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This article studies the fault‐tolerant consensus issue of a class of nonlinear two‐time‐scale‐agent systems with heterogeneous sensor faults and external disturbances. First, the decentralized proportional integral (PI) observer for each agent is constructed to estimate the states and sensor faults simultaneously. Then, a distributed adaptive protocol based on the decentralized PI observer is designed to guarantee the consensus of the underlying systems. Some sufficient existence conditions are given in terms of linear matrix inequalities (LMIs) for the decentralized PI observer and the fault tolerant consensus protocol. Note that H∞$$ {H}_{\infty } $$ performance index is employed to attenuate the influence of sensor faults and disturbances on state estimation and the consensus of the underlying systems. Finally, the effectiveness and superiority of the proposed method are demonstrated by an application example and a numerical example. [ABSTRACT FROM AUTHOR]

With the advancement in sensor and communication technology, autonomous systems have been incrementally reshaping the execution of tasks in commercial and military sectors. Since the systems are designed to complete tasks without or with minimal human intervention, fault diagnosis based on sensor data has been crucial to preventing accidents and fatalities. In this paper, fault diagnosis for autonomous systems is designed based on nonlinear adaptive observers, tested in numerical simulations, and implemented in a robotic platform. To this end, we utilize the persistence of excitation conditions on the parametric model of the faults. We derive sufficient conditions for the nonlinear adaptive observer in terms of linear matrix inequality to ensure the convergence of the estimates. Furthermore, we consider one‐sided Lipschitz conditions to obtain less conservative results. The main advantage of using the nonlinear adaptive observer is that the method converges quickly to the actual fault and requires minimum computational effort. However, solving the linear matrix inequality might not be trivial. Numerical simulations based on a single‐link flexible joint robot model and experimental tests in an autonomous quadcopter are performed to validate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we study the absolute stabilization of switched Lurie system via dynamic output feedback, where the nonlinearity is unknown and is restricted in a sector. In most works, the nonlinearity is assumed to be known exactly or is restricted in a bounded sector. Here, we consider the most general case with unbounded sector. With the help of switched time‐varying Lyapunov–Lurie function, a dynamic output feedback controller with time‐varying control gain is presented. On this basis, sufficient conditions for absolute stabilization are derived in the framework of mode‐dependent minimum dwell time and mode‐dependent range dwell time. It turns out that this time‐varying control strategy can solve the absolute stabilization of switched Lurie systems that all subsystems are not stabilizable. Moreover, the stability criteria in terms of linear matrix inequality we derived can be easily checked via Matlab toolbox. Finally, the effectiveness of presented methods is verified by several numerical examples. [ABSTRACT FROM AUTHOR]

In this work we study the design of H2$$ {H}_2 $$ filters for phase‐type (PH) semi‐Markov jump linear systems, considering partial information on the system's operating mode and possible parameter uncertainties. With respect to the mode of operation, it is assumed that the state space of the semi‐Markov chain can be written as the union of disjoint sets, called clusters, and the only information available to the filter is which cluster the state of the semi‐Markov chain belongs to. A new linear matrix inequality (LMI) parameterization employing the slack variable technique is introduced for the design of switching full‐order filters according to the cluster observations so that suitable bounds on the H2$$ {H}_2 $$ norm of the estimation error are guaranteed for the uncertain system. If the system is restricted to be a Markov jump linear system and the Markov chain is assumed to be perfectly measured, the design conditions are shown to be also necessary leading to the optimal full‐order filter. Furthermore, the general filter can be particularized into an observer form for the case in which the system matrices are the same within each cluster and there are no parameter uncertainties except for possible uncertainties affecting the transition rates of the jumping process. The paper concludes with an illustrative example in the context of networked control systems. [ABSTRACT FROM AUTHOR]

