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Simple adaptive control – a stable direct model reference adaptive control methodology – brief survey. (English) Zbl 1332.93163

Summary: In spite of successful proofs of stability and even successful demonstrations of performance, the eventual use of model reference adaptive control methodologies in practical real-world systems has met a rather strong resistance from practitioners and has remained very limited. Apparently, the practitioners have a hard time understanding the conditions that can guarantee stable operations of adaptive control systems under realistic operational environments. Besides, it is difficult to measure the robustness of adaptive control system stability and allow it to be compared with the common and widely used measure of phase margin and gain margin that is utilized by present, mainly LTI, controllers. Furthermore, recent counterexamples seem to show that adaptive systems may diverge even when all required conditions are fulfilled. This paper attempts to revisit the fundamental qualities of the common direct model reference adaptive control methodology based on gradient and to show that some of its basic drawbacks have been addressed and eliminated within the so-called simple adaptive control methodology. The sufficient conditions that guarantee stability are clearly stated and lead to similarly clear proofs of stability. The main claim of the paper is that if sufficient information exists for a robust classical design control, same information can be used to implement robust simple adaptive controllers. As many real world applications show, the added value of using add-on adaptive control techniques, the use is pushing the desired performance beyond any previous limits. The paper also shows that the previous counterexamples to model reference adaptive control become just simple, successful, and stable applications of simple adaptive control.

MSC:

93C40 Adaptive control/observation systems
93C15 Control/observation systems governed by ordinary differential equations
93C35 Multivariable systems, multidimensional control systems
Full Text: DOI

References:

[1] WhitakerHP. An adaptive performance of aircraft and spacecraft. Inst. Aeronautical Sciences, Paper 59‐100, 1959.
[2] OsbornPV, WhitakerHP, KezerA. New developments in the design of model reference adaptive control systems. Inst. Aeronautical Sciences, Paper 61-39. 1961.
[3] HahnW. Stability of Motion. Springer‐Verlag: New York, 1967.
[4] MonopoliRV. Model reference adaptive control with an augmented error signal. IEEE Transactions on Automatic Control1974; AC‐19(5):474‐484. · Zbl 0288.93022
[5] Van AmerongenJ, Ten CateAU. Model reference adaptive controller for ships. Automatica1975; 11:441-449.
[6] FeuerA, MorseAS. Adaptive control of single‐input, single‐output linear systems. IEEE Transactions on Automatic Control1978; 23(4):557-569. · Zbl 0384.93028
[7] MorseAS. Global stability of parameter adaptive control systems. IEEE Transactions on Automatic Control1980; 25(3):433-439. · Zbl 0438.93042
[8] LandauID. A survey of model reference adaptive techniques: theory and applications. Automatica1974; 10(4):353-379. · Zbl 0284.93018
[9] LandauID. Adaptive Control ‐ The Model Reference Approach. Marcel Dekker: New York, NY, 1979. · Zbl 0475.93002
[10] NarendraKS, ValavaniLS. Adaptive controller design ‐ direct control. IEEE Transactions on Automatic Control1978; 23:570-583. · Zbl 0389.93025
[11] NarendraKS, ValavaniLS. Direct and indirect model reference adaptive control. Automatica1979; 15:653-664. · Zbl 0429.93036
[12] NarendraKS, LinYH, ValavaniLS. Stable adaptive controller design ‐ part II: proof of stability. IEEE Transactions on Automatic Control1980; 25:440-448. · Zbl 0467.93049
[13] NarendraKS, AnnaswamiA. Stable Adaptive Systems. Prentice Hall: Englewood Cliffs, NJ, 1989. · Zbl 0758.93039
[14] GoodwinGC, RamadgePJ, CainesPE. Discrete time multivariable adaptive control. IEEE Transactions on Automatic Control1980; 25:449-456. · Zbl 0429.93034
[15] GoodwinGC, SinK. Adaptive Filtering, Prediction and Control. Prentice Hall: Englewood Cliffs, NJ, 1984. · Zbl 0653.93001
[16] AstromKJ. Theory and applications of adaptive control ‐ a survey. Automatica1983; 19(5):471-486. · Zbl 0537.93048
[17] AstromKJ, WittenmarkB. Adaptive Control. Addison Wesley: Reading, MA, 1989. · Zbl 0697.93033
[18] IoannouP, KokotovicP. Adaptive Systems with Reduced Models. Springer‐Verlag: Berlin, 1983. · Zbl 0503.93001
[19] MoirT, GrimbleM. Optimal self‐tuning filtering, prediction, and smoothing for discrete multivariable processes. IEEE Transactions on Automatic Control1984; 29(2):128-137. · Zbl 0537.93063
[20] MareelsI. A simple selftuning controller for stable invertible systems. Systems and Control Letters1984; 4:5-16. · Zbl 0528.93046
[21] KreisselmayerG, AndersonB. Robust model reference adaptive control. IEEE Transactions on Automatic Control1986; 31(2):127-133. · Zbl 0583.93039
[22] OrtegaR, YuT. Theoretical results on robustness of direct adaptive controllers. Proceedings of IFAC Triennial World Conference1987; 10:1-15.
