Higher-order properties and extensions for indirect MRAC and APPC of linear systems

Recently, a reference derived some new higher-order output tracking properties for direct model reference adaptive control (MRAC) of linear time-invariant (LTI) systems: lim_t→∞e⁽ⁱ⁾(t) = 0, i = 1,…, n* − 1, where n* and e⁽ⁱ⁾(t) denote the relative degree of the system and the i-th derivative of the output tracking error, respectively. However, a naturally arising question involves whether indirect adaptive control (including indirect MRAC and indirect adaptive pole placement control) of LTI systems still has higher-order tracking properties. Such properties have not been reported in the literature. Therefore, this paper provides an affirmative answer to this question. Such higher-order tracking properties are new discoveries since they hold without any additional design conditions and, in particular, without the persistent excitation condition. Given the higher-order properties, a new adaptive control system is developed with stronger tracking features. (1) It can track a reference signal with any order derivatives being unknown. (2) It has higher-order exponential or practical output tracking properties. (3) Finally, it is different from the usual MRAC system, whose reference signal’s derivatives up to the n* order are assumed to be known. Finally, two simulation examples are provided to verify the theoretical results obtained in this paper.