论文标题
具有控制约束的汉密尔顿 - 雅各比 - 贝尔曼方程的政策迭代
Policy iteration for Hamilton-Jacobi-Bellman equations with control constraints
论文作者
论文摘要
政策迭代是一种广泛使用的技术，可以解决汉密尔顿雅各比·贝尔曼（HJB）方程，该方程是由非线性最佳反馈控制理论引起的。在无约束的情况下，其收敛分析引起了很多关注。在这里，我们对案例进行了控制约束，这既针对确定性和随机控制案例中出现的HJB方程。每个迭代步骤中的线性方程都通过隐式上风方案求解。进行了数值示例，以通过控制约束求解HJB方程，并显示了与不受约束的情况的比较。
Policy iteration is a widely used technique to solve the Hamilton Jacobi Bellman (HJB) equation, which arises from nonlinear optimal feedback control theory. Its convergence analysis has attracted much attention in the unconstrained case. Here we analyze the case with control constraints both for the HJB equations which arise in deterministic and in stochastic control cases. The linear equations in each iteration step are solved by an implicit upwind scheme. Numerical examples are conducted to solve the HJB equation with control constraints and comparisons are shown with the unconstrained cases.
