Conventional fault-tolerant control (FTC) schemes typically assume the exponent of the faulty input to be 1, overlooking its impact on actuator power. In this article, we propose a novel FTC strategy that extends the exponent to any positive odd integer, thus capturing higher-order fault effects. In addition, by integrating a Gaussian function to modify the constraint boundaries, a novel suction-cup-type prescribed performance function is proposed. Unlike existing prescribed performance functions, this design uses a suction cup module to regulate output overshoot without requiring asymmetric design. This design is globally effective, eliminating the initial feasibility conditions. Simulation results validate the effectiveness of the proposed scheme.

This paper presents an optimal control scheme for a class of nonlinear systems subject to input saturation and external disturbances, achieved through the integration of reinforcement learning (RL) and a self-regulated prescribed performance control (SRPPC) algorithm. The proposed architecture employs an Identifier-Critic-Actor RL structure, implemented via interval type-2 fuzzy logic systems (IT2FLSs), to accurately approximate unknown nonlinear dynamics while optimizing control performance. To circumvent the singularity issues inherent in conventional PPC, the SRPPC strategy is developed to dynamically initialize the prescribed performance bounds (PPBs) and autonomously relax them during severe disturbances or actuator saturation, thereby maintaining the tracking error within a feasible envelope. By synergizing RL-based optimization with the SRPPC safety mechanism, the resulting RL-SRPPC controller not only minimizes operational costs but also guarantees transient safety and strict adherence to performance specifications. Numerical simulations on a one-link manipulator demonstrate the robustness and superiority of the proposed scheme compared to existing methodologies.

This paper proposes a fuzzy control scheme that enforces a unified prescribed performance for full-state errors in input-saturated systems with external disturbances. The proposed scheme is characterized by three key innovations: First, a series of functional transformations are designed to guarantee multiple performance behaviors within a unified control framework, enabling desired behaviors through parameter selection without controller redesign. Second, a novel performance function for virtual errors completely eliminates strict initial value constraints, thereby removing offline verification computations and streamlining the design/implementation process. Third, an error-driven mechanism is developed to prevent singularities induced by input saturation and disturbances. Unlike existing flexible prescribed performance control methods that rely on a control input-driven mechanism, this mechanism offers two distinct advantages: it directly adjusts only a single boundary for a more straightforward adjustment, and operates without dependency on auxiliary system integration. This design eliminates adjustment delays while minimizing performance degradation caused by boundary relaxation. Simulations confirm the scheme’s efficacy and superiority.

This paper proposes a novel prescribed performance control scheme for stochastic micro-electro-mechanical system (MEMS) gyroscopes, addressing three critical issues overlooked by existing methods: control torque oscillation during rapid convergence, deviation in steady-state tracking errors in a global asymmetric design, and violation of monotonic constraints due to insufficient input capability. To tackle these challenges, the paper proposes a quadratic prescribed performance function design, a local asymmetric constraint design, and a customized non-monotonic design. These innovations effectively resolve the technical difficulties and establish comprehensive performance specifications for stochastic MEMS gyroscopes. The proposed scheme ensures boundedness in probability for all closed-loop signals and convergence of the tracking error to an arbitrarily small residual within a prescribed time. Simulation results confirm the effectiveness and superiority of the scheme.

This article presents an adaptive neural network control scheme with prescribed performance for stochastic nonlinear systems. Unlike existing adaptive stochastic control schemes that primarily utilize deterministic neural networks for approximations in complex stochastic environments, we employ stochastic neural networks to approximate the stochastic nonlinear terms, effectively resolving the "memory overflow" issue. Moreover, we propose a novel prescribed performance design method, which distinguishes itself from the previous prescribed performance control schemes by integrating a quadratic characteristic capable of suppressing transient input vibrations, along with a local asymmetric characteristic that optimize both transient output overshoot and steady-state error bias. Furthermore, the proposed control scheme is implemented within a fixed-time framework to ensure that all closed-loop systems are fixed-time bounded in probability, with the tracking error consistently within the predefined performance bounds. Simulation results validate the effectiveness of the proposed control scheme.

This research proposes a neural network-based super-twisting controller for robot joints. A modified fast nonsingular terminal sliding surface is introduced, which not only avoids singularity but also increases the convergence rate of the sliding mode control. To address the challenge of system uncertainty modeling, a type-2 fuzzy single hidden layer recurrent neural network (T2FSHLRNN) is proposed. The T2FSHLRNN, configured as a weighted combination of a type-2 fuzzy neural network and a single hidden layer network, demonstrates strong global learning ability. Leveraging its internal and external double-layer feedback mechanism, the network can incorporate both current and previous error information during the approximation process, effectively improving the approximation accuracy and reducing system chattering. Furthermore, an adaptive gain function is proposed and an adaptive terminal super-twisting controller based on T2FSHLRNN (ATSC-T2FSHLRNN) is developed. The system’s stability under unknown disturbance is ensured using Lyapunov synthesis. Based on this, the online parameter learning algorithm for T2FSHLRNN and the variable gains of ATSC are derived. Simulation confirms the effectiveness of the proposed ATSC-T2FSHLRNN.

This article presents an adaptive fuzzy control scheme capable of guaranteeing prescribed performance for stochastic nonlinear systems with unknown control directions. Unlike the majority of existing prescribed performance control schemes, the proposed scheme ensures the independence from initial errors and guarantees controllable overshoot. Moreover, the proposed prescribed function exhibits nonmonotonicity, which can be beneficial in control applications with input constraints. To address the challenge posed by unknown control directions, a novel class of multiple Nussbaum functions is introduced. Compared to the existing single Nussbaum function, the multiple Nussbaum functions can mitigate instability arising from the cancelation of multiple unknown signs. Additionally, to tackle unknown nonlinearities, a single-parameter fuzzy approximator is introduced, aiming to concurrently reduce computational complexity. Furthermore, a novel class of switching threshold event-triggered mechanisms is designed to address issues encountered in existing designs where parameter inequalities impose conservative constraints. The control scheme ensures that the tracking error converges to prescribed asymmetric boundaries with arbitrarily small residuals in a prescribed time, while also guaranteeing that all closed-loop signals are bounded in probability. The effectiveness and superiority of the control scheme are verified by simulation results.

The microelectromechanical system (MEMS) gyroscope is a complex nonlinear system with multiple variables, strong coupling, and susceptibility to stochastic disturbances. This paper presents an adaptive fuzzy control scheme for stochastic MEMS gyroscopes, with the primary objectives of reducing control vibration and achieving high precision prescribed performance tracking with low communication resources within a fixed-time backstepping framework. To address the stochastic disturbances and unknown nonlinear system dynamics, the interval type-3 fuzzy logic system (IT3FLS) is introduced. Additionally, a novel quadratic prescribed performance function (QPPF) is proposed to ensure satisfactory transient and steady-state performance of the system while mitigating initial control vibrations during fast error convergence. Furthermore, an event-triggered mechanism (ETM) is developed using a switching threshold strategy to minimize the communication load without compromising control accuracy. By utilizing the fixedtime command-filtered backstepping design method and newly introduced error-compensating signals, the issue of “explosion of complexity” is effectively resolved, and filtering errors are adequately compensated. The proposed control scheme guarantees that the tracking errors converge to a predefined set of arbitrarily small residuals in probability. In addition, all the closed-loop signals are within a fixed time bounded in probability (FTBIP). The simulation results validate the effectiveness and superiority of the proposed scheme.