As equipment complexity continues to increase, failures become increasingly difficult to avoid. In repetitive process, traditional iterative learning fault-tolerant control methods cannot simultaneously account for the dynamic characteristics across both time and cycle domains, resulting in limited fault tolerance capabilities and requiring multiple learning cycles to achieve effective tracking. To address this challenge, for repetitive systems with uncertainty and fault, based on the high-order fully actuated (HOFA) system approach, an iterative learning fault compensation control method is developed. Based on this model, a fault observer is designed to estimate system uncertainties, faults, and state deviations, thereby providing essential information for controller design. Subsequently, an iterative learning fault-compensation controller is developed along the time domains to achieve stable reference tracking from the initial operation cycle. Meanwhile, compensation is incorporated based on the estimated fault signals to ensure both real-time tracking performance and long-term fault tolerance. Furthermore, the input-output stability of the closed-loop system is analyzed, and the controller parameters are derived using a parameterization-based algorithm. Ultimately, the effectiveness and feasibility of the developed method are demonstrated through an injection molding process.

This article addresses the robust model predictive control (MPC) problem for a class of networked control systems (NCSs) with polytopic uncertainties and hard constraints, where the controller design is complicated by the joint presence of an energy harvesting sensor (EHS) in the forward channel and the round-robin (RR) protocol in the backward channel. In such a setting, stochastic transmission behavior caused by random energy availability, together with fixed communication scheduling and immeasurable states, makes it difficult to guarantee recursive feasibility of the online optimization and mean-square (MS) stability of the closed-loop system. To capture these features, the mathematical expectation of a quadratic function depending on both the sensor energy level and the transmission order over an infinite horizon is constructed to formulate the optimization problem. To cope with the terminal constraint set (TCS) and the immeasurability of system states, an auxiliary optimization problem with guaranteed solvability is developed by employing inequality analysis and slack-matrix techniques, through which a suboptimal solution is obtained. Furthermore, sufficient conditions are derived to ensure the recursive feasibility of the proposed algorithm and the MS stability of the resulting closed-loop system with and without hard constraints. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.

As demand for personalized and customized products continues to rise, an increasing number of batch processes are being deployed into networked control systems to enhance control efficiency. However, the ensuing cybersecurity challenges have made the demand for efficient and secure control of batch processes increasingly urgent. Aiming at ensuring the stability of complex batch processes under potential deception attacks, a robust safety predictive tracking control strategy is developed to maintain reliable performance. Considering the issue of deception attacks, an extended deception attack model incorporating output error integration has been established. This model ensures controller design while enhancing the system's control accuracy effectively. According to the design model, a robust safety predictive tracking controller is crafted to ensure system safety and stability. Then, the linear matrix inequality conditions (sufficient conditions) guaranteeing system stability are derived using the robust safe invariant set and terminal constraint set. By solving sufficient conditions in real time, controller gain is obtained, thereby the control inputs can be adjusted dynamically, which overcomes the limitations of traditional offline methods when it comes to effectively handling the real-time dynamic characteristics of systems. Finally, the effectiveness of the presented method was validated through simulation of the injection molding process.

This paper proposes a novel reaching law for the sliding mode control (SMC) of uncertain nonlinear systems to address the inherent limitations of conventional reaching laws, such as chattering and slow convergence. The proposed strategy discards the traditional sign function in favor of a composite formulation integrating hyperbolic tangent (tanh) and arctangent (arctan) functions. By leveraging the continuity and saturation properties of these functions, the reaching law ensures that system states reach the sliding manifold rapidly when deviations are large and enter it smoothly as the sliding variable approaches zero. Theoretical analysis using Lyapunov stability theory proves that the system can achieve fixed-time convergence to the equilibrium point. To verify the effectiveness of the method, simulations were conducted on a two-link robot manipulator. The results demonstrate that the proposed controller effectively eliminates the singularity problem, suppresses chattering, and provides superior control precision compared to classical reaching laws.

Despite extensive investigations into the multi-user haptic-enabled robotic system (M-Hers), achieving scalable control design in the presence of non-passive human operators remains a key challenge. This is primarily due to the increasing complexity of stability conditions and interaction coupling as the number of operators grows. In this study, we address this challenge in two steps. First, we introduce the individual interaction environment (IIE) to isolate the passivity violations, which facilitates the independent control design for each human-robot subsystem, thereby enhancing the scalability with respect to the number of subsystems. Second, within the IIE framework, we identify passivity-violating components caused by partners' active behaviors and propose a novel augmented tank-based controller (ATBC) to guarantee passive IIE while maintaining high rendering accuracy. Specifically, the ATBC employs an energy-related power regulation strategy to enhance interaction safety and a time-varying control gain to mitigate the negative effects of power regulation on rendering fidelity. We validated the proposed method through collaborative haptic tasks on a customized M-Hers composed of three robots in four different scenarios. Comparative studies demonstrate that our approach effectively ensures IIE passivity in the presence of active human behaviors, while ensuring high reproducibility and achieving a favorable balance between passivity and rendering accuracy.