[23] SastriS, BodsonM. Adaptive Control: Stability, Convergence and Robustness. Prentice‐Hall: Upper Saddle River, NJ, 1989. · Zbl 0721.93046
[24] IoannouP, SunJ. Robust Adaptive Control. Prentice‐Hall: Upper Saddle River, NJ, 1996. · Zbl 0839.93002
[25] BitmeadR, GeversM, WertzV. Adaptive Optimal Control, The Thinking Man’s GPC. Prentice Hall: Englewood Cliffs, New Jersey, 1990. · Zbl 0751.93052
[26] WellsteadP, ZarropM. Self‐Tuning Control Systems. Wiley: Chichester, UK, 1991.
[27] KrsticM, KanellakopoulosI, KokotovicP. Nonlinear and Adaptive Control Design. Wiley: New York, 1995.
[28] AndersonBDO. Failures of adaptive control theory and their resolution. Communications in Information and Systems2005; 5(1):1-20. · Zbl 1138.93362
[29] HovakimyanN, CaoC. L1 Adaptive Control Theory. Society for Industrial and Applied Mathematics: Philadelphia, PA, 2010. · Zbl 1214.93004
[30] KalmanR. When is a linear system optimal?Transactions of ASME , Journal of Basic Engineering, Serries D1964; 86:81-90.
[31] KaufmanH, BarkanaI, SobelK. Direct Adaptive Control Algorithm, 2nd ed., Springer‐Verlag: New York, 1998.
[32] CauerW. Synthesis of Linear Communication Networks. McGraw‐Hill: New York, 1958. · Zbl 0092.44602
[33] PopovVM. Absolute stability of nonlinear control systems of automatic control. Automation and Remote Control1962; 22:857-862.
[34] AndersonBDO, VongpanitlerdS. Network Analysis and Synthesis: A Modern Systems Theory Approach. Prentice‐Hall, Inc.: Englewood Cliffs, NJ, 1973.
[35] IoannouPA, TaoG. Frequency domain conditions for strictly positive real functions. IEEE Transactions on Automatic Control1987; 32:53-54. · Zbl 0618.93059
[36] WenJT. Time‐domain and frequency domain conditions for strictly positive realness. IEEE Transactions on Automatic Control1988; 33:988-992. · Zbl 0664.93013
[37] BarkanaI, KaufmanH. Global stability and performance of an adaptive control algorithm. International Journal of Control1985; 46(6):1491-1505. · Zbl 0587.93045
[38] BarkanaI. Parallel feedforward and simplified adaptive control. International Journal on Adaptive Control and Signal Processing1987; 1(2):95-109. · Zbl 0736.93042
[39] FradkovAL. Passification of non‐square linear systems and feedback Yakubovich ‐ Kalman ‐ Popov lemma. European Journal of Control2003; 6:573-582.
