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首页> 外文会议>Proceedings of the Fifteenth international conference on civil, structural and environmental engineering computing >Optimal Feedback Control in case of Stochastic Uncertainty and Tracking Error Constraints
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Optimal Feedback Control in case of Stochastic Uncertainty and Tracking Error Constraints

机译：随机不确定性和跟踪误差约束下的最优反馈控制

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摘要

A predetermined optimal feedback control should be "robust", i.e., the feedback law should guarantee satisfying results also in case of observational random errors and variations of the different stochastic parameters occurring in the model. In addition, for the tracking error several constraints have to be taken into account. Based on the (optimal) reference trajectory and the related feedforward control, for the computation of a stochastic optimal feedback control, deterministic substitute control problems of the following type are considered: Minimize the expected total costs arising from the tracking error and the costs for the control correction, where the following constraints have to be taken into account: ⅰ) Dynamic equation of the stochastic control system with the total control input being the sum of the feedforward control and the control correction, ⅱ) constraints "in the mean" and "almost sure" for the tracking error, ⅲ) stochastic initial conditions, and ⅳ) possible additional conditions for the feedback law. The occurring expectations are determined approximatively by means of Taylor expansions with respect to the vector of parameter deviations and observation errors at zero means. The stochastic optimization problem for the feedback control law is converted then into a standard deterministic optimal control problem involving the gain matrices as the unknown matrix decision variables to be determined.
机译：预定的最佳反馈控制应该是“稳健的”，即在观察随机误差和模型中出现的不同随机参数变化的情况下，反馈定律也应保证令人满意的结果。另外，对于跟踪误差，必须考虑几个约束。基于（最佳）参考轨迹和相关的前馈控制，为了计算随机最优反馈控制，应考虑以下类型的确定性替代控制问题：最小化由跟踪误差引起的预期总成本和控制校正，其中必须考虑以下约束：ⅰ）随机控制系统的动力学方程，总控制输入为前馈控制和控制校正之和，ⅱ）约束“均值”和“跟踪误差，“）随机初始条件，ⅳ）反馈定律的可能附加条件。相对于参数偏差和零均值处的观察误差的矢量，通过泰勒展开近似确定发生的期望值。然后将反馈控制律的随机优化问题转换为标准确定性最优控制问题，该问题涉及将增益矩阵作为待确定的未知矩阵决策变量。

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