Nonlinear second cost cumulant control using Hamilton-Jacobi-Bellman equation and neural network approximation
Nonlinear second cost cumulant control using Hamilton-Jacobi-Bellman equation and neural network approximation
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DOI：
10.1109/acc.2010.5530930
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发表时间：
2010-07
期刊：
影响因子：
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通讯作者：
Bei Kang;Chang-Hee Won
中科院分区：
文献类型：
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作者：
Bei Kang;Chang-Hee Won
成本累积控制是一种应用于随机系统的最优控制方法。与确定性系统不同，随机系统中的成本函数是随机变量。我们使用统计控制通过成本累积量来优化成本函数的分布。我们分析了非线性随机系统的第一和第二成本累积优化问题。 Hamilton-Jacobi-Bellman (HJB) 方程是针对每个累积量最小化情况导出的。然后使用神经网络近似方法对 HJB 方程进行数值求解，进而找到最优控制器。给出了两个例子，包括非线性系统和线性化卫星姿态控制系统。找到第一和第二累积量最优控制器。然后通过算例比较了第一和第二累积量的最优控制器的性能。
Cost cumulant control is an optimal control method applied to the stochastic systems. Unlike the deterministic systems, the cost function in a stochastic system is a random variable. We use statistical control to optimize the distribution of the cost function via cost cumulants. We analyze the first and second cost cumulant optimization problems for nonlinear stochastic systems. The Hamilton-Jacobi-Bellman (HJB) equations are derived with respect to each cumulant minimization case. Then a neural network approximation method is used to numerically solve the HJB equations, which in turn is used to find the optimal controller. Two examples including a nonlinear system and a linearized satellite attitude control system are presented. The first and second cumulant optimal controllers are found. Then the performance of the optimal controllers for the first and the second cumulants are compared through the examples.