In the classical theory of self-tuning regulators, it always requires that the conditional variances of the systems noises are bounded. However, such a requirement may not be satisfied when modeling many practical systems, and one significant example is the well-known ARCH (autoregressive conditional heteroscedasticity) model in econometrics. The aim of this paper is to consider self-tuning regulators of linear stochastic systems with both unknown parameters and conditional heteroscedastic noises, where the adaptive controller will be designed based on both the weighted least-squares algorithm and the certainty equivalence principle. The authors will show that under some natural conditions on the system structure and the noises with unbounded conditional variances, the closed-loop adaptive control system will be globally stable and the tracking error will be asymptotically optimal. Thus, this paper provides a significant extension of the classical theory on self-tuning regulators with expanded applicability.

在自整定调节器的经典理论中，始终要求系统噪声的条件方差是有界的。但是，在对许多实际系统进行建模时，可能无法满足这一要求，而一个重要的例子就是计量经济学中众所周知的ARCH（自回归条件异方差）模型。本文的目的是考虑具有未知参数和条件异方差噪声的线性随机系统的自调整调节器，其中自适应控制器将基于加权最小二乘算法和确定性等效原理进行设计。作者将证明，在某些自然条件下，系统结构和具有无条件条件方差的噪声，闭环自适应控制系统将是全局稳定的，并且跟踪误差将渐近最优。因此，本文提供了自校正调节器的经典理论的重要扩展，具有扩展的适用性。