In this article, the problem of the optimal reset control design for Lipschitz nonlinear systems is addressed. The reset controller includes a base linear controller and a reset law that enforces resets to the controller states. The reset law design is strongly dependent on the appropriate design of the base controller. For this reason, in this article, the base controller and reset law are simultaneously designed. More precisely, an optimal dynamic output feedback is considered as the base controller which minimizes the upper bound of a quadratic performance index, and a reset law is used to improve the transient response of the closed‐loop system. This design is done in a full offline procedure. The problem is transformed into a set of linear matrix inequalities (LMIs), and the reset controller is obtained by solving an offline LMI optimization problem. Finally, two examples are presented to illustrate the effectiveness and validity of the proposed method. [ABSTRACT FROM AUTHOR]

This article investigates the problem of secure memory adaptive event‐triggered filter design for nonlinear network systems under hybrid network attacks. First, the introduction of memory adaptive event‐triggered mechanism and numerical quantization is employed to enhance system performance, optimize network channel utilization, and prevent network congestion. Second, we consider the impact of deceptive attacks and DoS attacks occurring in the network channel on data transmission, which form the hybrid network attacks studied in this article. Subsequently, based on the established error model, we derive sufficient conditions for the mean‐square exponential stability of the system under a given H∞$$ H\infty $$ performance index using Lyapunov–Krasovskii function and linear matrix inequality (LMI) techniques. Furthermore, the filter parameters are determined using the LMI method. Finally, we illustrate the feasibility and generality of the conclusions through numerical simulation examples and a tunnel diode circuit system. [ABSTRACT FROM AUTHOR]

Due to the disturbances and varying latency, a teleoperated robotic manipulator might not comply with the master control commands. Although prior studies on minimising the impact of network latency and disturbances on teleoperated robots were conducted, there has been very little research on the prediction of minimal operation regions of robotic arms, especially in the worst‐case scenarios when the disturbances and time delays still prevail even after impact minimisation. This study investigates the problem and proposes a novel solution to predicting minimal operation regions of networked control robotic manipulators. The proposed method can be used to forecast safe operation regions in which the manipulators will certainly enter and exclude regions that the robots will never penetrate. Leveraging on a Lyanonov Krasovskii criterion, the method performs region prediction by establishing minimal reachable bounding sets of the nonlinear, perturbed robotic arm's state vectors guided via a time‐varying delay‐dominant network. Though predominantly nonlinear, the entire prediction process is formulated as a tractable Linear Matrix Inequality (LMI) optimisation problem, which can be solved efficiently and effectively. Efficacy of the proposed method is validated with simulations where a simulated robotic arm is distorted with time‐varying delays and disturbances. [ABSTRACT FROM AUTHOR]

The structured singular value (SSV), or μ$$ \mu $$, is used to assess the robust stability and performance of an uncertain linear time‐invariant system. Existing algorithms compute upper and lower bounds on the SSV for structured uncertainties that contain repeated (real or complex) scalars and/or nonrepeated complex full‐blocks. This paper presents algorithms to compute bounds on the SSV for the case of repeated complex full‐blocks. This specific class of uncertainty is relevant for the input‐output analysis of many convective systems, such as fluid flows. Specifically, we present a power iteration to compute the SSV lower bound for the case of repeated complex full‐blocks. This generalizes existing power iterations for repeated complex scalars and nonrepeated complex full‐blocks. The upper bound can be formulated as a semi‐definite program (SDP), which we solve using a standard interior‐point method to compute optimal scaling matrices associated with the repeated full‐blocks. Our implementation of the method only requires gradient information, which improves the computational efficiency of the method. Finally, we test our proposed algorithms on an example model of incompressible fluid flow. The proposed methods provide less conservative bounds as compared to prior results, which ignore the repeated full‐block structure. [ABSTRACT FROM AUTHOR]

