Analysis of \(\mathcal L_1\) adaptive state feedback control. why does it approximate an implementable LTI controller? (English) Zbl 1360.93371
Summary: The analysis in this paper shows that \(\mathcal L_1\) adaptive state feedback control approximates an implementable LTI controller because: (1) the addition of a low-pass filter in the controller structure leads to an internal loop in the controller and (2) high gain feedback within this loop leads to inversion of the linear reference model and cancellation of nonlinear characteristics of the adaptation law. This result holds for a variety of adaptation laws and the achieved performance does not depend on the exact formulation of this law.
MSC:
| 93C40 | Adaptive control/observation systems |
| 93B35 | Sensitivity (robustness) |
| 93B52 | Feedback control |
| 93C10 | Nonlinear systems in control theory |
References:
| [3] | Hovakimyan, N.; Cao, C.; Kharisov, E.; Xargay, E.; Gregory, I. M., \(L_1\) Adaptive control for safety-critical systems, IEEE Control Syst. Mag., 31, 5, 54-104 (2011) · Zbl 1395.93297 |
| [4] | Ioannou, P.; Annaswamy, A.; Narendra, K.; Jafari, S.; Rudd, L.; Ortega, R.; Boskovic, J., \(L_1\)-Adaptive control: stability, robustness, and interpretations, IEEE Trans. Autom. Control, 59, 11, 3075-3080 (2014) · Zbl 1360.93353 |
| [7] | Kharisov, E.; Hovakimyan, N.; Aström, K. J., Comparison of architectures and robustness of model reference adaptive controllers and L1adaptive controllers, Int. J. Adapt. Control Signal Process, 28, 7-8, 633-663 (2014) · Zbl 1332.93169 |
| [9] | Ortega, R.; Panteley, E., Comments on \(L_1\)-adaptive control: stabilisation mechanism, existing conditions for stability and performance limitations, Int. J. Control, 87, 3, 581-588 (2014) · Zbl 1317.93153 |
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