论文标题
迈向数据驱动的LQR，并具有koopmanizing Flow
Towards Data-driven LQR with Koopmanizing Flows
论文作者
论文摘要
我们为学习基于Koopman操作员的表示，为一类连续的非自治非线性动力学学习线性时变（LTI）模型提供了一个新颖的框架。通常，操作员是无限尺寸的，但至关重要的是线性。为了将其用于有效的LTI控制设计，我们学习了Koopman操作员的有限表示，该代表是在控制中线性的，同时同时学习有意义的举重坐标。对于后者，我们依靠KoopManization Flows-基于差异的Koopman操作员表示，并将其扩展到具有线性控制输入的系统。通过这种学习的模型，我们可以用二次成本替换非线性最佳控制问题，从而将二次调节器（LQR）替换为二次成本，从而促进了非线性系统的有效最佳控制。在模拟示例中证明了所提出方法的出色控制性能。
We propose a novel framework for learning linear time-invariant (LTI) models for a class of continuous-time non-autonomous nonlinear dynamics based on a representation of Koopman operators. In general, the operator is infinite-dimensional but, crucially, linear. To utilize it for efficient LTI control design, we learn a finite representation of the Koopman operator that is linear in controls while concurrently learning meaningful lifting coordinates. For the latter, we rely on Koopmanizing Flows - a diffeomorphism-based representation of Koopman operators and extend it to systems with linear control entry. With such a learned model, we can replace the nonlinear optimal control problem with quadratic cost to that of a linear quadratic regulator (LQR), facilitating efficacious optimal control for nonlinear systems. The superior control performance of the proposed method is demonstrated on simulation examples.
