Traditional Lyapunov stability theory cannot directly apply to constrained stochastic nonlinear systems when using barrier Lyapunov functions due to their inherent lack of radial unboundedness. This article presents a novel approach to establishing finite-time stability for such systems by employing Lyapunov functions. The proposed stability analysis relies on a time-varying gain function that remains uniformly bounded. This approach ensures that the system achieves finite-time stability with an arbitrarily prescribed upper bound on the settling time, thereby effectively avoiding the unbounded controller gain problem. The resulting stability is further extended to the finite-time state-feedback control for strict-feedback stochastic nonlinear systems with output constraints. Simulation studies validate the effectiveness of the proposed control scheme.

In this study, we investigate the prescribed-time non-singular terminal sliding mode control (TSMC) for high-order nonlinear systems. Initially, a novel time-varying, high-order terminal sliding mode manifold is recursively constructed. Based on this newly proposed manifold, a prescribed-time non-singular TSM controller is subsequently developed. The proposed algorithm effectively eliminates the singularity problem and offers a simpler method for specifying the convergence time, independent of initial system conditions and other design parameters. To mitigate the chattering issue of the controller, we introduce a variable-gain prescribed-time disturbance observer. Leveraging this observer, we develop a prescribed-time non-singular TSMC strategy. A rigorous Lyapunov analysis demonstrates the prescribed-time stability of both the proposed observer and controller. The uniform boundedness of the state signals and control input is also established using an inductive method. Finally, experimental validation is provided, confirming the effectiveness of the proposed control algorithm.

This study presents a novel prescribed-time high-order sliding mode (HOSM) controller for uncertain nonlinear systems. First, a new sliding mode dynamic system with mismatched terms is constructed. In contrast to existing HOSM algorithms, the proposed approach relaxes the assumption of gain functions imposed on the growth condition of the mismatched terms, allowing them to be unknown. Second, a novel prescribed-time HOSM controller is designed for the new sliding mode dynamic system using the concept of time-varying scaling function. Lyapunov analysis demonstrates that the proposed controller guarantees the convergence of the sliding variables to zero within a prescribed time, irrespective of the initial conditions of the system and other control parameters. Finally, simulation comparisons are provided to verify the theoretical results.

For full-state constrained nonlinear systems with input saturation, this article studies the output-feedback tracking control under the condition that the states and external disturbances are both unmeasurable. A novel composite observer consisting of state observer and disturbance observer is designed to deal with the unmeasurable states and disturbances simultaneously. Distinct from the related literature, an auxiliary system with approximate coordinate transformation is used to attenuate the effects generated by input saturation. Then, using radial basis function neural networks (RBF NNs) and the barrier Lyapunov function (BLF), an opportune backstepping design procedure is given with employing the dynamic surface control (DSC) to avoid the problem of "explosion of complexity." Based on the given design procedure, an output-feedback controller is constructed and guarantees all the signals in the closed-loop system are semiglobally uniformly ultimately bounded. It is shown that the tracking error is regulated by the saturated input error and design parameters without the violation of the state constraints. Finally, a simulation example of a robot arm is given to demonstrate the effectiveness of the proposed controller.

In this article, we extend the adaptive tracking control to more general nonlinear systems with multiple uncertainties, including output constraint, input delay, unknown parameter, and external disturbances for the first time. Without any growth assumptions, the adaptive backstepping technique is combined with the parameter separation technique to solve the parametric nonlinearities while the related results need to apply restrictive assumptions or use an approximation-based scheme to deal with them. To alleviate the serious uncertainties caused by output constraint and input delay, the barrier Lyapunov function (BLF) and the Pade approximation method are employed in a unified framework when the control coefficient is known. Under the case of the unknown control coefficient, the Nussbaum gain technique is further combined to compensate it. Then, under both cases, universal adaptive state-feedback control strategies merged with rigorous stability analysis are proposed, respectively, which guarantees all the signals are uniformly ultimately bounded. In addition, the reference signal tracks the system output into a compact set of the origin and the constraint of output is not violated. Finally, the proposed controllers are applied to an inverted pendulum system, which demonstrates the designed controller is effective.

This paper concerns the adaptive state-feedback control for a class of high-order stochastic nonlinear systems with uncertainties including time-varying delay, unknown control gain, and parameter perturbation. The commonly used growth assumptions on system nonlinearities are removed, and the adaptive control technique is combined with the sign function to deal with the unknown control gain. Then, with the help of the radial basis function neural network approximation approach and Lyapunov-Krasovskii functional, an adaptive state-feedback controller is obtained through the backstepping design procedure. It is verified that the constructed controller can render the closed-loop system semiglobally uniformly ultimately bounded. Finally, both the practical and numerical examples are presented to validate the effectiveness of the proposed scheme.

This paper is concerned with the practically finite-time (PFT) control problem for a class of more general nonlinear systems subject to mismatching time-varying disturbances. Without any extra assumptions on system nonlinearities, a composite controller is developed by introducing a disturbance observer and finite-time control technique. Based on the designed controller and Lyapunov stability theory, the PFT stability of the closed-loop system is strictly verified and proven to be a better convergence performance. Furthermore, as a byproduct of the proposed design method, the disturbance observer-based PFT control for high-order nonlinear systems is also shown to be possible. To the best of the authors' knowledge, it is the first PFT control result for high-order nonlinear systems with external disturbances. Finally, an application example of a singlelink robot system with disturbances and a numerical example are presented to demonstrate the effectiveness of the proposed scheme, respectively.

This paper is concerned with the state-feedback control for a class of stochastic high-order nonlinear systems with multiple time delays. A distinctive novelty lies in the removal of the traditional growth assumptions imposed on the delay-dependent nonlinear terms. Then, without any extra assumptions, a state-feedback controller is explicitly constructed based on the Lyapunov-Krasovskii functionals and recursive backstepping design, which guarantees the closed-loop system to be globally uniformly ultimately bounded (GUUB). Finally, a simulation example is shown to demonstrate the effectiveness of the proposed scheme.