Timely and reliable estimation of Ferrous Oxide (FeO) in sintered ore is increasingly critical for blast furnace control under tightening energy and emission constraints. Offline chemical assays incur substantial delays and high costs, depriving operators of the rapid feedback needed for timely set-point correction. Meanwhile, the sintering process is strongly nonlinear and heterogeneous across sensing modalities, making single-source soft sensors brittle in production. To address this, we present a multimodal fusion Transformer for online FeO soft sensing that couples mechanistic models with data-driven learning: thermodynamic state variables from a temperature-field model are fused with process time series at the data level to inject physics-informed context, and a dual-stream encoder performs deep fusion of time series and image sequences via cross-attention to achieve fine-grained temporal–spatial alignment. Experimental results on a real-world sintering dataset demonstrate that the proposed model significantly outperforms baseline methods in terms of RMSE and R2. Furthermore, the fusion strategy generalizes to stronger Transformer backbones, indicating architectural portability and robustness. The results highlight that incorporating domain knowledge with attention-based multimodal fusion is an effective route to industrial soft sensing under real-world constraints.

In this article, we investigate fault-tolerant and resilient control approaches for cyber-physical systems within a unified control and detection framework. Particularly, a novel strategy is presented to simultaneously detect and accommodate anomalies in cyber-physical systems subject to multiplicative physical faults and additive integrity cyberattacks. An observer-based cyber-secure system configuration is first analyzed by means of the coprime factorization technique, wherein multiplicative faults are characterized by coprime factor uncertainties. It is revealed that fault- and cyberattack-induced variations possess distinct attributes with respect to the closed-loop dynamics. This observation motivates a collaborative detection scheme to distinguish both types of anomalies. Specifically, a performance-based fault detector is implemented on the plant side, delivering fault detection results to the monitoring and control (MC) side, where an observer-based attack detector operates collaboratively. Subsequently, the local and remote controllers are reconfigured to enhance the fault tolerance and attack resilience against faults and cyberattacks. To provide more independent design freedoms, the residual signal derived from the controller dynamics is incorporated into the Youla parameterization-based stabilizing controller. Finally, the proposed scheme is verified on a leader-follower robot system.

This article is devoted to providing a method for quantifying fault diagnosability of nonlinear networked control systems under weak transmission conditions. The receiving signals of fault detection and isolation systems are characterized under packet dropouts and communication constraints with the help of Bernoulli random variables and a round-robin protocol. Then, the statistical characteristics of system dynamics under the impact of different faults are characterized by defined statistical functions combining probability density functions. Furthermore, a quantitative fault diagnosability evaluation framework for nonlinear networked control systems is established based on Takagi–Sugeno fuzzy models and Kullback–Leibler divergence. Moreover, an evaluation metric is proposed, which can be applied to system dynamics following both Gaussian distribution and mixed distribution consisting of Bernoulli distribution and Gaussian distribution, eliminating the constraint of assuming purely Gaussian distribution. In addition, a necessary and sufficient condition is given to reveal the relations between the qualitative fault diagnosability evaluation results and the proposed metric.

Practically inaccessible precise probability distribution for disturbance poses significant challenges to stochastic active fault detection (AFD) in achieving satisfactory detection accuracy. In this paper, without making specific distribution assumption on disturbance, a distributionally robust data-driven approach is proposed to AFD for stochastic linear dynamic systems. On the basis of constructing a data-driven stable kernel representation-based residual generator, the distributional uncertainty of disturbance is characterized by the mean-covariance-based ambiguity set of residual both for the fault-free and faulty cases. To minimize the energy of input while guarantee tolerable false alarm rate (FAR) and missed detection rate (MDR), the design of AFD system is formulated as an optimization problem subject to distributionally robust chance constraints (DRCCs). By bridging the DRCCs with deterministic constraints in the probabilistic context, the targeting optimization problem is then converted into a generalized eigenvalue-eigenvector problem, by solving which analytical solutions of the input and separating hyperplane for online detection are derived. Hence, the developed AFD system can not only ensure the FAR and MDR criteria not exceeding predefined levels, but also improve the robustness of the system against distributional uncertainties of disturbance. Besides, a batch-wise realization algorithm is developed for continuous online fault detection. A simulation study based on a four-tank system is demonstrated to validate the effectiveness of the proposed approach.