[40] FradkovAL, HillD. Exponential feedback passivity and stabilizability of nonlinear systems. Automatica1998; 34(6):697-703. · Zbl 0937.93036
[41] FradkovAL. Quadratic Lyapunov function in the adaptive stabilization problem of a linear dynamic plant. Siberian Mathematical Journal1976; 17(2):341-348. · Zbl 0357.93024
[42] BarkanaI. Comments on ‘Design of strictly positive real systems using constant output feedback’. IEEE Transactions on Automatic Control2004; 49:2091-2093. · Zbl 1365.93168
[43] HuangCH, IoannouPA, MaroulasJ, SafonovMG. Design of strictly positive real systems using constant output feedback. IEEE Transactions on Automatic Control1999; 44(3):569-573. · Zbl 0965.93082
[44] BarkanaI, TeixeiraMCM, HsuL. Mitigation of symmetry condition from positive realness for adaptive control. Automatica2006; 42(9):1611-1616. · Zbl 1128.93350
[45] BarkanaI. On adaptive model tracking with mitigated passivity conditions. 52nd Israel Annual Conference on Aerospace Sciences, Israel, February 2012.
[46] BarkanaI. Extensions in adaptive model tracking with mitigated passivity conditions. Chinese Journal of Aeronautics2013; 26(1):136-150. (Available from: http://dx.doi.org/10.1016/j.cja.2012.12.027).
[47] HsuL, CostaR. MIMO direct adaptive control with reduced prior knowledge of the high‐frequency gain. Proceedings of 38th IEEE Conference on Decision and Control, Phoenix, AZ, 1999; 3303-3308.
[48] SobelK, KaufmanH, MabusL. Implicit adaptive control for a class of MIMO systems. IEEE Transactions on Aerospace1982; 18(5):576-590.
[49] BarkanaI, KaufmanH. Discrete direct multivariable adaptive control. Proceedings 1st IFAC Workshop on Adaptive Systems in Control and Signal Processing, San Francisco, Ca, June 1983; 357-362.
[50] KaufmanH, BalasM, BarkanaI, RaoL. Model reference adaptive control of large scale systems. Proceedings 20th IEEE Conference on Decision and Control, San Diego, CA, December 1981; 984-989.
[51] BarkanaI, KaufmanH. Model reference adaptive control for time‐variable input commands. Proceedings 1982 Conference on Informational Sciences and Systems, Princeton, NJ, March 1982; 208-211.
[52] BarkanaI, KaufmanH, BalasM. Model reference adaptive control of large structural systems. AIAA Journal of Guidance1983; 6(2):112-118. · Zbl 0537.93049
[53] BarkanaI. Direct multivariable adaptive control with application to large structural systems. PhD Dissertation, ECSE Dept., Rensselaer Polytechnic Institute, Troy, New York, May 1983.
[54] WenJ, BalasM. Finite‐dimensional direct adaptive control for discrete‐time infinite‐dimensional Hilbert space. Journal of Mathematical Analysis & Applications1989; 143:1-26. · Zbl 0701.93086
[55] BalasM. Direct model reference adaptive control in infinite‐dimensional linear spaces. Journal of Mathematical Analysis & Applications1995; 196(1):153-171. · Zbl 0853.93063
[56] NussbaumRO. Some remarks on a conjecture in parameter adaptive control. Systems and Control Letters1983; 3:243-246. · Zbl 0524.93037
[57] MorseAS. New directions in parameter adaptive control systems. Proceedings of the 23rd IEEE Conference on Decision and Control, Las Vegas, NV, 1984; 1566-1568.
[58] HeymanM, LewisJH, MeyerG. Remarks on the adaptive control of linear plants with unknown high frequency gain. Systems and Control Letters1985; 5(6):357-362. · Zbl 0571.93036
[59] ByrnesCI, WillemsJC. Adaptive stabilization of multivariable linear systems. Proceedings of the 23rd IEEE Conference on Decision and Control, Las Vegas, NV, 1984; 1547-1577.
