储器并且相关联的计算成本很高。本文针对一类控制仿射可逆的非线性离散时间系统，提出了一种搜索空间降维策略。具体而言，生物启发的运动规则与逆动力学相结合，以减少值迭代搜索空间到一维。给出了相应的次优控制算法，并分析了其最优性。一个自适应规则的发展，以估计不确定性和改进的基本政策。闭环系统被证明是渐近稳定的。通过两个仿真实例证明了该算法的优点，包括更小的计算成本和显着减少内存的使用。
Dynamic programming based methods have been widely used in solving discrete-time nonlinear constrained optimal control problems. However, applying these methods in real-time is challenging because a large amount of memory is needed and the associated computational cost is high. Here, a search space dimension reduction strategy is proposed for a class of nonlinear discrete-time systems that are control-affine and invertible. Specifically, a bio-inspired motion rule is combined with inverse dynamics to reduce the value iteration search space to one dimension. The corresponding suboptimal control algorithm is developed and its optimality is analysed. An adaptation rule is developed to estimate uncertainties and improve the base policy. The closed-loop system is proven to be asymptotically stable. The advantages of the algorithm including much smaller computational cost and significantly reduced memory usage are demonstrated with two simulation examples.