Convergence of the Relative Value Iteration for the Ergodic Control Problem of Nondegenerate Diffusions under Near-Monotone Costs
Convergence of the Relative Value Iteration for the Ergodic Control Problem of Nondegenerate Diffusions under Near-Monotone Costs
复制标题
近单调成本下非简并扩散遍历控制问题相对值迭代的收敛性
DOI：
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发表时间：
2013
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通讯作者：
And K Suresh Kumar
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作者：
A. Arapostathis;V. Borkar;And K Suresh Kumar
研究了一类非退化扩散系统在近似单调运行成本结构下的遍历控制问题的相对值迭代。该算法的形式为$mathbb{R}^{d}$中的拟线性抛物柯西初值问题。我们表明，这个柯西问题的稳定，或者换句话说，该解决方案的拟线性抛物方程收敛于每一个有界的初始条件在$mathcal{C}^{2}（mathbb{R}^{d}）$的解决方案的汉密尔顿-雅可比-贝尔曼方程与遍历控制问题。
We study the relative value iteration for the ergodic control problem under a near-monotone running cost structure for a nondegenerate diffusion controlled through its drift. This algorithm takes the form of a quasi-linear parabolic Cauchy initial value problem in $mathbb{R}^{d}$. We show that this Cauchy problem stabilizes or, in other words, that the solution of the quasi-linear parabolic equation converges for every bounded initial condition in $mathcal{C}^{2}(mathbb{R}^{d})$ to the solution of the Hamilton--Jacobi--Bellman equation associated with the ergodic control problem.