论文标题
直接数据驱动的离散时间双线性双线性二级调节器
Direct Data-Driven Discrete-time Bilinear Biquadratic Regulator
论文作者
论文摘要
我们提出了一种新颖的直接数据驱动算法，该算法学习了双线性双线性系统的双线性生物固定调节剂（BBR）的最佳控制策略。由于存在非线性生物段性能指数和动力学中的双线性跨度，因此BBR难以解决。为了解决这些困难，我们对状态决策变量进行了多种转换，以通过线性性能指数和仿射（在参数化控制）状态依赖性平等获得非线性优化问题。对哈密顿素和蓬蒂拉宁的最低原理的adroit使用使我们得出一对一对必要条件，在每个时间点，这些条件易于溶解，这是易于求解的线性矩阵相等性（LME），从而赋予最佳状态依赖性控制法。然后，我们使用收集到的数据的边缘样品自相关，以获得与这些LME相当的直接数据驱动的。我们通过说明性数值示例证明了所提出的算法的性能。
We present a novel direct data-driven algorithm that learns an optimal control policy for the Bilinear Biquadratic Regulator (BBR) for an unknown bilinear system. The BBR is difficult to solve owing to the presence of the nonlinear biquadratic performance index and the bilinear cross-term in the dynamics. To address these difficulties, we apply several transformations on the state decision variables to obtain a nonlinear optimization problem with a linear performance index and affine (in the parameterized control) state-dependent equality. The adroit use of the Hamiltonian and Pontryagin's Minimum Principle allows us to derive a pair of first-order necessary conditions that, at each point in time, are easily solvable linear matrix equalities (LMEs) which give the optimal state-dependent control law. We then use the marginal sample autocorrelation of the collected data to obtain a direct data-driven equivalent of these LMEs. We demonstrate the performance of the proposed algorithm via illustrative numerical examples.
