This article proposes a design of an adaptive control for nonlinear systems which satisfy the Lipschitz condition. The objective is the use of the new reformulation of reciprocal-state space form in adaptive control designs. The presented controller is composed of a state-derivative feedback approach with adaptive gains based on the Lyapunov stability theorem. The first control approach deals with the case of system stabilization. The second is an extension to the tracking problem. High performances are shown through real-time implementation with digital signal processing device (ARDUINO UNO R3 and MEGA 2560).
MahapatraSSubudhiB.Design and experimental realization of a backstepping nonlinear H∞ control for an autonomous underwater vehicle using a nonlinear matrix inequality approach. T I Meas Control2018; 40(11): 3390–3403.
2.
SchmidtPMorenoJSchaumA. Observer design for a class of complex networks with unknown topoloy. In: Proceedings of the 19th IFAC World Congress the international federation of automatic control, Cape Town, South Africa, 24–29 August 2014, pp.2812–2817.
3.
GripaHSaberiAJohansenbT.Observers for interconnected nonlinear and linear systems. Automatica2012; 48: 1339–1346.
4.
IovineASiadSDammGet al. Nonlinear control of a DC microgrid for the integration of photovoltaic panels. IEEE T Autom Sci Eng2017; 14: 524–535.
5.
KravarisCChungC.Nonlinear state feedback synthesis by global input/output linearization. AICHE J1987; 33(4): 592–603.
6.
TeelAPralyL.Tools for smiglobal stabilization by partial state and output feedback. SIAM J Control Optim1995; 33(5): 1443–1488.
7.
CemUKachrooP.Sliding mode measurement feedback control for antilock braking systems. IEEE T Contr Syst T1999; 7(2): 271–281.
8.
RodriguezANijmeijerH.Mutual synchronization of robots via estimated state feedback: a cooperative approach. IEEE T Contr Syst T2004; 12(4): 542–554.
9.
LiYZhengTLiY.Extended state observer based adaptive back-stepping sliding mode control of electronic throttle in transportation cyber-physical systems. Math Probl Eng2015; 2015: 301656.
10.
PanHSunWGaoHet al. Disturbance observer-based adaptive tracking control with actuator saturation and its application. IEEE T Autom Sci Eng2016; 13: 868–875.
11.
PagillaPZhuY. Controller and observer design for Lipschitz nonlinear systems. In: Proceedings of the American control conference, Boston, MA, 30 June–July 2, pp.2379–2384. New York: IEEE.
12.
ThabetAFrejGBHBoutayebM.Observer-based feedback stabilization for Lipschitz nonlinear systems with extension to H∞ performance analysis: design and experimental results. IEEE T Contr Syst T2018; 26: 321–328.
13.
SakthivelRSelvarajPLimYet al. Adaptive reliable output tracking of networked control systems against actuator faults. J Franklin Inst2017; 354: 3813–3837.
14.
WuRZhangWSongFet al. Observer-based stabilization of one-sided Lipschitz systems with application to flexible link manipulator. Adv Mech Eng2015; 7: 1–8.
15.
YaoBTomizukaM.Adaptive robust control of mimo nonlinear systems in semi-strict feedback forms. Automatica2001; 37(9): 1305–1321.
16.
LiDLiuYTongSet al. Neural networks-based adaptive control for nonlinear state constrained systems with input delay. IEEE T Cybernetics2018; PP: 1–10.
17.
LiuYLuSTongSet al. Adaptive control-based barrier Lyapunov functions for a class of stochastic nonlinear systems with full state constraints. Automatica2018; 87: 83–93.
18.
LiuYTongS.Barrier Lyapunov functions for Nussbaum gain adaptive control of full state constrained nonlinear systems. Automatica2017; 76: 143–152.
19.
YaoJJiaoZMaD.Extended state observer based output feedback nonlinear robust control of hydraulic systems with backstepping. IEEE T Ind Electron2014; 61(11): 6285–6293.
20.
LiuHZhangTTianX.Continuous output-fedback finite time control for a class of second-order nonlinear systems with disturbances. Int J Robust Nonlin2016; 26: 218–234.
21.
GeSHangCZhangT.Adaptive neural network control of nonlinear systems by state and output feedback. IEEE T Syst Man Cyb1999; 29(6): 818–828.
22.
LiDLiD.Adaptive neural tracking control for an uncertain state constrained robotic manipulator with unknown time-varying delays. IEEE T Syst Man Cyb2017; PP: 1–10.
23.
KaewpraekNAssawinchaichoteW.H∞ fuzzy state-feedback control plus state-derivative-feedback control synthesis for photovoltaic systems. Asian J Control2016; 18: 1441–1452.
24.
HeS.Non fragile passive controller design for nonlinear markovian jumping systems via obserber-based control. Neurocomputing2015; 147: 350–357.
25.
GiuaASeatzuCBasileF.Observer-based state-feedback control of timed petri nets with deadlock recovery. IEEE T Automat Contr2004; 49: 17–29.
26.
TsengY. Control design for system with Lipschitz nonlinearity of state derivative variables in reciprocal state space form. In: International conference on image processing, electrical and computer engineering, Singapore, 8–9 July 2015, pp.26–32.
27.
KwakSWashingtonGYedavalliR. Full-state derivative feedback control based on the reciprocal state space framework using smart materials. In: 7th annual international symposium on smart structures and materials, Newport Beach, CA, 19 June 2000. Mathematics and Control in Smart Structures.
28.
FallahSKhajepourAFidanBet al. Vehicle optimal torque vectoring using state-derivative feedback and linear matrix inequality. IEEE T Veh Technol2013; 2: 1540–1552.
29.
TsengY.Vibration control of piezoelectric smart plate using estimated state derivatives feedback in reciprocal state space framework. Int J Contr Theory Appl2009; 2: 61–71.
30.
TsengY.Sliding mode control with state derivative feedback in novel reciprocal state space form. Adv Appl Nonlin Contr Syst2016; 635: 159–184
31.
MirmomeniMShafieeM. Tracking problem for mobile robot via singular systems theorem. In: Proceedings of Iranian Conference on Electrical Engineering 2015, ICEE15, Tehran, Iran, 19 June 2007, pp. 61–66.
32.
TsengYW. Stability, controllability and observability criteria for the reciprocal state space framework. In: Proceedings of the American control conference, Denver, CO, 4–6 June 2003. New York: IEEE.
BoukasE. Static output feedback control for linear descriptor systems: LMI approach. In: IEEE international conference on mechatronics and automation, Niagara Falls, ON, Canada, 20 July–1 August 2005, pp.1230–1234. New York: IEEE.
35.
TsengY.Control designs of singular systems expressed in reciprocal state space framework with state derivative feedback. Int J Contr Theory Appl2008; 1: 55–67.
