In this article, an overview of principle research works regarding control of nonlinear nonminimum-phase systems is presented. Key concepts of some research of fundamental importance that has been done in this area are discussed. The research is categorized into the five fundamental methodologies, and further work based on particular methodology is also discussed. Limitations of each concept are also highlighted at the end.
EnnsDBugajskiDHendrickR. Dynamic inversion: an evolving methodology for flight control. Int J Control1994; 59: 71–91.
2.
BugajskiDEnnsD. Nonlinear control law with application to high angle-of-attack flight. J Guid Control1992; 15: 761–767.
3.
SamadTAnnaswamyAM (eds) The impact of control technology: overview, success stories and research challenges. Report, February2011. IEEE Control Systems Society, www.ieeecss.org
4.
LaneSHStengelRF. Flight control using nonlinear inverse dynamics. Automatica1988; 24: 471–483.
5.
GopalswamySHedrickJK. Control of a high performance aircraft with unacceptable zero dynamics. In: Proceedings of the IEEE American control conference, Piscataway, NJ, 24–26 June 1992, pp.1834–1838. New York: IEEE.
6.
ShkolnikovIAShtesselYB. Aircraft nonminimum phase control in dynamic sliding manifolds. J Guid Control Dynam2001; 24: 566–572.
7.
GunnarssonSNorrlöfM. On the design of ILC algorithms using optimization. Automatica2001; 37: 2011–2016.
8.
DingZ. Adaptive stabilization of a class of nonlinear systems with unstable internal dynamics. IEEE T Automat Contr2003; 48: 1788–1792.
9.
YanXGEdwardsCSpurgeonSK. Output feedback stabilization of a class of uncertain non-minimum phase system with nonlinear disturbance. Int J Control2004; 77: 1353–1361.
10.
LeeCH. Stabilization of nonlinear nonminimum phase systems: adaptive parallel approach using recurrent fuzzy neural network. IEEE T Syst Man Cy B2004; 34: 1075–1088.
11.
HovakimyanNYangBJCaliseAJ. Adaptive output feedback control methodology applicable to non-minimum phase nonlinear systems. Automatica2006; 42: 513–522.
12.
KhalilHK. Nonlinear systems. 3rd ed.Upper Saddle River, NJ: Prentice Hall Inc., 2002.
13.
IsidoriA. Nonlinear control systems. 3rd ed.Berlin: Springer-Verlag, 1995.
14.
IsidoriAMoogCH. On the nonlinear equivalent of the notion of transmission zeros. In: ByrnesCIKurzhanskiA (eds) Modeling and adaptive control. Berlin: Springer-Verlag, 1989, pp.146–158.
15.
IsidoriAByrensCI. Output regulation of nonlinear systems. IEEE T Automat Contr1990; 35: 131–140.
16.
HauserJSastrySMeyerG. Nonlinear control design for slightly non-minimum phase system: application to V/STOL aircraft. Automatica1992; 28(4): 665–679.
17.
KooTJSastryS. Output tracking control design of a helicopter model based on approximate linearization. In: Proceedings of the 37th IEEE conference on decision and control, Tampa, FL, 16–18 December 1998, vol. 4, pp.3635–3640. New York: IEEE.
18.
ShimHKooTJHoffmannF. A comprehensive study of control design for an autonomous helicopter. In: Proceedings of the 37th IEEE conference on decision and control, Tampa, FL, 16–18 December 1998, vol. 4, pp.3653–3658. New York: IEEE.
19.
ParkerJTSerraniAYurkovichS. Control-oriented modeling of an air-breathing hypersonic vehicle. J Guid Control Dynam2007; 30(3): 856–869.
20.
BolenderMADomanDB. A nonlinear model for the longitudinal dynamics of a hypersonic air-breathing vehicle. In: Proceeding of the 2005 guidance, navigation and control conference, San Francisco, CA, 28–31 August 2005, AIAA paper no. 2005-6255. Reston, VA: AIAA.
21.
BanaszukAHauserJ. Approximate feedback linearization: a homotopy operator approach. SIAM J Control Optim1996; 34(5): 1533–1554.
22.
BortoffSA. Approximate state-feedback linearization using spline functions. Automatica1997; 33(8): 1449–1458.
23.
HauserJSastrySKokotovicP. Nonlinear control via approximate input-output linearization: the ball and beam example. IEEE T Automat Contr1992; 37(3): 392–398.
24.
GuardabassiGOSavaresiSM. Approximate linearization via feedback—an overview. Automatica2001; 37(1): 1–15.
25.
HedrickJKGopalswamyS. Nonlinear flight control design via sliding methods. J Guid Control Dynam1990; 13(5): 850–858.
26.
GopalswamyS. Adaptive control of nonlinear nonminimum phase systems. PhD Dissertation, University of California, Berkeley, CA, 1991.
27.
GopalswamySHedrickJK. Tracking nonlinear nonminimum phase systems using sliding control. Int J Control1993; 57(5): 1141–1158.
28.
KimSGTahkMJ. Output-redefinition based on robust zero dynamics. In: Proceedings of the AIAA guidance navigation and control conference, Boston, MA, 10–12 August 1998. Reston, VA: AIAA.
29.
WallnerEMWellKH. Attitude control of a reentry vehicle with internal dynamics. J Guid Control Dynam2003; 26(6): 846–854.
30.
WangDVidyasagarM. Transfer functions for a single flexible link. Int J Robot Res1991; 10(5): 540–549.
31.
MoallemMPatelRVKhorasaniK. An inverse dynamics control strategy for tip position tracking of flexible multi-link manipulators. J Robotic Syst1997; 14(9): 649–658.
