Optimal steering of inertial particles diffusing anisotropically with losses
Optimal steering of inertial particles diffusing anisotropically with losses
复制标题
具有损耗的各向异性扩散惯性粒子的最佳转向
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
M. Pavon
中科院分区：
文献类型：
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作者：
Yongxin Chen;T. Georgiou;M. Pavon
利用一个可能无法得到概率对应的流体动力学公式，我们将Schrödinger桥梁理论扩展到具有损失和一般扩散系数的惯性粒子的情况。我们发现，对于常扩散系数矩阵，最优控制律是通过求解两个p.d.e系统得到的。包含伴随算子，并通过它们的边值耦合。在具有二次损失函数的线性情况下，系统转化为具有耦合分裂边界条件的两个矩阵Riccati方程。控制问题的另一种形式是半确定规划问题，允许计算次优解。这在一个惯性粒子受恒速率杀伤的例子中得到说明。
Exploiting a fluid dynamic formulation for which a probabilistic counterpart might not be available, we extend the theory of Schrödinger bridges to the case of inertial particles with losses and general, possibly singular diffusion coefficient. We find that, as for the case of constant diffusion coefficient matrix, the optimal control law is obtained by solving a system of two p.d.e.'s involving adjoint operators and coupled through their boundary values. In the linear case with quadratic loss function, the system turns into two matrix Riccati equations with coupled split boundary conditions. An alternative formulation of the control problem as a semidefinite programming problem allows computation of suboptimal solutions. This is illustrated in one example of inertial particles subject to a constant rate killing.
影响因子：
6.8
作者：
Chen, Yongxin;Georgiou, Tryphon T.;Pavon, Michele
通讯作者：
Pavon, Michele