In this paper, the singularity-free adaptive fuzzy fixed-time control problem is studied for an uncertain n-link robotic system with the position tracking error constraint. The controlled robotic system can be described as multiple input multiple output system. So as to implement the user-defined performance, an improved error conversion mechanism based on performance functions is presented such that the converted error is limited to an interval greater than zero, and an appropriate barrier Lyapunov function (BLF) is constructed to avoid the breach of position tracking error constraint. The fuzzy approximator is utilized to estimate the unknown functions. The significance and challenges of this paper are to establish a new error conversion mechanism and design corresponding BLF that can be integrated in fixed-time control design to present a singularity-free adaptive fuzzy fixed-time control scheme. Benefits of the proposed adaptive fixed-time controller in comparison to the current approaches are that it cannot cause the singularity issue appearing in backstpping-based fixed-time control design and ensures quick transient response. Combining with Lyapunov stability theory, the boundedness of the closed-loop signals is ensured, and the position tracking error can be constrained in the user-defined performance boundaries. Finally, simulation results demonstrate the feasibility of the proposed control strategy.

This paper investigates the problem of event-based decentralized adaptive fuzzy output-feedback finite-time control for the large-scale nonlinear systems. The full-state tracking error constraints, unmeasured states and external disturbances are simultaneously considered in the controlled systems. The unknown auxiliary functions are modelled by using fuzzy logic systems (FLSs), and a state observer is established to estimate unmeasured states. By taking a new error transformation method based on prescribed performance functions (PPFs) and constructing corresponding barrier Lyapunov functions (BLFs), the predefined system error dynamic performance is ensured. Then, on the basis of the event-triggered control technique and the backstepping recursive design technique, a new eventbased adaptive fuzzy nonsingular finite-time control strategy is proposed, and the “singularity” problem existing in backstepping design procedure is avoided. Moreover, by using the finite-time stability criterion, it is proven that the proposed control strategy can ensure the boundedness of the whole system variables and achieve all the state tracking errors evolve within the predesigned performance regions in finite time. Finally, the effectiveness of the proposed control strategy is verified by using some simulation results.

This article proposes a variable-gain state observer-based sliding mode self-healing control (VSO-based SMSHC) method for a wastewater treatment process (WWTP) with changeable external disturbances and sensor failures. To reconstruct the disturbances and unmeasured system states, a novel VSO is developed, in which the VSO gains are adjusted by following an automatic variable-gain mechanism for adapting to the variation of external disturbances. An adaptive compensation coefficient of failure factor is designed to counteract the failure effects on observation and tracking performance. By utilizing the cubic absolute-value Lyapunov stability criterion, it is shown that system stability and tracking performance of WWTP are guaranteed. Experimental studies are carried out on a standardized platform of WWTP, and the results on dissolved oxygen and nitrate nitrogen regulation indicate that the proposed control strategy can ensure excellent control performance and reduce both failure and disturbance impacts.

The increasing utilization of wastewater necessitates dedicated attentions to the potential security threats, and formulate strategies for defense, response, and future protection. The nonideal actuator subject to the faults and constraints may underload the driving force and reduce the sewage purification efficiency. This article proposes an adaptive performance self-recovery control strategy for the wastewater treatment process (WWTP) with nonideal actuator. Therein, a Gaussian error function is reconstructed to imitate the asymmetrical actuator constraints. A fault effect identifier is designed to indirectly acquire fault information. Two boundary estimators are co-designed to estimate the infimum of virtual controller gain and the supremum of lumped uncertainty, respectively. The proposed control strategy can largely enhance the faulty performance self-recovery capability of the WWTP, while ensuring robust output regulation and fast convergence. Extensive experiments on dissolved oxygen control are executed on a WWTP platform to show the efficacy of the suggested control scheme.

With the increase of wastewater treatment volume and the insufficiency of preventive maintenance measures, the potential safety hazards of wastewater treatment process (WWTP) are gradually emerging. The unplanned sensor failures may result in false information feedback and reduce the reliability of the control system. This paper attempts to formulate a working mode substitution-based performance self-recovery control (WMS-based PSRC) strategy for the WWTP against sensor failures. Therein, a substitution indication-based switching function scheme is developed to automatically activate different sensor working modes. The transient and steady-state process regulation performance after one working mode substitution are guaranteed by establishing the prescribed-time performance function and error transformation dynamics. Then, an adaptive performance self-recovery control is developed to ensure the desired regulation level of the WWTP. Extensive studies on a recognized WWTP platform illustrate that the proposed control scheme can guarantee the working mode substitution and desired regulation performance while mitigating the failure detriment. Note to Practitioners —The vulnerability of industrial control systems in terms of policy, architecture and platform, as well as the hysteresis and subjectivity of manual operations on sensor maintenance, will result in unstable process performance, loss of critical control data, unnecessary workload and economic losses. In this paper, a WMS-based PSRC is presented for the WWTP with sensor failures. Three main aspects are contained: mode substitution, performance guarantee and WMS-based PSRC structure. The total sensor working modes are divided, meanwhile the switching function index is updated or maintained based on the mode substitution indication. After reconstructing performance function, the guaranteed performance technology is developed and applied to improve response rate and regulation accuracy. Then, a WMS-based PSRC structure is designed to comprehensively analyse the monitoring and control process. Finally, the industrial application results of WWTP demonstrate that the WMS-based PSRC can optimize process operation. This strategy is, therefore, useful for practitioners to achieve the fast performance self-recovery after the abnormal conditions.

Dear Editor, This letter is concerned with the data-driven fault compensation tracking control for a coupled wastewater treatment process (WWTP) subject to sensor faults. Invariant set theory is introduced to eliminate the completely bounded and differentiable conditions of coupled non-affine dynamics and to explicitly express the control inputs. An adaptive fault compensation mechanism is constructed to accommodate the effects of sensor faults. By employing a cubic absolute-value Lyapunov criteria, it is shown that all the signals are bounded and the tracking error converges to an adjustable neighborhood near the origin. Experiment studies are executed on a standardized platform of WWTP to illustrate the effectiveness of the proposed strategy.