A robust adaptive nonlinear control design. (English) Zbl 0847.93031

The authors describe a robust adaptive control design for a class of nonlinear systems with uncertainty. The uncertainty in the class of systems they consider is due to both parametric uncertainty and unknown nonlinear functions. These unknown functions could arise from modeling errors, external disturbances, time variations in the system, or a combination of these. The authors’ main assumption is that these unknown functions satisfy a “triangular bounds” condition which is similar to the pure feedback condition of earlier studies. Specifically, the unknown functions are assumed to satisfy some growth conditions characterized by bounding functions composed of known functions multiplied by unknown parameters. The authors’ formulation expands the class of nonlinear systems for which global adaptive stabilization methods can be used. The overall adaptive scheme is shown to guarantee global uniform ultimate boundedness.


93C40 Adaptive control/observation systems
93C10 Nonlinear systems in control theory
93D21 Adaptive or robust stabilization
Full Text: DOI


[1] Åström, K.J.; Whittenmark, B., ()
[2] Barmish, B.R.; Corless, M.; Leitmann, G., A new class of stabilizing controllers for uncertain dynamical systems, SIAM J. control optim., 21, 246-255, (1983) · Zbl 0503.93049
[3] Byrnes, C.I.; Isidori, A., New results and examples in nonlinear feedback stabilization, Syst. control lett., 12, 437-442, (1989) · Zbl 0684.93059
[4] Campion, G.; Bastin, G., Analysis of an adaptive controller for manipulators: robustness versus flexibility, Syst. control lett., 12, 251-258, (1989) · Zbl 0673.93046
[5] Corless, M.; Leitmann, G., Continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems, IEEE trans. autom. control, AC-26, 1139-1144, (1981) · Zbl 0473.93056
[6] Corless, M.; Leitmann, G., Adaptive control of systems containing uncertain functions and unknown functions with uncertain bounds, J. optim. theory applics, 41, 155-168, (1983) · Zbl 0497.93028
[7] Freeman, R.A.; Kokotovic, P.V., Backstepping design of robust controllers for a class of nonlinear systems, (), 307-312
[8] Hàjek, O., Discontinuous differential equations, J. diff. eqns., 32, 149-170, (1979), Part I · Zbl 0365.34017
[9] Ioannou, P.A.; Datta, A., Robust adaptive control: a unified approach, (), 1736-1768
[10] Ioannou, P.A.; Kokotovic, P.V., ()
[11] Jiang, Z.-P.; Praly, L., Iterative designs of adaptive controllers for systems with nonlinear integrators, (), 2482-2487
[12] Kanellakopoulos, I.; Kokotovic, P.V.; Morse, A.S., Systematic design of adaptive controllers for feedback linearizable systems, IEEE trans. autom. control, AC-36, 1241-1253, (1991) · Zbl 0768.93044
[13] Kanellakopoulos, I.; Kokotovic, P.V.; Morse, A.S., A toolkit for nonlinear feedback design, Syst. control lett., 18, 83-92, (1992) · Zbl 0743.93039
[14] Kokotovic, P.V.; Sussman, H.J., A positive real condition for global stabilization of nonlinear systems, Syst. control lett., 12, 125-133, (1989) · Zbl 0684.93066
[15] Krstic, M.; Kanellakopoulos, I.; Kokotovic, P.V., Adaptive nonlinear control without overparametrization, Syst. control lett., 19, 177-185, (1992) · Zbl 0763.93043
[16] Marino, R.; Tomei, P., Robust stabilization of feedback linearizable time-varying uncertain nonlinear systems, (1991), Preprint
[17] Marino, R.; Tomei, P., Global adaptive output-feedback control of nonlinear systems, part II: nonlinear parametrization, IEEE trans. autom. control, AC-38, 33-48, (1993) · Zbl 0799.93023
[18] Nam, K.; Arapostathis, A., A model-reference adaptive control scheme for pure-feedback nonlinear systems, IEEE trans. autom. control, AC-33, 803-811, (1988) · Zbl 0649.93040
[19] Polycarpou, M.M.; Ioannou, P.A., On the existence and uniqueness of solutions in adaptive control systems, IEEE trans. autom. control, AC-38, 474-479, (1993) · Zbl 0789.93084
[20] Pomet, J.-B.; Praly, L., Adaptive nonlinear regulation: estimation from the Lyapunov equation, IEEE trans. autom. control, AC-37, 729-740, (1992) · Zbl 0755.93071
[21] Reed, J.S.; Ioannou, P.A., Instability analysis and robust adaptive control of robotic manipulators, IEEE trans. robotics and automation, RA-5, 381-386, (1989)
[22] Sastry, S.S.; Isidori, A., Adaptive control of linearizable systems, IEEE trans. autom. control, AC-34, 1123-1131, (1989) · Zbl 0693.93046
[23] Seto, D.; Annaswamy, A.M.; Baillieul, J., Adaptive control of nonlinear systems with triangular structure, IEEE trans. autom. control, AC-39, 1411-1428, (1994) · Zbl 0806.93034
[24] Slotine, J.-J.E.; Li, W., ()
[25] Taylor, D.G.; Kokotovic, P.V.; Marino, R.; Kanellakopoulos, I., Adaptive regulation of nonlinear systems with unmodelled dynamics, IEEE trans. autom. control, AC-34, 405-412, (1989) · Zbl 0671.93033
[26] Tsinias, J., Sufficient Lyapunov-like conditions for stabilization, Math. control sig. syst., 2, 343-357, (1989) · Zbl 0688.93048
[27] Utkin, V.I., ()
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