To address the issue that the outlet temperature control of the ethylene cracking furnace is significantly impacted by fuel gas flow, external disturbances and time delays, a novel multi-step compensated robust predictive cascade control method is proposed, aiming to reduce the fluctuation of outlet temperature and enhance control precision. Thermodynamic and heat transfer principles are first systematically integrated to derive and establish an outer-loop control model for the outlet temperature, which includes time delay, and an inner-loop control model for fuel gas flow. Subsequently, in the outer-loop, a robust time delay predictive controller is designed for the linear component, while a multi-step time delay compensator is developed to compensate for the impacts caused by unmodeled dynamics including high-order nonlinear terms and disturbances. This combined strategy effectively mitigates frequent fluctuations in the setpoint for fuel gas flow by compensating for the impacts of time delay and unmodeled dynamics. Furthermore, for the inner-loop, a robust model predictive controller is employed for the linear component, and a one-step optimal compensator is designed to compensate for the impacts of unmodeled dynamics. This one-step optimal compensation strategy enhances the transient response speed and control precision, enabling precise tracking of rapidly varying setpoints from the outer-loop input. Theoretical analysis demonstrates the stability and convergence of both loop systems. When the proposed method is applied to ethylene cracking furnaces and compared with the cascade fractional-order PI-PD control design method, the results show that the developed control strategy effectively enhances control performance.

With the rapid growth of new energy vehicle penetration rate, there has been widespread attention given to the in-wheel motor due to its structural simplicity and near-unity transmission efficiency. Traditional control strategies, such as popular proportional-integral-derivative control and existing model predictive control, are difficult to regulate the in-wheel motor precisely within the desired speed range under nonlinearities and unknown disturbances. In this paper, a novel approach is proposed for the speed control system of the in-wheel motor. A dynamic model is derived first comprising a linear part and the unmodeled dynamics through mechanistic analysis and parameter identification. Then, a multi-step compensation controller of the unmodeled dynamics is proposed using precisely calculated value from previous step. It is feasible to achieve reduced control signal oscillations and lowered actuator switching losses, hence extending the operational lifetime of the system. In addition, a change rate compensation controller of the unmodeled dynamics is developed to eliminate tracking error of the system. Theoretical studies on stability and convergence analysis are conducted. Finally, experimental results demonstrate that the proposed method reduces the mean squared error by 20.01% compared to the existing nonlinear predictive functional control method.

A class of discrete-time switched systems with peak-bounded disturbances and time delays is investigated for sensor fault detection. By constructing multiple Lyapunov-Krasovskii functionals and combining with the free weight matrix, the accurate estimation of the residual reachable set under disturbances is realized. The fault sensitivity analysis is integrated with the reachable set estimation through introducing the l- performance index, which balances disturbance robustness and fault sensitivity. This evaluation mechanism is designed according to the set membership relationship between the residual and the reachable set. The final simulation study confirms that the proposed method not only accurately detects faults but also has superior advantages in detection accuracy, false alarm rate, and false negative rate for different fault types, outperforming the comparison approach in detection effectiveness.

Traditional one-dimensional reinforcement learning methods neither utilize batch data effectively, nor does their control capability improve with increasing batch numbers. Meanwhile, most existing two-dimensional reinforcement learning methods are designed for linear systems, which makes it difficult to cope with the strong nonlinearities and non-repetitive disturbances prevalent in real batch processes. To address these issues, a novel model-free min-max control method via unmodeled dynamic compensation is proposed within the two-dimensional system framework. The method fully incorporates batch-wise information by extending the state space into a form with two-dimensional characteristics and constructing a value function based on a performance index. By establishing the relationship between the two-dimensional value function and the Q-function, a Bellman equation independent of an explicit system model is derived. A two-dimensional off-policy zero-sum self-learning method is proposed to resolve and compensate for the unmodeled dynamics containing nonlinear terms, thereby determining the optimal control gains for the system. This method offers the advantages of fast convergence speed and small tracking error. Unbiasedness and convergence analyses establish theoretical guarantees for the method’s efficacy. Finally, simulation results performed on injection molding demonstrate that by learning from information across both time and batch dimensions, the control gains can rapidly converge to optimal values.

