基于滚动优化的对偶控制策略

考虑具有未知参数的随机系统的最优控制问题.提出了一种新的基于滚动优化的对偶控制算法.在动态规划泛函方程中,用Kalman滤波对系统的状态进行估计;用线性化方法对阶段损失函数中的后验概率进行近似,然后,用滚动优化策略对控制与学习之间的耦合关系进行解耦.从而获得了原不可解泛函方程的解析递推表达式和一个易于实施的控制律的解析解.用一个例子说明了控制律的性能,仿真结果表明:该控制律具有良好的对偶性质,在学习和控制之间实现了较好的平衡.

Dual control strategy based on receding horizon

The control of a stochastic system with unknown parameter was considered.A novel dual control algorithm based on receding horizon was proposed.In dynamic programming functional equation,the Kalman fliter is used to estimate the state of such system,and the linearization method is applied to approximate the nonlinear cost-to-go function with respect to posterior probabilities,the receding horizon strategy is then proposed to decouple the coupling relation between control and learning.Thus,the explicit recursive expression of the original unsolvable functional equation and a control law with easy implementation are obtained.The performance of the control law derived in this paper is also illustrated with an example.The simulation results show that the control law with dual property can achieve preferable compromise between learning and control.