论文标题
对未知的非线性系统具有额线遗憾
On-the-fly control of unknown nonlinear systems with sublinear regret
论文作者
论文摘要
我们研究了来自单个正在进行的和有限的途径对未知非线性动力学的数据驱动，受约束的控制的问题。我们考虑一个单步的最佳控制问题，具有光滑，黑色的目标，通常是已知成本函数和未知动态的组成。我们研究了一个直立的控制范式，即，在每个时间步骤中，动态的演变和成本的一阶信息仅适用于执行的控制操作。我们提出了一种基于优化的控制算法，该算法迭代地将数据驱动的替代功能最小化，以确保未知目标。我们证明，所提出的方法会引起透明的累积遗憾（相对于最佳的一步控制器，逐步屈服于次优），并且在广泛的数据驱动的控制算法中是最佳案例。我们还介绍了可以利用现成的求解器进行有效实施的方法的可易处理的重新进行的重新进行。
We study the problem of data-driven, constrained control of unknown nonlinear dynamics from a single ongoing and finite-horizon trajectory. We consider a one-step optimal control problem with a smooth, black-box objective, typically a composition of a known cost function and the unknown dynamics. We investigate an on-the-fly control paradigm, i.e., at each time step, the evolution of the dynamics and the first-order information of the cost are provided only for the executed control action. We propose an optimization-based control algorithm that iteratively minimizes a data-driven surrogate function for the unknown objective. We prove that the proposed approach incurs sublinear cumulative regret (step-wise suboptimality with respect to an optimal one-step controller) and is worst-case optimal among a broad class of data-driven control algorithms. We also present tractable reformulations of the approach that can leverage off-the-shelf solvers for efficient implementations.
