Integrator backstepping with the nonlinear PI method: an integral equation approach. (English) Zbl 1336.93050
Summary: In this paper we extend the nonlinear PI method within an integrator backstepping framework. The main idea of our approach is a novel selection of the virtual control laws through suitable nonlinear integral equations. Using the proposed methodology a new robust regulation control scheme is developed for time-varying strict feedback nonlinear systems with unknown control directions. A simulation study demonstrates the validity of our theoretical results.
MSC:
| 93B35 | Sensitivity (robustness) |
| 93B51 | Design techniques (robust design, computer-aided design, etc.) |
| 93C10 | Nonlinear systems in control theory |
| 93B52 | Feedback control |
References:
| [1] | Astolfi, A.; Karagiannis, D.; Ortega, R., Nonlinear and Adaptive Control with Applications (2008), Springer-Verlag: Springer-Verlag London · Zbl 1119.93059 |
| [2] | Ding, Z., Adaptive consensus output regulation of a class of nonlinear systems with unknown high-frequency gain, Automatica, 51, 348-355 (2015) · Zbl 1309.93084 |
| [3] | Du, J.; Abraham, A.; Yu, S.; Zhao, J., Adaptive dynamic surface control with Nussbaum gain for course-keeping of ships, Eng. Appl. Artif. Intell., 27, 236-240 (2014) |
| [5] | Georgiou, T. T.; Smith, M. C., Robustness analysis of nonlinear feedback systemsan input-output approach, IEEE Trans. Autom. Control, 42, 1200-1221 (1997) · Zbl 0889.93043 |
| [6] | Hirsch, M. W.; Smale, S., Differential Equations, Dynamical Systems, and Linear Algebra (1974), Academic Press: Academic Press New York · Zbl 0309.34001 |
| [7] | Ilcmann, A.; Ryan, E. P., Universal \(λ\)-tracking for nonlinearly perturbed systems in the presence of noise, Automatica, 30, 2, 337-346 (1994) · Zbl 0800.93793 |
| [8] | Jiang, Z. P.; Mareels, I.; Hill, D. J.; Huang, J., A unifying framework for global regulation via nonlinear output feedbackfrom ISS to iISS, IEEE Trans. Autom. Control, 49, 549-562 (2004) · Zbl 1365.93177 |
| [9] | Kanellakopoulos, I.; Kokotovic, P.; Morse, S., Systematic design of adaptive controllers for Feedback linearizable systems, IEEE Trans. Automat. Control, 36, 1241-1253 (1991) · Zbl 0768.93044 |
| [10] | Khalil, H., Nonlinear Systems (2002), Prentice Hall: Prentice Hall Upper Saddle River, NJ · Zbl 1003.34002 |
| [11] | Krstic, M.; Kanellakopoulos, I.; Kokotovic, P., Nonlinear and Adaptive Control Design (1995), John Wiley and Sons: John Wiley and Sons New York · Zbl 0763.93043 |
| [12] | Liu, L.; Huang, J., Global robust output regulation of output feedback systems with unknown high-frequency gain sign, IEEE Trans. Automat. Control, 51, 625-631 (2006) · Zbl 1366.93209 |
| [13] | Marino, R.; Tomei, P., Robust stabilization of feedback linearizable time-varying uncertain nonlinear systems, Automatica, 29, 181-189 (1993) · Zbl 0778.93094 |
| [14] | Nussbaum, R. D., Some remarks on a conjecture in parameter adaptive control, Syst. Control Lett., 3, 243-246 (1983) · Zbl 0524.93037 |
| [15] | Ortega, R.; Astolfi, A.; Barabanov, N. E., Nonlinear PI control of uncertain systemsan alternative to parameter adaptation, Syst. Control Lett., 47, 259-278 (2002) · Zbl 1106.93314 |
| [16] | Peng, J.; Ye, X., Cooperative control of multiple heterogeneous agents with unknown high-frequency-gain signs, Syst. Control Lett., 68, 51-56 (2014) · Zbl 1288.93007 |
| [19] | Yan, X.; Liu, Y., Global practical tracking for high-order uncertain nonlinear systems with unknown control directions, SIAM J. Control Optim., 48, 7, 4453-4473 (2010) · Zbl 1210.93035 |
| [20] | Ye, X., Asymptotic regulation of time-varying uncertain nonlinear systems with unknown control directions, Automatica, 35, 929-935 (1999) · Zbl 0945.93542 |
| [21] | Ye, X., Universal \(λ\)-tracking for nonlinearly-perturbed systems without restrictions on the relative degree, Automatica, 35, 109-119 (1999) · Zbl 0947.93025 |
| [22] | Ye, X.; Ding, Z., Robust tracking control of uncertain nonlinear systems with unknown control directions, Syst. Control Lett., 42, 1-10 (2001) · Zbl 0985.93022 |
| [23] | Ye, X.; Jiang, J., Adaptive nonlinear design without a priori knowledge of control directions, IEEE Trans. Autom. Control, 43, 1617-1621 (1998) · Zbl 0957.93048 |
| [24] | Zhang, Y.; Wen, C.; Soh, Y., Adaptive backstepping control design for systems with unknown high-frequency gain, IEEE Trans. Autom. Control, 45, 2350-2354 (2000) · Zbl 0990.93061 |
| [25] | Zhao, Q.; Li, Y.; Lin, Y., Adaptive nonlinear output-feedback dynamic surface control with unknown high-frequency gain sign, Int. J. Control, 86, 2203-2214 (2013) · Zbl 1311.93050 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