This paper proposes a monitoring scheme for nonlinear dynamic systems characterized by uncertainties and partially known models. We first establish a monitoring framework grounded in nonlinear control theory, specifically utilizing the normalized stable kernel representation (SKR). By analyzing the associated Hamiltonian system, we identify the conditions under which the normalized SKR can be constructed, ensuring optimal uncertainty estimation via the solution of a corresponding Hamilton-Jacobi Equation (HJE). These conditions further lead to the formulation of residual-based monitoring indicators. Subsequently, we present a data-driven implementation of this framework that integrates control-theoretic principles with machine learning, termed control theory-informed machine learning (CTIML). In this approach, neural networks are employed to approximate the HJE solution and the corresponding observer gain. These networks are trained using fault-free operational data, incorporating loss terms designed to enforce the satisfaction of the HJE and related theoretical properties, thus preserving crucial system characteristics like the lossless property. The resulting CTIML-based normalized SKR generates residuals and HJE satisfaction metrics used for online monitoring. Finally, the efficacy of the proposed methodology is validated through a case study.

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.

In this article, a distributed semi-consensus-based data-driven fault detection scheme is developed based on the process variables collected by sensor networks to ensure the safety of the large-scale dynamic processes. For our purpose, the distributed data-driven process modeling scheme is developed for dynamic systems first by considering the communication topology of the sensor networks. Then, a distributed Kalman filter-based fault detection approach is developed aiming at achieving optimal detection performance at each sensor node. Specifically, the distributed iterative learning algorithm is implemented to calculate the needed parameter matrices for Kalman filter-based residual generator offline with the aid of average consensus algorithm. It is followed by a distributed fusion of local residual signals to perform online optimal fault detection. To avoid the detection delay caused by the traditional average consensus method, the semi-consensus algorithm is developed for the first time to ensure the timely detection of potential faults. A case study on the multiphase flow facility process is given in the end to demonstrate the proposed method.

In this article, an$\mathit {H_{i}/H_{\infty }}$optimization approach to fault detection (FD) is proposed for high-speed train traction motor under complex environment and working conditions. Considering the inherent system nonlinearity, the dynamics of the traction motor are firstly described by a Takagi–Sugeno (T-S) fuzzy model subject to$\mathit {l}_{2}$norm-bounded disturbances and additive faults. Then, a T–S fuzzy observer-based fault detection filter (FDF) is proposed as a residual generator, and, in order to enhance simultaneously the robustness of residual to disturbances and the sensitivity to fault, the design of the FDF is formulated as the maximization problem of finite horizon$\mathit {H_{-}/{H}_{\infty }}$and$\mathit {H_{\infty }/{H}_{\infty }}$indices. Moreover, an$\mathit {H_{i}/H_{\infty }}$optimization approach is developed to find a solution of the T–S fuzzy FDF, which can achieve an optimal tradeoff between the sensitivity to fault and the robustness to disturbances. It shows that the optimal solution is not unique, and the feasible solutions including static and dynamic postfilter are obtained by recursive computing of Riccati equations. Finally, a case study of traction motor in CRH5 EMUs is presented to exhibit the efficacy of the developed FD approach.

This article is concerned with the optimal fault detection issues for discrete-time nonlinear systems with the aid of Takagi–Sugeno fuzzy dynamic modeling technique. To this end, in the first part of this article, the nonlinear system is formulated in the time-varying fuzzy manner, and based on it, a unified fault detection approach is developed by solving a multiobjective optimization problem. In this sense, the optimal tradeoff between fault detectability and robustness against unknown inputs is ensured by solving the Riccati equation. Meanwhile, a fuzzy fault detection approach is studied in the second part of this article based on piecewise-fuzzy Lyapunov functions, which is realized by solving linear matrix inequalities. Two examples are given at the end of this article to demonstrate the proposed approaches.

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.

This article focuses on fault detection for nonlinear industrial processes with multiple operating conditions, in which transfer learning is used to deal with the limited training data issue for unusual operating conditions. To this end, the Tucker decomposition is first implemented to deliver the Gaussian kernel of the nonlinear processes with multiple operation conditions. Then, transfer learning is carried out based on correlation analysis to achieve fault detection for the target process. It is noted that the traditional statistic will lead to false alarms due to the switching of the operating conditions. To deal with this issue, a stationary statistic is investigated based on co-integration analysis. Finally, by transferring the fault detection systems from multiple operating conditions to unusual operating conditions based on extended manifold regularization, fault detection for unusual operating condition can be achieved with both the traditional statistics and the stationary statistic. The experimental result demonstrates the efficiency of the proposed fault detection method for the wastewater treatment process.

