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首页> 外文期刊>IEEE Transactions on Automatic Control >Batch-to-Batch Finite-Horizon LQ Control for Unknown Discrete-Time Linear Systems Via Stochastic Extremum Seeking
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Batch-to-Batch Finite-Horizon LQ Control for Unknown Discrete-Time Linear Systems Via Stochastic Extremum Seeking

机译：未知离散线性系统通过随机极值寻道的逐批有限水平LQ控制

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摘要

We employ our recent discrete-time stochastic averaging theorems and stochastic extremum seeking to iteratively (batch-to-batch) optimize open-loop control sequences for unknown but reachable discrete-time linear systems with a scalar input and without known system dimension, for a cost that is quadratic in the measurable output and the input. First, for a multivariable gradient-based stochastic extremum seeking algorithm we prove local exponential convergence to the optimal open-loop control sequence. Second, to remove the convergence rate's dependence on the Hessian matrix of the cost function, which is unknown since the system's model (the system matrices ) is unknown, we develop a multivariable discrete-time Newton-based stochastic extremum seeking method, design the Newton-based algorithm for the iteration of the input sequence, and prove local exponential convergence to the optimal input sequence. Finally, two simulation examples are given to illustrate the effectiveness of the two methods.
机译：我们使用最近的离散时间随机平均定理和随机极值来迭代（批到批）优化具有标量输入但没有已知系统尺寸的未知但可到达的离散时间线性系统的开环控制序列。在可测量的输出和输入中是二次方的成本。首先，对于基于变量的基于梯度的随机极值搜索算法，我们证明了局部指数收敛到最优开环控制序列。其次，为了消除收敛率对成本函数的Hessian矩阵的依赖（由于系统模型（系统矩阵）未知，因此未知），我们开发了一种基于牛顿的多变量离散时间随机极值搜索方法，设计了牛顿序列的迭代算法，证明局部指数收敛到最优输入序列。最后，给出两个仿真实例来说明这两种方法的有效性。

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