Integral MRAC with Minimal Controller Synthesis and bounded adaptive gains: The continuous-time case

• Published in: Journal of the Franklin Institute Vol. 353; no. 18; pp. 5040 - 5067
• Main Authors: Montanaro, Umberto, Olm, Josep M.
• Format: Journal Article Publication
• Language: English
• Published: Elmsford Elsevier Ltd 01.12.2016; Elsevier Science Ltd
• Subjects: Adaptive algorithms; Algorithms; Continuous-time; Control; Control systems; Control theory; Controllers; Disturbances; Integrals; Matemàtica; Matemàtica aplicada a les ciències; Matemàtiques i estadística; Mathematical models; Model Reference Adaptive Control; Parameter; Robust control; Stability; Synthesis; Tracking; Uncertainty; Àrees temàtiques de la UPC
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2016.09.006

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 [1]. 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 σ-modification strategy. The former is used to preserve convergence to zero of the tracking error when the disturbance is bounded and L2, while the latter guarantees global uniform ultimate boundedness under continuous L∞ 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. •Continuous-time Minimal Control Synthesis algorithms with bounded adaptive gains.•Convergence to zero of the closed-loop error despite L2 disturbances.•Global uniform ultimate boundedness of the closed-loop system to L∞ disturbances.•Analytical derivation of the ultimate bound of the closed-loop system to L∞ disturbances.•Application of the proposed adaptive solutions to an engineering case study.