Summary: The reduced‐order observer‐based finite‐time control problem for one‐sided Lipschitz nonlinear switched singular systems is addressed in this paper. First, the design method of the reduced‐order observer is given via state transformation. Then, based on the average dwell time (ADT) approach, some new sufficient conditions for regularity, impulse‐freeness, have a unique solution and finite‐time boundedness (FTB) of the dynamic augmented systems are obtained by exploring the reduced‐order observer‐based controller. Further, the lower finite‐time bound can be obtained by using singular value decomposition method. And the state feedback gain and the observer gain are computed by solving linear matrix inequalities (LMIs). Finally, the validity of the obtained method is illustrated by means of a numerical example and a DC motor system. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes a set‐membership state estimation method for Switched Linear Parameter Varying (SLPV) systems subject to unknown but bounded parametric uncertainties, disturbances and noises. A zonotopic outer approximation of the state estimation domain is computed at every time iteration. The size of this zonotope is designed to be convergent and bounded by satisfying P$$ P $$‐radius‐based and Average Dwell Time (ADT) conditions that are formulated in the Linear Matrix Inequality (LMI) framework. An extension of the state estimation method is presented to address the fault/disturbance estimation problem for SLPV systems. By using the state augmentation technique, the fault/disturbance estimation problem is transformed into a state estimation problem of the generated augmented descriptor switched LPV system. An application to vehicle lateral dynamics fault estimation is used for assessment purposes. Simulation results demonstrate the effectiveness of the proposed algorithm and highlight its advantages over the existing methods. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of fault detection in DC microgrids in the presence of denial-of-service (DoS) attacks. To deal with the nonlinear term in DC microgrids, a Takagi-Sugeno (T-S) model is employed. In contrast to the conventional approach of utilizing current sampling data in the traditional event-triggered mechanism (ETM), a novel integrated ETM employs historical information from measured data. This innovative strategy mitigates the generation of additional triggering packets resulting from random perturbations, thus reducing redundant transmission data. Under the assumption of faults occurring within a finite-frequency domain, a resilient event-based H − / H ∞ fault detection filter (FDF) is designed to withstand DoS attacks. The exponential stability conditions are derived in the form of linear matrix inequalities to ensure the performance of fault detected systems. Finally, the simulation results are presented, demonstrating that the designed FDF effectively detects finite-frequency faults in time even under DoS attacks. Furthermore, the FDF exhibits superior fault detection sensitivity compared to the conventional H ∞ method, thus confirming the efficacy of the proposed approach. Additionally, it is observed that a trade-off exists between fault detection performance and the data releasing rate (DRR). [ABSTRACT FROM AUTHOR]

This paper addresses the problem of maximum power point tracking of photovoltaic (PV) systems in the presence of model uncertainty as well as varying load and atmospheric conditions using techniques based on a Takagi–Sugeno fuzzy model. The proposed approach relies on the linear matrix inequality tool, Lambert W function, and the Newton–Raphson method. First, adopting a quadratic Lyapunov function, an active observer-based fuzzy non-parallel distributed compensation (non-PDC) controller is designed for asymptotic tracking of the desired reference input. Next, to subdue the impact of uncertainty on the PV system, the closed-loop nominal system is regarded as a reference model, and then the main control law is developed using an online lumped uncertainty estimator and keeping the nominal control law within the staple controller. This control law does not require that the bounds on uncertainties be known. The reference voltage is determined by a novel maximum power point-seeking algorithm that is organized based on the one-diode model of PV panel, Lambert W function, and Newton–Raphson method. Finally, simulations are performed for three scenarios to point out the merits and effectiveness of the proposed methodology in the presence of system uncertainties, environmental changes, and load variations. [ABSTRACT FROM AUTHOR]

Practical stability can describe qualitative behavior and quantitative properties of systems in comparison with traditional Lyapunov stability theory. In this paper, such stability problem is formulated for nonlinear delayed urban traffic systems described by uncertain differential equations which are a type of differential equations driven by Liu processes. First of all, we prove the existence and uniqueness of the solution. Then, we analyze the pth moment practically exponential stability and quasi surely globally practically uniformly exponential stability of the system by employing general It'o formula, Gronwall's inequality, Holder inequality and Borel-Cantelli lemma. Moreover, an example is presented to verify the validity of our theoretical methods. [ABSTRACT FROM AUTHOR]

