This paper proposes a novel recursive terminal sliding mode structure for tracking control of third-order chained–form nonholonomic systems in the presence of the unknown external disturbances. Finite-time convergence of the disturbance approximation error is guaranteed using the designed disturbance observer. Under the proposed terminal sliding model tracking control technique, the finite-time convergence of the states of the closed-loop system is guaranteed via Lyapunov analysis. A new reaching control law is proposed to guarantee the existence of the sliding mode around the recursive TSM surface in a finite-time. Simulation results are illustrated on a benchmark example of third-order chained-form nonholonomic systems: a wheeled mobile robot. The results demonstrate that the proposed control technique achieves promising tracking performance for nonholonomic systems.
AghababaMP (2012) Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique. Nonlinear Dynamics69: 247–261.
2.
AghababaMP (2014) Chaotic behavior in fractional-order horizontal platform systems and its suppression using a fractional finite-time control strategy. Journal of Mechanical Science and Technology28: 1875–1880.
3.
AghababaMPAghababaHP (2012) A general nonlinear adaptive control scheme for finite-time synchronization of chaotic systems with uncertain parameters and nonlinear inputs. Nonlinear Dynamics69: 1903–1914.
4.
AghababaMPAghababaHP (2013) A Novel Finite-Time Sliding Mode Controller for Synchronization of Chaotic Systems with Input Nonlinearity. Arabian Journal for Science and Engineering38: 3221–3232.
5.
AghababaMPAghababaHP (2014) Finite-time stabilization of non-autonomous uncertain chaotic centrifugal flywheel governor systems with input nonlinearities. Journal of Vibration and Control20: 436–446.
6.
ChaouchDEFoitihZAKhelfiMF (2012) A self-tuning fuzzy inference sliding mode control scheme for a class of nonlinear systems. Journal of Vibration and Control18: 1494–1505.
7.
ChenWH (2004) Disturbance observer based control for nonlinear systems. IEEE Transactions on Mechatronics9: 706–710.
8.
ChenMWuQXCuiRX (2013) Terminal sliding mode tracking control for a class of SISO uncertain nonlinear systems. ISA Transactions52: 198–206.
9.
ChenMChenWH (2010) Sliding mode controller design for a class of uncertain nonlinear system based disturbance observer. International Journal of Adaptive Control and Signal Processing24: 51–64.
10.
FerraraAGiacominiLVecchioC (2008) Control of nonholonomic systems with uncertainties via second-order sliding modes. International Journal of Robust and Nonlinear Control18: 515–528.
11.
FuJChaiTSuCYJinY (2013) Motion/force tracking control of nonholonomic mechanical systems via combining cascaded design and backstepping. Automatica49: 3682–3686.
12.
GhommamJMehrjerdiHMnifFSaadM (2011) Cascade design for formation control of nonholonomic systems in chained form. Journal of the Franklin Institute348: 973–998.
13.
HuangJWenCWangWJiangZP (2013) Adaptive stabilization and tracking control of a nonholonomic mobile robot with input saturation and disturbance. Systems & Control Letters62: 234–241.
14.
JaniakMTchonK (2011) Constrained motion planning of nonholonomic systems. Systems & Control Letters60: 625–631.
15.
JawaadaWNooraniMSMAl-sawalhaMM (2012) Robust active sliding mode anti-synchronization of hyperchaotic systems with uncertainties and external disturbances. Nonlinear Analysis: Real World Applications13: 2403–2413.
16.
KimE (2002) A fuzzy disturbance observer and its application to control. IEEE Transactions on Fuzzy Systems10: 77–84.
17.
LuYS (2009) Sliding-mode disturbance observer with switching-gain adaptation and its application to optical disk drives. IEEE Transactions on Industrial Electronics56: 3743–3750.
18.
Majd VJ and Mobayen S (2015) An ISM-based CNF tracking controller design for uncertain MIMO linear systems with multiple time-delays and external disturbances. Nonlinear Dynamics 80: 591–613.
19.
MobayenS (2014a) Robust tracking controller for multivariable delayed systems with input saturation via composite nonlinear feedback. Nonlinear Dynamics76: 827–838.
20.
MobayenS (2014b) Design of LMI-based global sliding mode controller for uncertain nonlinear systems with application to Genesio's chaotic system. Complexity. doi: 10.1002/cplx.21545.
21.
Mobayen S (2014c) Design of CNF-based nonlinear integral sliding surface for matched uncertain linear systems with multiple state-delays. Nonlinear Dynamics 77: 1047–1054.
22.
MobayenS (2014d) Finite-time robust-tracking and model-following controller for uncertain dynamical systems. Journal of Vibration and Control. doi: 10.1177/1077546314538991.
23.
MobayenS (2014e) Fast terminal sliding mode controller design for nonlinear second-order systems with time-varying uncertainties. Complexity. doi:10.1002/cplx.21600.
24.
MobayenS (2014f) Finite-time stabilization of a class of chaotic systems with matched and unmatched uncertainties: An LMI approach. Complexity. doi:10.1002/cplx.21624.
25.
Mobayen S (2015a) Finite-time tracking control of chained-form nonholonomic systems with external disturbances based on recursive terminal sliding mode method. Nonlinear Dynamics 80: 669–683.
26.
Mobayen S (2015b) An LMI-based robust tracker for uncertain linear systems with multiple time-varying delays using optimal composite nonlinear feedback technique. Nonlinear Dynamics 80: 917–927.
27.
MobayenSMajdVJ (2012) Robust tracking control method based on composite nonlinear feedback technique for linear systems with time-varying uncertain parameters and disturbances. Nonlinear Dynamics70: 171–180.
28.
MobayenSMajdVJSojoodiM (2012) An LMI-based composite nonlinear feedback terminal sliding-mode controller design for disturbed MIMO systems. Mathematics and Computers in Simulation85: 1–10.
29.
Mobayen S, Yazdanpanah MJ and Majd VJ (2011) A finite-time tracker for nonholonomic systems using recursive singularity-free FTSM. American Control Conference, San Francisco, CA, USA, pp. 1720–1725.
30.
MoulayEPerruquettiW (2006) Finite time stability and stabilization of a class of continuous systems. Journal of Mathematical Analysis and Applications323: 1430–1443.
31.
NgoQHHongKS (2012) Adaptive sliding mode control of container cranes. IET Control Theory and Applications6: 662–668.
32.
OuMDuHLiS (2014) Finite-time formation control of multiple nonholonomic mobile robots. International Journal of Robust and Nonlinear Control24: 140–165.
33.
PamosoajiAKCatPTHongKS (2014) Sliding-mode and proportional-derivative-type motion control with radial basis function neural network based estimators for wheeled vehicles. International Journal of Systems Science45: 2515–2528.
SongBSunJQ (2011) Sliding mode control of uncertain dynamical systems with time delay using the continuous time approximation method. Journal of Vibration and Control18: 1254–1260.
36.
TianYPCaoKC (2007) Time-varying linear controllers for exponential of non-holonomic sysems in chained form. International Journal of Robust and Nonlinear Control17: 631–647.
37.
WeiXJZhangHFGuoL (2009) Composite disturbance-observer-based control and terminal sliding mode control for uncertain structural systems. International Journal of Systems Science40: 1009–1017.
38.
WuYWangBZongGD (2005) Finite-time tracking controller design for nonholonomic systems with extended chained form. IEEE Transactions on Circuits and Systems52: 798–802.
39.
XuYWangHLiuDHuangH (2013) Sliding mode control of a class of fractional chaotic systems in the presence of parameter perturbations. Journal of Vibration and Control. doi:1077546313486283.