An innovative detection technique for replay attacks in discrete-time systems with uncertain parameters and bounded noises is presented. Utilizing the interval model provides a novel approach to handling uncertain parameters, which significantly lessens the impact of uncertainty. The dynamic event-triggered algorithm based on ellipsoid is created to decrease redundant data transmission. It can intelligently adjust the trigger conditions and affect the update of set-membership estimation. On this basis, a new ellipsoidal set-membership estimator is formulated to predict the state of the linear parameter-varying system when subjected to bounded noises. Subsequently, an auxiliary separation function is brought in to establish the detection scheme for replay attacks. The existence of the replay attack can be confirmed by determining whether the residual signal falls inside the residual ellipsoid. Unlike other existing detection methods, the established detection framework can detect replay attacks with 100% accuracy. Finally, the effectiveness and superiority of the designed strategy are further demonstrated by the simulation example of the direct current motor.

The process of controlling the outlet temperature in ethylene cracking furnaces exhibits notable nonlinearity. Variations in feedstock and fuel properties prevent accurate modeling, resulting in suboptimal performance of predictive functional control in practical implementations. This research analyzes the causal linkage between outlet temperature and fuel gas flow rate. A mechanism model is derived along with its input-output characteristics, and the controlled object is represented as a composite state-space system combining a linear model with unmodeled dynamics. By using the available unmodeled dynamics values from the previous time and the tracking errors caused by their increment, a state-space compensation performance index for unmodeled dynamics is designed. This index is based on the closed-loop system established by a predictive functional controller developed for the linear model. An innovative compensation strategy is developed to mitigate unmodeled dynamics' impact on the closed-loop system, resulting in an improved predictive functional control approach for ethylene cracking furnace temperature regulation. The closed-loop system's input-output relationship is formulated, and system stability and convergence are rigorously analyzed. Experimental validation at a petrochemical plant in Northeast China demonstrates that the proposed method reduces the mean squared error by 48.72% and the integrated absolute error by 30.52% when compared to the current method.

With the increasing complexity of equipment, faults in batch processes have become increasingly unavoidable. Conventional iterative learning fault-tolerant control methods, which rely solely on enhancing robustness, are often insufficient to meet the system's tracking accuracy requirements. To address this challenge, a two-dimensional iterative learning fault-tolerant control strategy is developed for batch processes subject to disturbances and actuator faults, based on the high-order fully actuated framework. Different from the observer-controller co-design strategies, the developed approach structurally separates the design of the observer and controller, thereby eliminating the negative impact of gain coupling on estimation accuracy. Moreover, historical control inputs are incorporated into the control law design to effectively remove historical input terms from the closed-loop system, significantly reducing system dimensionality and computational burden. Finally, the simulation results of the batch stirred reactor show that the root mean square error, integral absolute error, and average dynamic tracking indicator of the developed method with compensation (the 10th cycle) are 0.6801, 0.6207, and 391.05, respectively, which are significantly reduced compared with the case without compensation, indicating that the developed method achieves superior tracking performance.

Considering that existing methods for handling unknown disturbances in multi-phase batch processes mostly adopt passive elimination schemes, while traditional offline iterative learning control strategies fail to fully utilize historical information in both time and batch dimensions, this paper proposes a two-dimensional robust iterative learning hybrid predictive control method based on active disturbance rejection to address these issues. To characterize both match and mismatch scenarios under asynchronous conditions, a two-dimensional switching model framework is first formulated. By incorporating state deviations and output tracking errors, an extended switching model is developed to enhance the flexibility of controller design. Based on this model, the proposed control law integrates the concept of active disturbance rejection, bridging the gap in active disturbance counteraction techniques for multi-phase batch processes. Subsequently, sufficient conditions for asymptotic and exponential stability are derived using Lyapunov functions and linear matrix inequalities, thus theoretically validating the method. The average dwell time technique is further employed to dynamically optimize control gains, decay coefficients, and corresponding runtime online. Prespecified switching signals based on these optimization results ensure smooth system switching. Simulation results demonstrate that the proposed method outperforms existing approaches in tracking accuracy, disturbance rejection, and robustness.

