论文标题
结构化的在线学习基于连续时间非线性系统的控制
Structured Online Learning-based Control of Continuous-time Nonlinear Systems
论文作者
论文摘要
基于模型的强化学习技术通过采用过渡模型进行预测来加速学习任务。在本文中，提出了一种基于模型的学习方法，该方法是根据模型的最新更新来计算最佳值函数。假设系统的结构化连续时间模型在一组基础方面，我们制定了一个无限的地平线最佳控制问题，以解决给定的控制目标。系统的结构以及以二次形式参数化的值函数在分析计算参数的更新规则方面具有灵活性。因此，在任何时间步骤中，都使用该解决方案来获得参数的矩阵微分方程，以根据基础来表征最佳反馈控制。此外，值函数的二次形式提出了一种更新参数的紧凑方法，该参数大大降低了计算复杂性。考虑到微分方程的状态依赖性，我们将获得的框架作为基于在线学习的算法利用。在数值结果中，在四个非线性基准示例上实现了呈现的算法，其中在其中确定的系统模型以有界的预测误差获得了调节问题。
Model-based reinforcement learning techniques accelerate the learning task by employing a transition model to make predictions. In this paper, a model-based learning approach is presented that iteratively computes the optimal value function based on the most recent update of the model. Assuming a structured continuous-time model of the system in terms of a set of bases, we formulate an infinite horizon optimal control problem addressing a given control objective. The structure of the system along with a value function parameterized in the quadratic form provides a flexibility in analytically calculating an update rule for the parameters. Hence, a matrix differential equation of the parameters is obtained, where the solution is used to characterize the optimal feedback control in terms of the bases, at any time step. Moreover, the quadratic form of the value function suggests a compact way of updating the parameters that considerably decreases the computational complexity. Considering the state-dependency of the differential equation, we exploit the obtained framework as an online learning-based algorithm. In the numerical results, the presented algorithm is implemented on four nonlinear benchmark examples, where the regulation problem is successfully solved while an identified model of the system is obtained with a bounded prediction error.