This article is concerned with data-driven realization of fault detection (FD) for nonlinear dynamic systems. In order to identify and parameterize nonlinear Hammerstein models using dynamic input and output data, a stacked neural network-aided canonical variate analysis (SNNCVA) method is proposed, based on which a data-driven residual generator is formed. Then, the threshold used for FD purposes is obtained via quantiles-based learning, where both estimation errors and approximation errors are considered. Compared with the existing work, the main novelties of this study include: 1) SNNCVA provides a new parameterization strategy for nonlinear Hammerstein systems by utilizing input and output data only; 2) the associated residual generator can ensure FD performance where both the system model and its nonlinearity are unknown; and 3) with consideration of modeling-induced errors, the quantiles are invoked and used to provide a reliable FD threshold in situations where only limited samples are available. Studies on a nonlinear hot rolling mill process demonstrate the effectiveness of the proposed method.

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.

Under closed-set scenarios (CSS), distributed modeling performs well in fault diagnosis of plant-wide industrial processes due to its flexibility and robustness. However, a more realistic scenario is often open, where unseen situations may arise unexpectedly, rendering existing methods infeasible. The advent of open-set recognition algorithms that can effectively distinguish known samples and reject unknown ones bridges this gap. Nevertheless, the poor scalability of these algorithms prevents them from being elegantly embedded in popular distributed modeling schemes, which hinders the implementation of plant-wide industrial process fault diagnosis toward open-set scenarios (OSS). In this work, we formulate a novel distributed fault diagnosis scheme toward OSS to solve this problem. First, a mutual information-based local module decomposition and expansion strategy is proposed to minimize the loss of intermodule relevant information. Second, a novel generalized basic probability assignments generation technique based on extreme value theory is developed for modeling unknown information. It enables any classifier capable of probabilistic prediction to be applied to OSS and easily embedded in distributed modeling schemes. Finally, a conflict management scheme combining supervised and unsupervised is devised to address the vulnerability of the modified generalized combination rule to counter-intuitive results from fusing conflicting evidence. Experimental results on two plant-wide industrial process datasets demonstrate the proposed approach's feasibility and superiority.

This article proposes a novel data-driven gap metric fault detection and isolation (FDI) approach for small multiplicative fault. First, the scheme of model-based fault classification and gradation is developed by means of the gap metric. Subsequently, the data-driven gap metric is utilized to detect a small fault via the mechanism model. Furthermore, fault detectability criterion is derived with the help of the developed fault detectability indicator. The relationship between fault detectability indicator and fault detection index is then investigated to analyze fault detection performance. To enhance fault isolability, a solution of appropriate fault cluster center model and radius is provided under the condition of fault isolation. Third, a gap metric fault-tolerant control strategy is exploited to guarantee system stability when a large fault is diagnosed by the developed FDI approach. The speed regulation of dc-motor and dc–dc converter are used for simulation and experiment verifications. Moreover, the comparison results and Monte Carlo simulation demonstrate the superiority and reliability of the proposed method.

This article proposes an integrated approach of model-based and data-driven gap metric fault detection and isolation in a stochastic framework. For actuator and sensor faults, an adaptive Kalman filter combining with the generalized likelihood ratio method is suggested. For component faults, especially incipient faults, the model-based scheme maybe not a good choice due to the existence of disturbances or noises. Hence, a novel data-driven gap metric strategy is presented. The design of the appropriate fault cluster center model and radius via the gap metric technique is put forward to enhance the isolability of the incipient faults. Numerical simulation results are given to demonstrate the effectiveness of the proposed fault detection and isolation algorithm.

In this article, optimal observer-based fault detection (FD) and estimation schemes for Takagi–Sugeno fuzzy systems with process faults are investigated. In particular, an optimal FD scheme for fuzzy systems is proposed first aiming at enhancing the sensitivity to the faults and simultaneously increasing robustness against unknown inputs, which gives the extension of the socalled unified solution to fuzzy systems. To further provide the fault information, a least squares fault estimation scheme is developed. It is noteworthy that, the observers for the proposed FD and estimation schemes are updated online recursively. A case study on the laboratory three-tank system is then given to demonstrate the proposed FD and estimation approaches.

This article studies the performance-oriented fault detection (FD) for nonlinear control systems in the data-driven framework. Unlike the traditional residual- or test statistic-based FD methods, the proposed approach focuses on evaluating the system performance changes/degradations caused by the faults. Specifically, the regulation performance described by an infinite-time cost function is first introduced as a control performance index of the feedback system. Using only the process input and output (I/O) data, a Takagi–Sugeno fuzzy dynamic model is constructed with the aid of subspace identification method. Then, the internal system state variables are expressed in terms of the I/O data and a fuzzy cost function is proposed to approximate the performance index. On this basis, the temporal difference error induced by the Bellman equation is adopted as the process evaluation indicator, whose threshold is determined through the randomized algorithm. To demonstrate the effectiveness of the proposed FD approach, case studies are performed in the end on a ship propulsion system and a three-tank system.

