Adaptive Prescribed-Time Tracking Control for Output-Constrained Hydraulic Servo Systems with Time-Varying Parameters

Fixed-time prescribed-performance path tracking control for intelligent vehicles based on adaptive neural network disturbance estimation

Intelligent vehicle path tracking is challenged by uncertain disturbances, such as modeling inaccuracies and external environmental influences, which will significantly compromise both the path tracking accuracy and stability. To address this, this paper proposes a fixed-time prescribed-performance (FTPP) path tracking control method based on adaptive neural network disturbance estimation. Firstly, a radial basis function neural network with an online-updated adaptive law is developed for real-time estimation of uncertain disturbances, effectively compensating for their impact within the control model. Subsequently, a backstepping controller with FTPP is designed by integrating a composite dynamic surface control method with finite-time control techniques. This approach not only enhances the system convergence rate but also mitigates the derivative explosion problem inherent in traditional backstepping, yielding a control law with adaptive disturbances compensation for precise steering control. Finally, based on Lyapunov stability analysis, the boundedness of the closed-loop signals is established under the given assumptions, and the lateral path tracking error is shown to remain within the prescribed-performance bounds under feasible initial conditions. CarSim-Simulink-based co-simulation results validate the effectiveness of the proposed control method in improving both path tracking accuracy and stability.

Predefined-time disturbance observer-based fuzzy tracking control for uncertain space robot with global prescribed performance.

In this paper, an adaptive fuzzy prescribed performance control strategy based on predefined-time theory is proposed for a space robot under external disturbances and dynamic uncertainties. Firstly, an adaptive fuzzy backstepping framework that integrates predefined-time control theory is presented. To mitigate the impact of external disturbances on tracking performance, a predefined-time nonlinear disturbance observer (PTNDO) is introduced to compensate for them, thereby enhancing the convergence accuracy of trajectory tracking control. Next, global predefined-time prescribed performance control (PTPPC) is introduced to improve the transient and steady-state performance of the control system. Additionally, a single-parameter fuzzy logic system (FLS) is introduced to compensate for dynamic uncertainties in the system. An adaptive fuzzy predefined-time controller is then developed based on PTNDO, PTPPC, and single-parameter FLS. Compared to multi-parameter FLS, single-parameter FLS reduces the consumption of computational resources while retaining the desired level of approximation accuracy. By utilizing PTNDO and PTPPC, the transient and steady-state performance of the space robot control system are enhanced and the limitations of traditional prescribed performance control caused by initial states are avoided. The predefined-time stability of the proposed controller is rigorously proven by using Lyapunov theory, and numerical simulations demonstrate its superiority and effectiveness compared with existing methods.

Adaptive predefined-time tracking control for stochastic nonlinear systems subject to asymmetric output constraints

This paper investigates the predefined-time tracking control problem for a type of strict-feedback stochastic nonlinear systems, in which the output variable is required to be constrained within an asymmetric interval and the nonlinearities are unknown. First, an improved practical predefined-time stability (PPTS) Lyapunov criterion for stochastic nonlinear systems is presented. Secondly, an asymmetric integral barrier Lyapunov function is constructed to handle the output constraint issue. On this basis, an adaptive predefined-time adaptive fuzzy tracking control algorithm is developed via the backstepping framework, where fuzzy logic systems (FLSs) are utilized to approximate unknown system dynamics. Through rigorous mathematical analysis and numerical simulations, it can be concluded that the proposed control scheme can not only drive all system variables to converge to steady states within a prescribed time in probability, but also make the output track the desired signal without violating the output constraint.

