The paper addresses the problem of transient performance improvement of direct model reference adaptive control (MRAC) of discrete linear time-invariant (LTI) plants. Two solutions to the problem are proposed and use the certainty equivalence principle and the idea of regressor recording over a past period of time. The first solution is based on the principle of augmented error, while the second one uses new scheme of high order tuner generating predicted values of adjustable parameters. The recording of the past regressor is provided by application of a special SISO filter (linear operators with “memory”) to the closed-loop error model. It is proven and demonstrated by numerical examples that the proposed solutions can provide asymptotic (not exponential) convergence of the adjustable parameters under some simple condition which is weaker than the persistent excitation one. The proposed solution can be considered as a generalization of the identification/adaptation algorithm proposed by Kreisselmeier for continuous systems [21, 22].

本文解决了离散线性时不变（LTI）工厂的直接模型参考自适应控制（MRAC）的瞬时性能改进问题。针对该问题，提出了两种解决方案，它们使用确定性等效原理和过去一段时间内回归记录的思想。第一种解决方案基于增加误差的原理，而第二种解决方案则采用了新的高阶调谐器方案生成可调参数的预测值。通过将特殊的SISO过滤器（带有“内存”的线性算子）应用于闭环误差模型，可以记录过去的回归变量。数值算例表明，所提出的解决方案能够在比持续激励弱的一些简单条件下提供可调整参数的渐近（非指数）收敛。所提出的解决方案可以看作是Kreisselmeier提出的针对连续系统的识别/自适应算法的概括[21，22]。