This article addresses the performance-based fault detection (FD) and fault-tolerant control (FTC) issues for nonlinear systems. For this purpose, in the first part of this article, the performance-based FD and FTC scheme is investigated with the aid of the nonlinear factorization technique. To be specific, the controller parameterization for nonlinear systems is first discussed. The so-called fault-tolerant margin is introduced as an indicator of the system fault-tolerant ability. Then, the FD scheme aiming at estimating and detecting the stability performance degradation of the closed-loop system caused by the system faults is developed. Furthermore, to recover the system performance, the performance-based FTC strategy is presented. In the second part of this article, the design approach of the performance-based FD and FTC scheme is studied by applying the Takagi-Sugeno fuzzy dynamic modeling technique. The achieved results are demonstrated in the end by a case study on the three-tank system.

This article addresses performance supervised fault detection (PSFD) issues for industrial feedback control systems based on performance degradation prediction. To be specific, three performance indicators are first introduced based on Bellman equation to predict system performance degradations for industrial processes with the aid of machine learning techniques. Based on them, three PSFD schemes are proposed by embedding the performance indicators as supervising information. In this context, the data-driven implementation of PSFD schemes are investigated for linear systems with unmeasurable state variables. A case study on rolling mill process, a typical benchmark in the steel manufacturing processes, is given at the end of this article to illustrate the applications of the proposed fault detection schemes.

In this article, two performance-based fault-tolerant control strategies are investigated for multiplicative faults in industrial processes. This is motivated by the fact that the changes in the system parameters caused by malfunctions generally lead to multiplicative faults, which may cause remarkable changes in system dynamics and performance. To be specific, the representation forms of the faulty plants are first given in terms of the so-called stable image and kernel representations, respectively. Then, by measuring the fault-induced system performance degradation, two performance-based fault-tolerant control strategies are formulated. Specifically, a residual-driven dynamic controller, which is also called plug-and-play control, is implemented to achieve control performance recovery in the context of stability margin. Finally, a benchmark study is demonstrated to show the efficiency of the proposed methods.

In this article, an optimal data-driven approach is proposed to deal with the problem of distribution independent fault detection (FD) for stochastic linear discrete-time systems. For this purpose, an observer-based residual generator is first constructed using process input and output data. Without exact probability distributions for noises and faults, the so-called confidence sets are constituted in terms of mean and covariance matrix to characterize residual in fault-free and faulty cases. On this basis, a stochastic optimization FD problem is formulated, which allows an integrated design of residual evaluation function and threshold toward maximizing fault detection rate (FDR) for an acceptable false alarm rate (FAR) in the worst-case setting. Furthermore, a data-driven formulation of the underlying FD problem is studied, wherein the estimation uncertainties caused by the deviation of empirical mean and covariance matrix from their real values are concerned. The robustness of the FD system is investigated in the probabilistic context. Confidence levels of the obtained FAR and FDR are achieved quantitatively. The main advantages of the proposed FD approach lie in its independence of probability distributions for noises and faults, the robustness to the estimation uncertainties and the quantitative probabilistic evaluation to the confidence levels of FAR and FDR. A case study on a three-tank system illustrates the effectiveness of the demonstrated approach.

This paper is concerned with a control performance-based fault-tolerant control strategy for singular systems in presence of multiplicative faults. To be specific, the observer-based realization of Youla parameterization is first addressed for singular systems. Then the fault-tolerant margin for closed-loop systems is studied and further modified to bring forth the stability margin degradation, which serves as an indicator for the performance change caused by the faults in the closed-loop. Based on it, a control performance-based fault detection scheme is realized, aiming at detecting those faults that may affect the system stability. Controller reconstruction rule is given afterwards to ensure the system performance when fault occurs. A circuit system model is finally provided to illustrate the validness of the derived control scheme.

This paper addresses fault-tolerant control (FTC) issues for linear systems with model uncertainty and multiplicative faults. The left and right coprime factorization techniques are first adopted for system modeling. Then, the fault detection (FD) approaches are investigated in the coprime factorization context. Based on the information provided by the FD systems, the corresponding FTC architectures and design schemes are presented. Moreover, the gap metric techniques are applied to fault detectability analysis, including the fault detectability indicators to quantify the detection performance in the presence of model uncertainty. The effectiveness of the developed methods for industrial application is illustrated by a case study on a dc motor.

