This research presents a composite learning–based finite-time nonsingular terminal sliding mode control (CL-FNTSMC) strategy for path tracking of intelligent vehicles. The controller is designed to handle parametric uncertainties, unmodeled dynamics, and external disturbances by combining three key elements: a unified error model that lumps uncertainties, a nonlinear disturbance observer for online disturbance estimation and compensation, and a composite learning law that fuses tracking and prediction errors for parameter adaptation. The nonsingular terminal sliding surface employs a continuously differentiable nonlinear function to guarantee finite-time convergence and to avoid singularity. Lyapunov-based proofs establish practical finite-time stability, and comparative simulations indicate improved tracking accuracy, faster convergence, and stronger disturbance rejection versus conventional NTSMC, adaptive fast NTSMC, and PID controllers.
The path tracking control (PTC) problem is posed for intelligent vehicles whose dynamics are nonlinear, strongly coupled, and affected by multiple sources of uncertainty. The paper formulates a unified path tracking error model that explicitly represents the lumped uncertainty, which comprises parametric perturbations, unmodeled dynamics, and external disturbances. This lumped-uncertainty formulation underpins the robust control design and motivates the inclusion of a real-time disturbance estimator to reduce conservativeness in controller gains.
The modeling aims to capture the essential tracking errors relevant to trajectory following while acknowledging that exact parameter values and some dynamic effects may be unknown or time-varying. The author emphasizes that many practical driving scenarios do not satisfy the restrictive persistent excitation (PE) condition required by conventional adaptive schemes, motivating alternative learning mechanisms that function under weaker excitation assumptions.
The proposed CL-FNTSMC controller integrates a nonsingular terminal sliding mode controller (NTSMC) with composite learning–based parameter adaptation and a disturbance observer. The sliding surface is constructed as a nonsingular terminal surface using a continuously differentiable nonlinear function. This design ensures finite-time convergence of sliding variables and avoids singularities that can occur in terminal sliding mode formulations.
The control law combines the sliding mode action for robustness to matched uncertainties with the feedforward compensation provided by the disturbance observer and the parameter estimates obtained from the composite learning mechanism. The resulting closed-loop design targets both fast transient response and high steady-state precision while maintaining robustness against lumped uncertainties.
Rigorous Lyapunov-based analysis is provided to show practical finite-time stability of the closed-loop system when the CL-FNTSMC scheme is applied. The theoretical development links the sliding surface properties, adaptive learning law, and observer dynamics to the overall stability and convergence results reported.
A central innovation in the paper is the composite learning law that drives online parameter estimation using two information sources: tracking errors and prediction errors generated by a serial–parallel estimation model. Unlike traditional adaptive sliding mode controllers that update parameters solely from tracking errors and therefore depend on the PE condition for convergence, the composite learning approach relaxes that requirement.
The serial–parallel estimation model constructs prediction errors which, combined with tracking errors, are used in a composite update law. This allows accurate online estimation of unknown parameters under the weaker interval excitation condition. The paper notes that interval excitation is significantly less restrictive and more likely to be satisfied in realistic driving scenarios than the classical PE condition, improving practical applicability of online adaptation.
Theoretical analysis within the article establishes parameter convergence properties facilitated by the composite learning law, tied to the weaker excitation condition.
To handle lumped disturbances arising from unmodeled dynamics and external inputs, the paper integrates a nonlinear disturbance observer (NDO). The NDO provides real-time estimates of lumped disturbances which are then fed forward into the controller to compensate for their effect, reducing the need for overly conservative robust gains.
The disturbance observer operates cooperatively with the sliding mode control and composite learning adaptation. By estimating disturbances online and compensating them in feedforward, the scheme improves disturbance rejection and enhances the overall robustness of path tracking performance. The disturbance observer's inclusion is explicitly cited as a mechanism that substantially enhances robustness when compared with controllers that lack such estimation and compensation.
Comprehensive simulations examine the CL-FNTSMC under scenarios with aggressive disturbances and significant parametric uncertainties. Comparative benchmarks include conventional nonsingular terminal sliding mode control (NTSMC), an adaptive fast NTSMC (AFNTSMC), and a PID controller.
Simulation outcomes reported in the article show that the proposed CL-FNTSMC achieves superior tracking accuracy and faster convergence to the reference trajectory, as well as markedly improved disturbance rejection. The author attributes these gains to the cooperative integration of the composite learning law, the nonsingular terminal sliding surface ensuring finite-time convergence, and the real-time disturbance estimation provided by the nonlinear observer.
The results are used to support the claim that CL-FNTSMC provides an effective balance of fast transient response, high steady-state precision, and strong robustness in the presence of real-world uncertainties and disturbances.
The paper concludes that the CL-FNTSMC framework effectively addresses key challenges in intelligent vehicle path tracking arising from uncertainties and disturbances. The chief contributions outlined are: the unified lumped-uncertainty error model with disturbance observation; the composite learning law that enables parameter convergence under interval excitation; and the nonsingular terminal sliding surface design that guarantees finite-time convergence without singularity.
The author reports that theoretical Lyapunov analysis supports practical finite-time stability and that simulations demonstrate performance improvements over several alternative controllers. The article states that all simulation parameter settings used to produce the reported results are included in the manuscript.