Summary: With the aid of a proportional integral framework, the presented article focuses on the problems of finite‐time boundedness and fault estimation for Takagi–Sugeno fuzzy singular systems subject to time delays, faults and external disturbances. To commence, we conjure up a fuzzy‐dependent intermediate variable and from thereon, a proportional integral‐based fuzzy intermediate estimator is constructed. Moreover, the constructed estimator precisely facilitates for estimating the fault signals and system states in simultaneously. Besides this, the integral term in the proportional integral estimator offers greater design flexibility and higher resilience. Secondly, an intermediate estimator‐based fault‐tolerant control is devised by availing the information from the proportional integral‐based fuzzy intermediate estimator, which aids in effectively compensating the faults arising in the system. Subsequently, by setting up an appropriate Lyapunov–Krasovskii functional, the set of adequate requirements asserting the finite‐time boundedness with the endorsed mixed H∞$$ {H}_{\infty } $$ and passivity performance index is established in terms of linear matrix inequalities. After that, an explicit framework for the requisite gain matrices can be found forth basing on the formed linear matrix inequality criteria. Ultimately, simulation findings are supplied to evaluate the utility and applicability of the theoretical insights. [ABSTRACT FROM AUTHOR]

The predictor feedback has been demonstrated to be quite effective in large delay compensation. However, few researches in the field of predictor feedback for large delays focused on output feedback control (OFC). This paper develops the previous work to design high-gain-observer-based predictive output feedback for nonlinear systems with large delays. Two methods are employed for large delay compensation: the backstepping-based partial differential equation (PDE) method and the reduction-based ordinary differential equation (ODE) method. It appears that, for continuous-time control, the first method leads to simpler linear matrix inequality (LMI) conditions and deal with larger delays, whereas the second method is easily exploited for sampled-data implementation under continuous-time measurement. Lyapunov-Krasovskii method is presented to guarantee the exponential stability of the nonlinear systems under predictor-based controllers. Through a simulation example of pendulum, the proposed methods are demonstrated to be efficient when the input delays are too large for the system to be stabilized without a predictor. [ABSTRACT FROM AUTHOR]

In this paper, the framework of dissipativity-based iterative learning control for singular systems (SSs) is established for the first time. Firstly, under the P-type learning algorithm, it has been demonstrated that the dissipative SSs can achieve the accurate tracking for the desired trajectory in a finite time interval. Secondly, a sufficient condition for the SSs to satisfy dissipativity is given by using the linear matrix inequality (LMI) method, and the solvability criterion of the LMI is further presented. Moreover, the relationship between dissipativity and positive realness is revealed. Finally, two examples are given to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This note investigates the adaptive security control issue for uncertain delayed semi-Markov jump systems (DSMJSs) within the framework of sliding mode control (SMC), in which the DSMJSs are affected by generally unknown transition rates (GUTRs), actuator failures (AFs) and cyber attacks. By the virtue of the strong approximation ability of neural network (NN), an adaptive NN-based SMC synthesis is carried out, which could not only force the state trajectories onto the proposed sliding surface but also ensure the DSMJSs operate as demanded in spite of the interference errors, structural uncertainty, hidden AFs, cyber attacks and GUTRs. Then, in view of the reachability of the proposed linear-type sliding mode surface (SMS), linear matrix inequalities (LMIs) and stochastic stability theory, a novel stochastically stable criterion for the resultant DSMJSs is obtained. At last, the single-link robot arm model is offered as an instance with simulation to illustrate the viability of the devised strategy. [ABSTRACT FROM AUTHOR]

A new adaptive observer is proposed for a class of uncertain time-delay parabolic systems. The uncertainties are located in both the state equation and the output equation which are also subjected to a distributed delay. Our algorithm is based on backstepping-like transformation and a classical persistent excitation condition. To illustrate the performances of this observer, simulation results are provided. [ABSTRACT FROM AUTHOR]

In general, the construction of observers for nonlinear descriptor systems depends on the solvability of a linear matrix inequality involving system matrices, and it is based on the system's nonlinearity. Therefore, the type of nonlinearity present in the system heavily affects the observer design process. There are significant developments in the literature for observer design for descriptor systems with various types of nonlinearity. Motivated by this, the current work reviews the literature on observer design for nonlinear descriptor systems with an extensive discussion on the type of nonlinearities that are considered. Here, an analysis and the comparison on the most common nonlinearities is presented, providing a roadmap to all researchers in the field. Furthermore, less common nonlinearities have been identified, presenting under-explored areas within the literature, and can open new domains for future research. [ABSTRACT FROM AUTHOR]

