This research outlines the development of an adaptive finite-time fractional-order sliding-mode controller aimed at achieving stabilization and control for the inverted pendulum cart system with limited sensing range of sensors. The proposed algorithm is formulated on the basis of a Barrier Lyapunov function, which unites the benefits of innovative adaptive fractional-order sliding-mode control with a finite-time methodology. The input force is established to stabilize the nonlinear inverted pendulum cart system while adjusting both the position and the pendulum angle to a value of zero. To enhance the robustness of the proposed controller in the face of uncertainties related to the friction and viscous coefficients of the system, these parameters are compensated through an adaptive multi-layer neural-network algorithm. Both the simulation results and the experimental findings validate that the stabilizing controller, which integrates a constrained adaptive finite-time fractional-order sliding-mode control, effectively stabilizes the nonlinear inverted pendulum cart system.
AlyAAThe VuMEl-SousyFF, et al. (2022) Fuzzy-based fixed-time nonsingular tracker of exoskeleton robots for disabilities using sliding mode state observer. Mathematics10(17): 3147.
2.
AyadMArichiFMegnafiH, et al. (2024) Real time stabilization of a rotary inverted pendulum using neural networks approach. Journal of Vibration and Control10775463251349249. doi: 10.1177/10775463251349249.
3.
BasaranS (2025) Modified inverted pendulum on a cart system with four-bar mechanism. ISA Transactions159: 364–374.
4.
ChuWLiCZhouY (2023) A rapid stabilization method of the flexible inverted pendulum based on constrained boundary circumferential motion. Mechanical Systems and Signal Processing187: 109895.
5.
DakshMSMishraP (2025) A feedback-assisted inverse neural network controller for cart-mounted inverted pendulum. Applied Computational Intelligence and Soft Computing1: 4873425.
6.
DeyBPandeySKSenguptaA (2025) Design of modified fractional order PID controller for cart inverted pendulum system. International Journal of Dynamics and Control13(4): 1–17.
7.
FengZLiRBWuL (2023) Adaptive decentralized control for constrained strong interconnected nonlinear systems and its application to inverted pendulum. IEEE Transactions on Neural Networks and Learning Systems35(7): 10110–10120.
8.
GuoZQXuJXLeeTH (2014) Design and implementation of a new sliding mode controller on an underactuated wheeled inverted pendulum. Journal of the Franklin Institute351(4): 2261–2282.
9.
HuJChenBGhoshBK (2024) Formation–circumnavigation switching control of multiple ODIN systems via finite-time intermittent control strategies. IEEE Transactions on Control of Network Systems11(4): 1986–1997.
10.
HuangJZhangTFanY, et al. (2019) Control of rotary inverted pendulum using model-free backstepping technique. IEEE Access7: 96965–96973.
11.
HuangBZhangSHeY, et al. (2020) Finite-time anti-saturation control for euler–lagrange systems with actuator failures. ISA Transactions124: 468–477.
12.
IrfanSMehmoodARazzaqMT, et al. (2018) Advanced sliding mode control techniques for inverted pendulum: modelling and simulation. Engineering Science and Technology, an International Journal21(4): 753–759.
13.
JafaryFATabatabaeiM (2022) Adaptive hierarchical fractional-order sliding mode control of an inverted pendulum–cart system. Arabian Journal for Science and Engineering47(11): 13927–13942.
14.
KangJSPaekSYRimCR (2022) A design of active disturbance rejection control with higher convergence rate and its application in inertia wheel pendulum stabilization. Journal of the Brazilian Society of Mechanical Sciences and Engineering44(10): 477.
15.
LeiCLiRZhuQ (2024) Design and stability analysis of semi-implicit cascaded proportional-derivative controller for underactuated cart-pole inverted pendulum system. Robotica42(1): 87–117.
16.
LiCCaiM (2019) Theory and Numerical Approximations of Fractional Integrals and Derivatives. Society for Industrial and Applied Mathematics.
17.
LiangSWangZStepanG (2021) Motion control of a two-wheeled inverted pendulum with uncertain rolling resistance and angle constraint based on slow-fast dynamics. Nonlinear Dynamics104(3): 2185–2199.
18.
MahmoudMSalehRMaarifA (2022) Stabilizing of inverted pendulum system using robust sliding mode control. International Journal of Robotics and Control Systems2(2): 230–239.
19.
MehediIMAnsariUAL-SaggafUM (2020) Three degrees of freedom rotary double inverted pendulum stabilization by using robust generalized dynamic inversion control: design and experiments. Journal of Vibration and Control26(23): 2174–2184.