32.
MoallemMKhorasaniKPatelRV. An inverse dynamics sliding control technique for flexible multi-link manipulators. In: Proceedings of the IEEE American control conference, Albuquerque, NM, 4–6 June 1997, vol. 3, pp.1407–1411. New York: IEEE.
33.
MoallemMPatelRVKhorasaniK. Nonlinear tip-position tracking control of a flexible-link manipulator: theory and experiments. Automatica2001; 37(11): 1825–1834.
34.
YangHKrishnanHAngMHJr. Tip-trajectory tracking control of single-link flexible robots via output redefinition. In: Proceedings of the IEEE international conference on robotics and automation, Detroit, MI, 10–15 May 1999, pp.1102–1107. New York: IEEE.
35.
TalebiHAKhorasaniKPatelRV. Tracking control of a flexible-link manipulator using neural networks: experimental results. Robotica2002; 20(4): 417–427.
36.
TalebiHAPatelRVKhorasaniK. A neural network controller for a class of nonlinear non-minimum phase systems with application to a flexible-link manipulator. J Dyn Syst: T ASME2005; 127(2): 289–294.
37.
AtashzarSFTalebiHAShahbaziM. Robust trajectory modification for tip position tracking of flexible-link manipulators. Proc IMechE, Part I: J Systems and Control Engineering2011; 226(4): 523–536.
38.
BenvenutiLDi BenedettoMDGrizzleJW. Approximate output tracking for nonlinear nonminimum phase systems with an application to flight control. Int J Robust Nonlin1994; 4(5): 397–414.
39.
DevasiaSPadenB. Exact output tracking for nonlinear time-varying systems. In: Proceedings of the 33rd IEEE conference on decision and control, Lake Buena Vista, FL, 14–16 December 1994, vol. 3, pp.2346–2355. New York: IEEE.
40.
ChenDPadenB. Stable inversion of nonlinear nonminimum phase systems. Int J Control1996; 64(1): 81–97.
TomlinCLygerosJBenvenutiL. Output tracking for a non-minimum phase dynamic CTOL aircraft model. In: Proceedings of the 34th IEEE conference on decision and control, New Orleans, LA, 13–15 December 1995, pp.1867–1872. New York: IEEE.
43.
MeyerGHuntLRSuR. Nonlinear system guidance. In: Proceedings of the 34th IEEE conference on decision and control, New Orleans, LA, 13–15 December 1995, pp.590–595. New York: IEEE.
44.
HuntLRMeyerG. Stable inversion for nonlinear systems. Automatica1997; 33(8): 1549–1554.
45.
Al-HiddabiSAMcClamrochNH. Tracking and maneuver regulation control for nonlinear nonminimum phase systems: application to flight control. IEEE T Contr Syst T2002; 10(6): 780–792.
46.
WuW. Stable inverse control for nonminimum-phase nonlinear processes. J Process Contr1999; 9(2): 171–183.
47.
ZhaoHChenD. A finite energy property of stable inversion to nonminimum phase nonlinear systems. IEEE T Automat Contr1998; 43(8): 1170–1174.
48.
DevasiaSPadenB. Stable inversion for nonlinear nonminimum-phase time-varying systems. IEEE T Automat Contr1998; 43(2): 283–288.
49.
DevasiaS. Approximated stable inversion for nonlinear systems with non-hyperbolic internal dynamics. IEEE T Automat Contr1999; 44(7): 1419–1425.
50.
TornambeA. Output feedback stabilization of a class of non-minimum phase nonlinear systems. Syst Contr Lett1992; 19(3): 193–204.
51.
EsfandiariFKhalilHK. Output feedback stabilization of fully linearizable systems. Int J Control1992; 56(5): 1007–1037.
52.
KhalilHKEsfandiariF. Semiglobal stabilization of a class of nonlinear systems using output feedback. IEEE T Automat Contr1993; 38(9): 1412–1415.
53.
MarinoRTomeiP. Global adaptive output-feedback control of nonlinear systems. I. Linear parameterization. IEEE T Automat Contr1993; 38(1): 17–32.
54.
MarinoRTomeiP. Global adaptive output-feedback control of nonlinear systems. II. Nonlinear parameterization. IEEE T Automat Contr1993; 38(1): 33–48.
55.
IsidoriA. A tool for semiglobal stabilization of uncertain non-minimum-phase nonlinear systems via output feedback. IEEE T Automat Contr2000; 45(10): 1817–1827.
56.
KaragiannisDJiangZPOrtegaR. Output-feedback stabilization of a class of uncertain non-minimum-phase nonlinear systems. Automatica2005; 41(9): 1609–1615.
57.
KaragiannisDAstolfiAOrtegaR. Two results for adaptive output feedback stabilization of nonlinear systems. Automatica2003; 39(5): 857–866.
58.
JiangZP. A combined backstepping and small-gain approach to adaptive output feedback control. Automatica1999; 35(6): 1131–1139.
59.
NazrullaSKhalilHK. Robust stabilization of non-minimum phase nonlinear systems using extended high-gain observers. IEEE T Automat Contr2011; 56(4): 802–813.
60.
MarinoRTomeiP. A class of globally output feedback stabilizable nonlinear nonminimum phase systems. IEEE T Automat Contr2005; 50(12): 2097–2101.
61.
Honeywell and Lockheed-Martin. Application of multivariable control theory to aircraft control laws. Final report, WL-TR-96-3099, May1996. Dayton, OH: Wright-Patterson AFB.