[60] IlchmanA, OwensD, Pratzel‐WoltersD. Remarks on the adaptive control of linear plants with unknown high frequency gain. Systems and Control Letters1987; 8:397-404. · Zbl 0632.93046
[61] MareelsI, PoldermanJ. Adaptive Systems: An Introduction. Birkhauser: Boston, MA, 1996. · Zbl 0923.93028
[62] BroussardJ, BerryP. Command generator tracking ‐ the continuous time case. Technical Report TASC, Technical Report TIM‐612‐1, 1978.
[63] IhCH, WangS, LeondesC. Application of adaptive control to space stations. AIAA Paper 85‐1970, August 1985.
[64] IhCH, BayardD, WangSJ. Adaptive controller design for space station structures with payload articulation. Proceedings of 4th IFAC Symposium on Control of Distributed Parameter Systems, University of California, Los Angeles, 1986.
[65] BayardD, IhCH, WangSJ. Adaptive control for flexible space structures with measurement noise. Proceedings of American Control Conference, Evanston, IL, 1987; 81-94.
[66] IhCH, WangS, LeondesC. Adaptive control for the space station. IEEE Control Systems Magazine1987; 7(1):29-34.
[67] LeeF, FongI, LinY. Decentralized model reference adaptive control for large flexible structures. Proceedings of American Control Conference, Evanston, IL, 1988; 1538-1544.
[68] MuftiIH. Model reference adaptive control for large structural systems. Journal of Guidance, Control, and Dynamics1987; 7(5):507-509.
[69] ShimadaY. Adaptive control of large space structures. Proceedings of the 16th International Symposium on Space Technology and Science, Sapporo, Japan, 1998.
[70] BalasM. Adaptive control of aerospace structures with persistent disturbances. Proceedings of 15th IFAC Symposium on Automatic Control in Aerospace, Bologna, Italy, 2001.
[71] SanchezE. Adaptive control robustness in flexible aircraft application. Proceedings of the American Control Conference, Evanston, IL, 1986; 494-496.
[72] MorseW, OssmanK. Model following reconfigurable flight control system for the AFTI/F‐16. Journal of Guidance, Control, and Dynamics1990; 13(6):969-976.
[73] BarkanaI, FischlR. A simple adaptive enhancer of voltage stability for generator excitation control. Proceedings of the American Control Conference, Evanston ,IL, 1992; 1705-1709.
[74] BarkanaI, GuezA. Simplified techniques for adaptive control of robots. In Control and Dynamic Systems‐Advances in Theory and Applications, Vol. 41, LeondesC (ed.) (ed.). Academic Press: New York, 1991. · Zbl 0727.00021
[75] ShibataH, SunY, FujinakaT, MaruokaG. Discrete‐time simplified adaptive control algorithm and its applications to a motor control. IEEE International Symposium on Industrial Electronics (ISIE’96), Warsaw, Poland, 1996; 248-253.
[76] SunY, ShibataH, MaruokaG. Discrete‐time simplified adaptive control of a DC motor based on asymptotic output tracker. Transactions of the Institute of Electrical Engineers of Japan2000; 120‐D(2):254-261.
[77] PalermCC, BequetteBW, OzcelikS. Robust control of drug infusion with time delays Using direct adaptive control: Experimental results. Proceedings of the American Control Conference, Evanston, IL, 2000; 2972-2976.
[78] PalermCC, BequetteBW. Direct model reference adaptive control and saturation constraints. Proceedings of the 15th Triennial IFAC World Congress, Barcelona, 2002; 2714-2719.
[79] BarkanaI, KaufmanH. Simple adaptive control of uncertain systems. International Journal of Adaptive Control and Signal Processing1988; 2(1):133-143.
[80] CohenK, BossertDE. Fuzzy logic non‐minimum phase autopilot design. Proceedings of AIAA Guidance, Navigation, and Control Conference, Austin, TX, August 2003. AIAA paper 2003‐5550.