20.
MessikhLGuechiEHBourahalaF, et al. (2022) Stabilization of the cart-inverted-pendulum system using trivial state-feedback to output-feedback control conversion. Automatika63(4): 640–655.
21.
MofidOKhalidAMobayenS, et al. (2023) Adaptive finite-time command-filtered backstepping sliding mode control for stabilization of a disturbed rotary-inverted-pendulum with experimental validation. Journal of Vibration and Control29(5): 1431–1446.
22.
MohrenTLDanielTLBruntonSL (2020) Learning precisely timed feedforward control of the sensor-denied inverted pendulum. IEEE Control Systems Letters4(3): 731–736.
23.
MokhtareZVuMTMobayenS, et al. (2022) Design of an LMI-based fuzzy fast terminal sliding mode control approach for uncertain MIMO systems. Mathematics10(8): 1236.
24.
MondalRDeyJ (2020) Performance analysis and implementation of fractional order 2-DOF control on cart–inverted pendulum system. IEEE Transactions on Industry Applications56(6): 7055–7066.
25.
NaderolasliA (2025a) Stabilization of plate and ball nonlinear system with limited field-of-view sensors using constrained adaptive sliding-mode controller. Advanced Control for Applications: Engineering and Industrial Systems7(3): e70025.
26.
NaderolasliA (2025b) Constrained super-twisting sliding-mode controller for beam and ball nonlinear system stabilization with limited field-of-view constraints. Iranian Journal of Science and Technology, Transactions of Electrical Engineering49(4): 1645–1659.
27.
NaderolasliAChatraeiA (2019) One DOF robot manipulator control through type-2 fuzzy robust adaptive controller. Journal of Automation, Mobile Robotics and Intelligent Systems13(1): 65–70.
28.
NaderolasliAHashemiMShojaeiK (2020) Approximation-based adaptive fault compensation backstepping control of fractional-order nonlinear systems: an output-feedback scheme. International Journal of Adaptive Control and Signal Processing34(3): 298–313.
NguyenTVADongBTBuiNT (2023) Enhancing stability control of inverted pendulum using Takagi–Sugeno fuzzy model with disturbance rejection and input–output constraints. Scientific Reports13(1): 14412.
31.
PathakRRMohantySSenguptaA (2024) An optimization-based adaptive sliding mode control for an inverted pendulum. IETE Journal of Research70(1): 542–557.
32.
PesterevAVEMorozovYV (2022) Stabilization of a cart with inverted pendulum. Automation and Remote Control83(1): 78–91.
33.
QuYLiuZCaiL (2025) Simultaneous planning and executing (SPAE) control for a fourth-order underactuated inverted pendulum with double-layer asynchronous convergence. ISA Transactions163: 162–171.
34.
SanjeewaSDParnichkunM (2022) Control of rotary double inverted pendulum system using LQR sliding surface based sliding mode controller. Journal of Control and Decision9(1): 89–101.
35.
TeeKPRenBGeSS (2011) Control of nonlinear systems with time-varying output constraints. Automatica47(11): 2511–2516.
36.
TianXPengHZengX, et al. (2021) A modelling and predictive control approach to linear two-stage inverted pendulum based on RBF-ARX model. International Journal of Control94(2): 351–369.
37.
TianHYiXZhangY, et al. (2025) Dynamical analysis, feedback control circuit implementation, and fixed-time sliding mode synchronization of a novel 4D chaotic system. Symmetry17(8): 1252.
38.
WangCWangFYuJ (2019) BLF-based asymptotic tracking control for a class of time-varying full state constrained nonlinear systems. Transactions of the Institute of Measurement and Control41(11): 3043–3052.
39.
XiongJJChenY (2025) RBFNN-Based parameter adaptive sliding mode control for an uncertain TQUAV with time-varying mass. International Journal of Robust and Nonlinear Control35(11): 4658–4668.
40.
XiongJJWangXYLiC (2025) Recurrent neural network based sliding mode control for an uncertain tilting quadrotor UAV. International Journal of Robust and Nonlinear Control35: 8030–8046.
41.
YaoQ (2020) Robust adaptive finite-time attitude tracking control of a 3D pendulum with external disturbance: numerical simulations and hardware experiments. Nonlinear Dynamics102(1): 223–239.
42.
ZaunerCGattringerHMullerA (2023) Multistage approach for trajectory optimization for a wheeled inverted pendulum passing under an obstacle. Robotica41(8): 2298–2313.