This paper deals with the fault detection observer (FDO) design for discrete-time switched singular systems (SSSs) under persistent dwell time (PDT) switching. Compared to the widely used dwell time and average dwell time switching in the literature, PDT switching is more general due to its covering such two switchings as special cases. The PDT switching is firstly employed to establish the admissibility criterion and the H ∞ and H - observer synthesis conditions for SSSs. Also, an efficient H - / H ∞ FDO design algorithm is proposed. First, the admissibility analysis of the observing error system is addressed by incorporating the PDT technique into the multiple Lyapunov function method, and an admissibility criterion in the form of linear matrix inequality is established. Based on this, two FDO synthesis conditions are then developed to guarantee that the generated residual signal achieves prescribed H ∞ and H - performance with regard to disturbances and faults, respectively. The FDO should be designed such that the effects of faults and disturbances on the residual signal are maximized and minimized, respectively. To this end, the FDO design is expressed as a multi-objective optimization problem, and the FDO gains are characterized in terms of the solution of the multi-objective optimization problem. Moreover, a suitable trade-off between the robustness to disturbances and the sensitivity to faults is obtained based on a corresponding proposed algorithm. Finally, one illustrative example is given to show the validity of the developed method. [ABSTRACT FROM AUTHOR]

This paper considers the finite-time H ∞ dynamic output feedback control for a class of one-sided Lipschitz nonlinear rectangular descriptor Markov jump systems (DMJSs). The differential matrix E ∈ R m × n is not subject to any constraints, i.e., it includes two cases of m ≥ n and m ≤ n . For making the closed-loop system as square DMJSs, the rectangular dynamic output feedback controller is proposed. Firstly, the sufficient conditions are given to guarantee that the augmented closed-loop systems are singular stochastic H ∞ finite-time bounded (SS H ∞ FTB) and have a unique solution simultaneously by adopting a mode-dependent Lyapunov functional and implicit function theorem. Then a novel and rigorous strict linear matrix inequality (LMI) sufficient condition for the existence of a rectangular dynamic output feedback controller is given based on the certain matrix decoupling techniques, and the controller is obtained. Ultimately, numerical examples are provided in order to substantiate the soundness of the results. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of dissipative-based stabilization for fractional-order nonlinear control systems with uncertainties, time-delay, external disturbances, actuator faults, actuator and sensor saturations. Specifically, a non-fragile reliable dynamic output feedback controller is designed for the purpose of stabilization of the addressed system. Due to the effect of saturation phenomena occurring in both the actuator and sensor, the anti-windup loops framed with the help of the observer design are incorporated into the controller design. Some sufficient conditions are formulated in terms of linear matrix inequalities by choosing a suitable Lyapunov function thereby assuring the dissipative-based stabilization. The derived results are thus validated by two numerical examples including the practical model of two-stage chemical reactor. [ABSTRACT FROM AUTHOR]

This article discusses the finite‐time mixed H∞$$ {H}_{\infty } $$ and passive filtering design problem for uncertain nonlinear singular systems. The parameter uncertainties are constrained by well‐defined upper bounds on their magnitudes. The objective is to design a full‐order filter to ensure that the augmented singular system to be finite‐time boundedness(FTB) with H∞$$ {H}_{\infty } $$ and passivity performance. Firstly, a sufficient condition for achieving singular finite‐time boundedness with mixed H∞$$ {H}_{\infty } $$ and passivity performance for uncertain nonlinear singular system is derived by introducing a free matrix. Secondly, a novel criterion is established for analyzing finite‐time H∞$$ {H}_{\infty } $$ and passivity problem of filtering error singular system based on augmented matrix technique. Thirdly, the filtering design conditions are presented and the relevant parameters of the desired filter are determined using linear matrix inequality decoupling principle. Finally, a practical circuit system and a numerical example are provided to demonstrate the feasibility of the proposed scheme. [ABSTRACT FROM AUTHOR]