[81] WangLX. A Course in Fuzzy Systems and Control. Prentice‐Hall: Upper Saddle River, NJ, 1997; pp. 221-225.
[82] BarkanaI. Classical and simple adaptive control for non‐minimum phase autopilot design. Journal of Guidance, Control, and Dynamics2005; 24(4):631-638. (also in shorter form in Proceedings of the AIAA GN&C 2004, paper AIAA2004‐4868).
[83] BarkanaI. Gain conditions and convergence of simple adaptive control. International Journal of Adaptive Control and Signal Processing2005; 19(1):13-40. · Zbl 1064.93024
[84] SlotineJJE, LiWP. Applied Nonlinear Control. Englewood Cliffs: Prentice‐Hall, 1991. · Zbl 0753.93036
[85] LaSalleJP. Stability of nonautonomous systems. Nonlinear Analysis, Theory, Methods and Applications1976; 1(1):83-90. · Zbl 0355.34037
[86] LaSalleJP. The Stability of Dynamical Systems, 2nd ed., SIAM: New York, 1976. · Zbl 0364.93002
[87] ArtsteinZ. Limiting Equations Stability of Nonautonomous Ordinary Differential Equations, Appendix A in LaSalle, The Stability of Dynamical Systems, 2nd ed., SIAM: New York, 1976. · Zbl 0364.93002
[88] ArtsteinZ. Uniform asymptotic stability via the limiting equations. Journal of Differential Equations1977; 25:184-202. · Zbl 0358.34045
[89] ArtsteinZ. Uniform asymptotic stability via the limiting equations. Journal of Differential Equations1978; 27:172-189. · Zbl 0383.34037
[90] SastriS. Nonlinear Systems. Springer: New York, 1999. · Zbl 0924.93001
[91] KhalilHK. Nonlinear Systems, 3rd ed., Prentice‐Hall: Englewood Cliffs, 2002.
[92] VidyasagarM. Nonlinear Systems Analysis, 2nd ed., SIAM: Philadelphia, 2002. · Zbl 1006.93001
[93] HouM, DuanG, GuoM. New versions of Barbalat’s lemma with applications. Journal of Control Theory and Applications2010; 8:545-547.
[94] LeeT‐C, LiawD‐C, ChenB‐S. A general invariance principle for nonlinear time‐varying systems and its applications. IEEE Transactions on Automatic Control2001; 46(12):1989-1993. · Zbl 1011.93058
[95] BarkanaI. Is there a simple and robust adaptive control?53rd Israel Annual Conference on Aerospace Sciences, Israel, March 2005; 1035-1063.
[96] BarkanaI. A modified invariance principle and gain convergence in adaptive control. 2008 IEEE 25th Convention of Electrical and Electronics Engineers in Israel (IEEEI 2008), Eilat, Israel, December 2008; 800-804.
[97] TorresS, MehielE. Nonlinear direct adaptive control and disturbance rejection for spacecraft. Proceedings of the AIAA GNC 2006, paper AIAA2006‐6038, Keystone, Colorado, 2006.
[98] MareelsI. A simple self‐tuning controller for stable invertible system. Systems and Control Letters1984; 4:5-16. · Zbl 0528.93046
[99] IwaiZ, MizumotoI. Robust and simple adaptive control systems. International Journal of Control1992; 55:1453-1470. · Zbl 0761.93043
[100] IwaiZ, MizumotoI. Realization of simple adaptive control by using parallel feedforward compensator. International Journal of Control1994; 59:1543-1565. · Zbl 0806.93032
[101] FradkovAL. Adaptive stabilization of minimal‐phase vector‐input objects without output derivative measurements. Physics‐Doklady1994; 39(8):550-552. · Zbl 0845.93076
[102] BarkanaI. Output feedback stabilizability and passivity in nonstationary and nonlinear systems. International Journal of Adaptive Control and Signal Processing2010; 24(7):568-591. (Published online 3 November 2009). · Zbl 1200.93111
[103] JohanssonR, RobertssonA. Observer‐based strict positive‐real (SPR) feedback control system design. Automatica2002; 38(9):1557-1564. · Zbl 1008.93059
[104] BarkanaI. Adatptive Control can Robustify Uncertain Control Systems. Proceedings American Control Conference, Baltimore, MD, 1994; 63-67.
