AI 中文总结
研究具有有限动作空间的非线性系统的识别与控制，利用库普曼算子回归从有限样本估计未知动力学得到线性切换预测模型，用于闭环控制的无限时域最优控制问题，推导学习率并量化模型预测控制策略次优性，数值模拟验证理论结果。
AI 中文摘要
在这项工作中，我们考虑具有有限动作空间的非线性系统的识别与控制。通过在再生核希尔伯特空间中利用库普曼算子回归从有限样本估计未知动力学，得到线性切换预测模型，其切换由控制变量的值决定。为进行闭环控制，将学习到的动力学应用于具有时变阶段成本的无限时域最优控制问题，通过模型预测控制求解。理论分析中，推导了库普曼动力学近似的学习率。还在适当假设下量化了模型预测控制策略分别在精确库普曼动力学和学习到的动力学情况下的次优性。对杜芬振子的数值模拟补充了理论结果。
英文摘要
In this work, we consider the identification and control of nonlinear systems with finite action spaces. The unknown dynamics are estimated from finite samples with Koopman operator regression in a reproducing kernel Hilbert space, yielding a linear switching predictive model, the switches governed by the value of the control variable. In order to perform control in closed-loop, the learned dynamics are employed in an infinite-horizon optimal control problem with time-varying stage cost, which is solved by means of model predictive control. In a theoretical analysis, we derive learning rates for the Koopman dynamics approximation. We further quantify, under suitable assumptions, the sub-optimality of the model predictive control strategy, both in the case of exact Koopman dynamics, and in the case of learned ones. Numerical simulations on the Duffing oscillator complement our theoretical findings.
