论文标题
优化静态线性反馈：梯度方法
Optimizing Static Linear Feedback: Gradient Method
论文作者
论文摘要
线性二次调节器是最佳控制的基本问题。它的国家反馈版本在1960年代初设置并解决了。但是，静态输出反馈问题没有明确的解决方案。建议从另一个角度将它们视为矩阵优化问题，其中变量是反馈矩阵增益。研究了这种函数的特性，事实证明，它是平滑的，但不是凸的，可能是可能的非连接域。然而，在状态反馈案例和输出反馈案例中的固定点中，具有特殊的阶梯选择的梯度方法将其收敛到最佳解决方案。可以扩展结果，以扩大不受约束的优化的一般框架，以及减少梯度方法，以通过相等类型的约束最小化。
The linear quadratic regulator is the fundamental problem of optimal control. Its state feedback version was set and solved in the early 1960s. However the static output feedback problem has no explicit-form solution. It is suggested to look at both of them from another point of view as matrix optimization problems, where the variable is a feedback matrix gain. The properties of such a function are investigated, it turns out to be smooth, but not convex, with possible non-connected domain. Nevertheless, the gradient method for it with the special step-size choice converges to the optimal solution in the state feedback case and to a stationary point in the output feedback case. The results can be extended for the general framework of unconstrained optimization and for reduced gradient method for minimization with equality-type constraints.