[105] RitonjaJ, DolinarD, GrcarB. Simple adaptive control for stability improvement. Proceedings of the 2001 IEEE International Conference on Control and Applications, (ICCA), Mexico City, Mexico, 2001; 29-35.
[106] JeongGJ, KimIH, SonYI. Application of simple adaptive control to a DC/DC boost converter with load variation. ICCAS‐SICE Conference, Fukuoka, Japan, 2009; 1747-1751.
[107] MorseQ, OssmanK. Model following reconfigurable flight control system for the AFTT/F‐16. Journal of Guidance, Control, and Dynamics1990; 13(6):969-976.
[108] YaeshI, ShakedU, YossefT. Simplified adaptive control of F16 aircraft pitch and angle‐of‐attack loops. 44th Israel Annual Conference on Aerospace Sciences, Israel, February 25-26, 2004.
[109] FradkovAL, AndrievskyB. Combined adaptive controller for UAV guidance. European Journal of Control2005; 11(1):71-79. · Zbl 1293.93445
[110] BelkharrazAI, SobelK. Simple adaptive control for aircraft control surface failures. IEEE Transactions on Aerospace and Electronic Systems2007; 43(2):600-611.
[111] AnS, MaY, CaoZ. Applying simple adaptive control to magnetic levitation system. Second International Conference on Intelligent Computation Technology and Automation, Changsha, Hunan, 2009; 746-749.
[112] YasserM, MizumotoI. Simple adaptive control using neural networks with offset error reduction for an SISO magnetic levitation system. International Journal of Advanced Mechatronic Systems2011; 3(5/6):355-364.
[113] FradkovAL, AndrievskyB, PeaucelleD. Adaptive control design and experiments for LAAS Helicopter benchmark. European Journal of Control2008; 14(4):329-339. · Zbl 1293.93444
[114] PeaucelleD, AndrievskyB, MahoutV, FradkovA. Robust simple adaptive control with relaxed passivity and PID control of a helicopter benchmark. The 18th IFAC World Congress, Milano, Italy, August 28 ‐ September 2, 2011; 2315-2320.
[115] MagantiGB, SinghSN. Simplified adaptive control of an orbiting flexible spacecraft. Acta Astronautica2007; 61:575-589.
[116] MooijE. Passivity analysis for non‐linear, non‐stationary entry capsules: Translational motion. The 18th IFAC World Congress, Milano, Italy, August 28 ‐ September 2, 2011; 6549-6554.
[117] PeaucelleD, DrouotA, PittetC, MignotJ. Simple adaptive control without passivity assumptions and experiments on satellite attitude control DEMETER benchmark. The 18th IFAC World Congress, Milano, Italy, August 28 ‐ September 2, 2011; 6535-6540.
[118] UlrichS, SasiadekJZ, BarkanaI. Modeling and direct adaptive control of a flexible‐joint manipulator. Journal Guidance, Control, and Dynamics2012; 35(1):25-39.
[119] RusnakI, WeissH, BarkanaI. Improving the performance of existing missile autopilot using simple adaptive control. The 18th IFAC World Congress, Milano, Italy, August 28 ‐ September 2, 2011.
[120] LiuM, XuS, HanC. A backstepping simple adaptive control application to flexible space structures. Chinese Journal of Aeronautics2012; 25(3):446-452.
[121] ItoK. Control performance comparison of simple adaptive control to water hydraulic servo cylinder system. Proceedings of 19th Mediterranean Conference on Control and Automation, Corfu, Greece, 2011; 195-200.
[122] ItoK, YamadaT, IkeoS, TakahashiK. Application of simple adaptive control to water hydraulic servo cylinder system. Chinese Journal of Mechanical Engineering2013; 25(5):882-888.
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