This paper solves the path following problem of unmanned surface vessels, where model uncertainties, external environmental disturbances, and input saturation are considered. Specifically, the fixed-time line of sight (FXTLOS) based on fixed-time theory is used to design a guidance subsystem where the convergence time is independent of multiple initial states. Given the unavailability of velocity information, novel cascaded extended state observers have been proposed to estimate velocities and unknown disturbances to provide feedback to the controller for better performance, where only position and heading information is required. Furthermore, fast finite-time sliding mode control is used to solve the motion control problem for the USV, where a suitable auxiliary system is designed to deal with the adverse effects of input saturation and to ensure the stability of the system. The stability of the whole system is demonstrated, and the stability of the kinematic and dynamic cascade system is analyzed. Finally, a large number of comparative simulation cases are given to demonstrate the effectiveness and superior performance of the proposed scheme.

Path following and obstacle avoidances are used in heading control and path replanning for unmanned surface vessels (USVs), which have attracted the interest of many researchers over the years. This paper investigates the path-following and obstacle avoidance problems for USVs. First, on the basis of the current position and desired path, an adaptive line-of-sight (ALOS) algorithm is used to obtain the desired heading angle, and the sideslip angle compensation is considered. Then, to ensure that the USV follows the desired path. Model predictive control (MPC) is used to reduce the lateral error. The event-triggered mechanism (ETM) strategy is utilized to reduce the computational cost of MPC. Moreover, to obtain accurate state quantities in real time, a linear extended state observer (LESO) is used to counteract the effects of external disturbances and the nonlinear term of the model. Furthermore, an improved obstacle avoidance algorithm based on the geometric relationship is proposed. This method can better ensure USV navigation safety and reduce consumption and computation. Lastly, multiple simulation experiments illustrate that the algorithm improves the path-following capability and security and ensures smooth input changes by setting input constraints. Therefore, the designed controller has better feasibility and robustness.

This paper addresses the tracking control of rigid spacecraft attitude systems that enable the user-defined error convergence domain, considering input saturation, asymmetric timevarying full-state constraints, event triggering, and disturbance compensation. Specifically, we first employ the Gaussian error function and the barrier Lyapunov function to address the input and full-state constraints. Then, to avoid solving the derivative of the virtual control signal directly, we introduce a command filter to estimate the derivative of the virtual control signal to simplify the controller design. Next, we propose an adaptive dynamic eventtriggering mechanism to reduce the communication burden and actuator wear. In addition, the barrier function guarantees that the convergence accuracy of the tracking error is not affected by the triggering mechanism. We design an effective switching self-tuning mechanism to compensate for the adverse effect of the uncertainty term, consisting of the external disturbance and the inertial matrix uncertainty, on the overall attitude system. Finally, the effectiveness and superiority of the proposed scheme are verified by theoretical analysis and simulation comparison

In this paper, we propose a global two-phase prescribed-time stable controller for rigid spacecraft attitude anti-disturbance tracking. This controller simultaneously addresses four critical problems: input saturation, explosion of complexity, external disturbances, and model uncertainty. First, an augmented input model is integrated into the controller design to handle saturation constraints. To avoid the “explosion of complexity” problem, we propose a global prescribed-time command filter to estimate the derivatives of the virtual inputs, where the settling time of the estimation error is prescribed by the user. Then, a switching self-tuning mechanism is designed to compensate for disturbances and model uncertainties affecting tracking performance. Next, based on this mechanism, we propose a global two-phase prescribed-time controller to achieve global two-phase prescribed-time convergence of the attitude tracking error. The global two-phase prescribed-time stability means dividing the whole time interval into two phases. In the first phase, the switching self-tuning mechanism updates the adaptive parameter online to find the upper bound of the uncertainty term. The closed-loop system is globally prescribed-time stable in the second phase, meaning that the user can prescribe the settling time of the system in this phase. Finally, we provide rigorous stability proofs and verify the effectiveness and superiority of our proposed scheme with numerical examples.

In this paper, we focus on solving the prescribed performance switchable trajectory tracking control problem for underactuated surface vessels, where input saturation, command communication burden, external disturbances, the user-defined convergence domain, and the “explosion of complexity” problem are considered. Specifically, first, we introduce a Gaussian error function to address the input saturation constraints and employ a command filter to avoid the “explosion of complexity” problem. Furthermore, we design a novel prescribed performance function to constrain the transient and steady-state indicators of the tracking error and allow switching the desired tracking trajectory. An adaptive hybrid event-triggering mechanism is subsequently proposed to mitigate redundant communication demands. Next, a switching self-tuning mechanism is constructed to compensate for the negative effects of the uncertainty term. Based on this mechanism, our scheme ensures that the error converges to a user-defined convergence domain that is independent of the uncertainty term. Finally, the effectiveness of the proposed scheme is demonstrated through Lyapunov-based stability analysis and numerical simulations.

Traditional finite-time/fixed-time control methods have been extensively studied due to their ability to quantitatively determine the settling time of a system. However, these approaches have several drawbacks, such as slow convergence rates, state-dependent settling times, and low control precision. To address these limitations, this article presents an innovative fast fixed-time control theory based on a variable exponential strategy. This approach significantly improves the practical convergence speed and control accuracy, while eliminating the drawback of state-dependent settling time inherent in conventional finite-time control frameworks. Leveraging the proposed theory, a high-precision fast fixed-time sliding mode control scheme is developed for permanent magnet synchronous motors. This methodology significantly improves control accuracy and reduces practical convergence time through the variable exponential strategy. Lyapunov stability analysis proves that the closed-loop tracking error can converge rapidly to an ultra-small neighborhood near the origin within a fixed time. Experimental results further validate the superiority of the proposed scheme, demonstrating exceptional performance in key metrics, including convergence speed and control accuracy. The latter achieves an enhancement of up to $\text{55.1}\%$. Compared with existing fixed-time control approaches, this approach has greater research significance and application potential, providing the technical basis for wider power electronics control applications.