This paper deals with a real-time-weighted observer-based fault-detection (FD) scheme for Takagi-Sugeno (T-S) fuzzy systems. The essential idea is to develop a weighted diagnostic observer-based FD system to optimize the worst case robustness and fault sensitivity simultaneously by using the information provided by each local system. To achieve an early detection of potential fault, the robustness issue is investigated in the L∞/L2observer-based FD context. Meanwhile, the L-fault sensitivity condition is addressed to optimize the fault detectability. Using fuzzy Lyapunov functions, sufficient conditions on the FD system design are studied. Two examples are given in the end to show the efficiency of the proposed results.

This paper is devoted to the data-driven fault detection of nonlinear systems. For our purpose, the definition of Takagi-Sugeno fuzzy data-driven forms of kernel representations for nonlinear systems is introduced first, which builds the basis of our work. The major contributions consist of two parts. In the first part, a data-driven method for fuzzy process modeling is proposed, and associated with it, some modeling issues are addressed with the aid of the so-called randomized algorithm technique in the probabilistic framework. It is followed by a data-driven realization of fuzzy kernel representation and its implementation in the fault detection system design. To link the data-driven methods to the well-established observer-based fault detection approaches, the recursive form of the fuzzy kernel representation is proposed. In the second part, the fuzzy-observer-based fault detection design scheme is investigated based on the recursive fuzzy kernel representation. The main results of our study are illustrated by an experimental study on the laboratory setup of a three-tank system.

This paper is concerned with a real-time observer-based fault detection (FD) approach for a general type of nonlinear systems in the presence of external disturbances. To this end, in the first part of this paper, we deal with the definition and the design condition for an £∞/£2type of nonlinear observer-based FD systems. This analytical framework is fundamental for the development of real-time nonlinear FD systems with the aid of some well-established techniques. In the second part, we address the integrated design of the £∞/£2observer-based FD systems by applying Takagi-Sugeno (T-S) fuzzy dynamic modeling technique as the solution tool. This fuzzy observer-based FD approach is developed via piecewise Lyapunov functions, and can be applied to the case that the premise variables of the FD system is nonsynchronous with the premise variables of the fuzzy model of the plant. In the end, a case study on the laboratory setup of three-tank system is given to show the efficiency of the proposed results.

This paper is concerned with the analysis and integrated design of a type of observer-based fault detection (FD) system for general nonlinear processes. To this end, the existence and design condition for this type of nonlinear observer-based FD systems is first introduced. In this context, the integrated design scheme is investigated by dealing with the design condition with the aid of Takagi-Sugeno (T-S) fuzzy dynamic modeling technique. To be specific, the universal T-S fuzzy observer-based residual generator is developed via fuzzy Lyapunov functions. Subsequently, an integrated observer-based FD scheme is proposed with an embedded dynamic threshold, which is generated to meet the real-time FD requirements from industrial processes. In the end, a numerical example and case simulation study on a continuous stirred tank heater process are performed to show the application of the proposed method.

The main focus of this paper is on the analysis and integrated design of $\mathcal {L}_2$ observer-based fault detection (FD) systems for discrete-time nonlinear industrial processes. To gain a deeper insight into this FD framework, the existence condition is introduced first. Then, an integrated design of $\mathcal {L}_2$ observer-based FD approach is realized by solving the proposed existence condition with the aid of Takagi-Sugeno fuzzy dynamic modeling technique and piecewise-fuzzy Lyapunov functions. Most importantly, a weighted piecewise-fuzzy observer-based residual generator is proposed, aiming at achieving an optimal integration of residual evaluation and threshold computation into FD systems. The core of this approach is to make use of the knowledge provided by fuzzy models of each local region and then to weight the local residual signal by means of different weighting factors. In comparison with the standard norm-based fuzzy observer-based FD methods, the proposed scheme may lead to a significant improvement of the FD performance. In the end, the effectiveness of the proposed method is verified by a numerical example and a case study on the laboratory setup of continuous stirred tank heater plant.

A stabilizing regulator designed by any technique whatsoever can be viewed as the combination of a state estimate feedback controller and additional feedback from a dynamic compensator driven by the residual signal (difference between actual and estimated system outputs). Motivated by such an observation, this paper presents the controller design from the premise that system stability is first guaranteed. Control performance can then be enhanced by the optimal design of a residual-driven dynamic compensator subject to some quadratic performance index. The resulting compensator design methods are carried out using both offline and online iterative algorithms with guaranteed convergence. Moreover, the final iterative realization strategy can be implemented online with observed state variables and input updates in case of unknown system dynamics or parameter changes. Simulation results are presented to illustrate design procedures as well as the feasibility of our proposed scheme.