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首页> 外文期刊>IEEE Transactions on Automatic Control >Controllability is not necessary for adaptive pole placement control
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Controllability is not necessary for adaptive pole placement control

机译：自适应磁极位置控制不需要可控性

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The key issue for adaptive pole-placement control of linear time-invariant systems is the possible singularity of the Sylvester matrix corresponding to the coefficient estimate. However, to overcome the difficulty, the estimate is modified by several methods which are either nonrecursive and with high computational load or recursive but with random search involved. All of the previous works are done under the assumption that the system is controllable. This paper gives the necessary and sufficient condition, which is weaker than controllability, for the system to be adaptively stabilizable. First, a nonrecursive algorithm is proposed to modify the estimates, and the algorithm is proved to terminate in finitely many steps. Then, with the help of stochastic approximation, a recursive algorithm is proposed for obtaining the modification parameters; it is proved that these modification parameters turn out to be a constant vector in a finite number of steps. This leads to the convergence of the modified coefficient estimates. For both algorithms the Sylvester matrices corresponding to the modified coefficient estimates are asymptotically uniformly nonsingular; thus, the adaptive pole-placement control problem can be solved, i.e., the system can be adaptively stabilized.
机译：线性时不变系统的自适应极点布置控制的关键问题是与系数估计相对应的Sylvester矩阵的奇异性。然而，为了克服困难，通过几种方法来修改估计，这些方法要么非递归且具有高计算量，要么递归但涉及随机搜索。所有先前的工作都是在系统可控的前提下完成的。本文给出了系统自适应适应所需的充要条件，该条件要比可控制性弱。首先，提出了一种非递归算法来修改估计值，并证明该算法以有限的多个步骤终止。然后，在随机逼近的基础上，提出了一种递推算法来获取修正参数。事实证明，这些修改参数在有限数量的步骤中成为常数向量。这导致修改系数估计的收敛。对于这两种算法，与修正系数估计相对应的Sylvester矩阵都是渐近一致非奇异的。因此，可以解决自适应极点布置控制问题，即可以使系统自适应地稳定。

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