Practical Predefined-Time Adaptive Tracking Control for Uncertain Nonlinear Systems With Input Saturation

This paper investigates the practical predefined-time adaptive tracking control problem for uncertain nonlinear systems with input saturation. First, a practical predefined-time stability lemma is established, providing a theoretical basis for the controller design. Second, to eliminate the adverse effect of input saturation, a desired trajectory modification module is constructed, making the tracking mission more feasible. This scheme prevents the internal instability that traditional control schemes may encounter in the presence of input saturation. By constructing the predefined performance function and performing the coordinate transformation, it can be guaranteed that the tracking error does not exceed the constraint boundary while improving the transient performance of nonlinear systems. In addition, by combining the core function with the smooth projection operator to design the adaptive law, the non-parametric uncertainty problem is solved. Based on the predefined-time stability lemma within the framework of adaptive backstepping control method, a predefined-time adaptive tracking controller is designed. Mathematically, it is rigorously proven that the closed-loop system is practical predefined-time stable, and tracking error always evolves within the prescribed performance boundary. Finally, simulations are performed using the Micro-Electro-Mechanical System to verify theoretical findings. Note to Practitioners—Uncertain nonlinear systems are prevalent in engineering applications, such as Micro-Electro-Mechanical Systems (MEMS), industrial robotic arms, and precision manufacturing equipment. For these systems, stable tracking control confronts three key practical challenges: non-parametric uncertainties that degrade control accuracy, input saturation that triggers system internal instability, and the requirement for tracking tasks to be completed within a predefined time while satisfying error constraints. To address these challenges, this paper proposes a practical predefined-time adaptive tracking control method. Specifically, this method employs: a desired trajectory modification module to mitigate input saturation, a predefined performance function to constrain tracking errors, and an adaptive law to address non-parametric uncertainties. As the method is rigorously proven to be stable, its effectiveness is further verified through MEMS-based simulations. For practitioners working on the control of uncertain nonlinear systems, this work provides a reliable, time-constrained solution that bridges the gap between theoretical control design and real-world engineering requirements.

Prescribed-Time Adaptive Tracking for Nonlinear Systems via Nonvanishing Disturbance Observer and Command Filtering

This paper addresses the prescribed-time (PT) tracking control problem for a class of nonlinear systems subjected to nonvanishing uncertain disturbances. To address the issue of discontinuous observation error derivatives caused by parameter constraints in conventional prescribed-time observer (PTO) designs, an improved PTO with a novel time-varying gain structure is proposed. The proposed observer removes the need for additional parameter conditions, ensures global continuity of the observation error derivatives, and enables smooth disturbance estimation and control input switching. To handle the inherent complexity explosion issue in backstepping design, a finite-time command filter (FTCF) is subsequently employed to approximate the virtual control signals. The continuity properties of the signals provided by the aforementioned observer naturally satisfy the requirement of the command filter that the input signal be continuous and possess a first-order derivative over the domain of definition. An adaptive compensation mechanism is further developed to correct the approximation errors introduced by the command filter in an online manner. Simulation results demonstrate that the proposed control scheme effectively achieves PT tracking control with prescribed performance for nonlinear systems under nonvanishing disturbances, while ensuring the continuity and boundedness of all closed-loop signals. Note to Practitioners—The practical control of nonlinear systems, such as robotic manipulators and uncrewed vehicles, is significantly complicated by the presence of persistent nonvanishing disturbances. These disturbances, which do not decay to zero over time, can severely degrade tracking performance and even lead to instability. This work proposes a practical PT control framework for nonlinear systems subject to persistent nonvanishing disturbances, enabling error convergence to zero within a user-defined timeframe regardless of initial conditions. The core innovation integrates an improved PTO, a FTCF, and an adaptive event-triggered mechanism (ETM). The improved PTO ensures the global continuity of disturbance estimation error and its derivatives via a novel time-varying gain structure, eliminating the control signal jumps typical at switching instants in traditional PT designs. The FTCF completely circumvents the complexity explosion problem inherent in standard backstepping. The scheme allows engineers to directly and independently prescribe the convergence times for both disturbance observation and final tracking, independent of initial conditions. A prescribed performance function, based on a barrier Lyapunov function, guarantees that the system output adheres to predefined transient and steady-state performance bounds throughout operation. This work provides practitioners with a robust, high-performance, and implementable PT control solution for a wide class of disturbed nonlinear systems.

Prescribed‐Time Tracking Control of Nonlinear Strict Feedback Systems With Time‐Varying Parameters and Disturbances Under Full‐State Constraints