论文标题
一组有限线性系统的最小自适应控制
Minimax Adaptive Control for a Finite Set of Linear Systems
论文作者
论文摘要
对于有限的参数限于有限集的线性时间流动系统，具有有界L2生成的自适应控制器。增益约束是指闭环系统，包括非线性学习程序。结果，对未建模的动力学（可能是非线性和无限二维）的鲁棒性来自较小的增益定理。该方法基于一种新的零和动态游戏公式，该配方优化了勘探和开发之间的权衡。最佳值函数上的显式上限按半准编程和适用于实现上限的自适应控制器的相应简单公式表示。一旦足够估计了不确定的参数，控制器就会像标准H-含量最佳控制一样行为。
An adaptive controller with bounded l2-gain from disturbances to errors is derived for linear time-invariant systems with uncertain parameters restricted to a finite set. The gain bound refers to the closed loop system, including the non-linear learning procedure. As a result, robustness to unmodelled dynamics (possibly nonlinear and infinite-dimensional) follows from the small gain theorem. The approach is based on a new zero-sum dynamic game formulation, which optimizes the trade-off between exploration and exploitation. An explicit upper bound on the optimal value function is stated in terms of semi-definite programming and a corresponding simple formula for an adaptive controller achieving the upper bound is given. Once the uncertain parameters have been sufficiently estimated, the controller behaves like standard H-infinity optimal control.