Nonparallel support vector machine (NPSVM) combines the advantages of support vector machine (SVM) and twin SVM, excelling in small-scale data classification. However, its inability to leverage the structural distribution of samples limits its generalization capability. NPSVM requires solving a pair of quadratic programming problems with inequality constraints, thereby reducing learning efficiency. To handle these draw-backs, we propose a fast NPSVM model with the margin hyper-planes (MH-fNPSVM), which introduces several key innovations. Firstly, by replacing inequality constraints with equality constraints, MH-fNPSVM transforms the optimization problem into solving a pair of linear equations, significantly improving computational efficiency. Secondly, MH-fNPSVM also incorporates margin distribution by optimizing the first and second-order statistics of the training samples, improving the generalization performance. Furthermore, MH-fNPSVM transforms the slack variables from 1-norm to 2-norm by employing a quadratic loss function, which overcomes the non-smoothness of the original loss function in NPSVM and enables the model to effectively fit the trends in data distribution, enhancing the robustness and generalization ability. Lastly, an iterative conjugate gradient method is designed for MH-fNPSVM to avoid kernel matrix inversion, thereby ensuring both accuracy and scalability. The model was validated on different datasets and demonstrated excellent performance in generalization and runtime compared to the baseline model.

Aiming at a series of multi-phase batch processes with unknown disturbances and asynchronous switching, a two-dimensional robust iterative learning predictive asynchronous switching control with disturbance input is proposed. In contrast to previous robust control methods for handling disturbances, disturbances are converted into a max-min optimization problem by leveraging the established max-min performance index in this study. Based on this, a control law for disturbance inputs is designed, which enables the system to remain stable even when subjected to significant disturbances. Moreover, compared with the traditional iterative learning control methods, the real-time optimized gains of the control laws observably reduce the learning time and make the control process more precise and efficient. Simultaneously, by conducting the exponential stability analysis of the system, the matching switching period and the delay time period are obtained, which allows for the provision of advanced switching signals to avoid asynchronous switching scenarios. Furthermore, a robustness analysis method is proposed for the system operating under adverse conditions, and a robust stability criterion is provided to ensure the robustness of the system. The injection molding process is implemented as a research object to validate the practicality and efficacy of the devised approach.

A fixed-time sliding mode control strategy is proposed for complex nonlinear systems subject to input saturation, which aims to achieve a faster convergence and higher accuracy. Firstly, in order to alleviate or eliminate the negative impact of the input saturation error, a fixed-time anti-saturation auxiliary system is constructed. Secondly, a fixed-time-delay sliding mode surface is designed and its convergence is guaranteed within a predetermined time independent of the initial conditions. By integrating these components with fixed-time control theory, the proposed fixed-time sliding mode controller is theoretically proven to be effective. Finally, simulation studies are conducted with the help of a van der Pol system and a two-link robotic manipulator. The simulation results further indicate that under input saturation, the controller still exhibits rapid dynamic response and effectively suppresses chattering. In the meantime, its strong resistance to external disturbances is demonstrated.

This research develops a fault detection approach that integrates the estimation of reachable sets with fault sensitivity analysis, addressing the robustness and fault sensitivity needs of systems experiencing time-varying delays. Firstly, a delay-dependent Lyapunov-Krasovskii functional is constructed in linear discrete-time systems with time-varying delays and disturbances bounded in peak amplitude. This functional rigorously defines the boundary of the reachable set for the residual signal and assesses the system's sensitivity to excitation caused by faults. The linear matrix inequality (LMI) conditions for observer design are derived. Secondly, a criterion for evaluation is formulated, which is based on the association between the residual vector and the boundary region of the reachable set. Finally, the effectiveness of the proposed method in the coexistence of time-varying delay and peak-bounded interference is verified by simulation.

This paper investigates a fixed-time active fault-tolerant tracking issue for unmanned aerial vehicle (UAV). Firstly, a nonsingular fixed-time fuzzy tracking control algorithm is proposed, enabling robust tracking performance. Building upon this algorithm, an adaptive controller is designed for the UAV system subject to stochastic disturbances, which are modeled as a standard Wiener processes. Unlike traditional control strategies, the proposed controller can effectively avoid the singularity of the control input. In addition, a Radial Basis Function Neural Network (RBFNN) is employed to approximate unknown nonlinearities. Meanwhile, the controller can guarantee the boundness of all system states in probability within afixed-time, independent of initial conditions. Futhermore, To address sensor faults, a robust three-step unscented Kalman filter (RTS-UKF) is utilized for fault detection and estimation. The estimated fault signals are structurally embedded into the control law, forming a closed-loop fault compensation mechanism. Finally, simulation is conducted to verify the effectiveness of the proposed approach.