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Integral MRAC with minimal controller synthesis and bounded adaptive gains: the continuous-time case. (English) Zbl 1349.93223
Summary: Model reference adaptive controllers designed via the Minimal Control Synthesis (MCS) approach are a viable solution to control plants affected by parameter uncertainty, unmodelled dynamics, and disturbances. Despite its effectiveness to impose the required reference dynamics, an apparent drift of the adaptive gains, which can eventually lead to closed-loop instability or alter tracking performance, may occasionally be induced by external disturbances. This problem has been recently addressed for this class of adaptive algorithms in the discrete-time case and for square-integrable perturbations by using a parameter projection strategy [the authors, “Discrete-time integral MRAC with minimal controller synthesis and parameter projection”, ibid. 352, No. 12, 5415–5436, (2015; doi:10.1016/j.jfranklin.2015.09.004)]. In this paper we tackle systematically this issue for MCS continuous-time adaptive systems with integral action by enhancing the adaptive mechanism not only with a parameter projection method, but also embedding a $$\sigma$$-modification strategy. The former is used to preserve convergence to zero of the tracking error when the disturbance is bounded and $$L_2$$, while the latter guarantees global uniform ultimate boundedness under continuous $$L_\infty$$ disturbances. In both cases, the proposed control schemes ensure boundedness of all the closed-loop signals. The strategies are numerically validated by considering systems subject to different kinds of disturbances. In addition, an electrical power circuit is used to show the applicability of the algorithms to engineering problems requiring a precise tracking of a reference profile over a long time range despite disturbances, unmodelled dynamics, and parameter uncertainty.

##### MSC:
 93C40 Adaptive control/observation systems 93C41 Control/observation systems with incomplete information 93C73 Perturbations in control/observation systems 93B50 Synthesis problems
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