This study presents novel formulations for ℋ∞$$ {\mathscr{H}}_{\infty } $$ robust state‐feedback control synthesis for discrete‐time linear time‐invariant systems based on linear matrix inequalities. The proposed formulations require searching for two adjustment matrices. The synthesis formulations include other formulations from the literature as particular cases according to specific values of the adjustment matrices. We propose the application of evolutionary optimization to determine the optimal values of these two adjustment matrices. One approach to obtaining a single‐step formulation for static output‐feedback control synthesis is to transform a state‐feedback control synthesis formulation via the simple change of variables. The alteration of variables considered in this study requires an adjustment matrix. The adjustment matrix influences the performance of the resulting controller or the existence of a feasible solution to the problem. Here, we also propose the application of evolutionary optimization to determine the optimal value of this adjustment matrix and the two adjustment matrices of the proposed formulations to obtain the optimal ℋ∞$$ {\mathscr{H}}_{\infty } $$ robust control system. Case studies verify that despite the increased complexity, the proposed formulations and the method required to tune them may be indispensable in achieving a robustly stable control system or an enhanced ℋ∞$$ {\mathscr{H}}_{\infty } $$ performance for more intricate problems. [ABSTRACT FROM AUTHOR]

Summary: This paper deals with observer‐based fault estimation (FE) and proportional derivative state feedback fault tolerant control (FTC) schemes for singular systems affected by actuator fault, interval time‐varying delay and external disturbance. Firstly, the system transformation method of constructing the derivative matrix into a full‐rank matrix is adopted to transform the singular system into a normal system, which effectively eliminates the impulse characteristic of the singular system. Secondly, in the design of the dynamic observer, fault estimation utilizes the real‐time output error and its derivative simultaneously, which can achieve better estimation performance when the fault change frequently. Most importantly, the observer‐based FTC adopts a proportional derivative state feedback control, considers disturbance and interval time‐varying delay, and the introduction of state estimation derivative term can eliminate the impulse property of the closed‐loop system, which optimizes the design scheme of the fault‐tolerant controller. The obtained sufficient conditions for stability can be solved by the strict linear matrix inequality (LMI), and the superiority of the conclusions will be further verified by the simulations. [ABSTRACT FROM AUTHOR]

The fault estimation (FE) and fault‐tolerant control (FTC) problems are studied for the switched system with sensor fault, actuator fault, and stochastic noise. The dynamic FE observers are used to reconstruct the system states and faults at the same time. Differently from the classical observer design method, in the process of observers design, both the output information and its derivative are introduced to improve the estimation performance, especially in the case of the systems subject time‐varying fault. Based on the coordinate transformation, the output derivative is not appeared in the observers, which means that the proposed dynamic observers can be used for the cased that the output derivative is unmeasured. Utilizing the estimate information, the observer‐based FTC scheme is given. For any switching signal, the linear matrix inequality (LMI) conditions are provided, which can ensure that the entire system is mean‐square exponentially stable (MSES). Finally, simulation examples show the effectiveness of the observer and controller. [ABSTRACT FROM AUTHOR]

Few biomechanical models of sitting stability have been proposed over the last decades and most of them control the trunk position through a lumbar torque. Unfortunately, this type of model is not valid for individuals living with a complete thoracic spinal cord injury (SCI) who generally experience paralysis of their abdominal and lower back muscles. Instead, individuals with SCI often engage their upper limbs as a compensatory strategy to control their sitting position. A new nonlinear biomechanical model is introduced to take into consideration the influence of the upper limbs for sitting control study of people living with SCI. The inherent nonlinearity of the model is taken into account via the Takagi–Sugeno (T‐S) framework. To estimate the internal controlling torques without measurements, an unknown input observer (UIO) is created. Its convergence is expressed by linear matrix inequalities (LMI), which are solved by convex optimization techniques. Numerical simulations with perturbations are used to assess the adequacy of the methodology and preliminary experimental data of one person living with SCI performing a sitting stabilization exercise is used to estimate internal torques of the upper limbs. The main contribution of this work is to provide a way to estimate human joint torques without invasive measurements; the results highlight the validity of both goals of this article, the nonlinear biomechanical modelling and the UIO methodology. [ABSTRACT FROM AUTHOR]

This paper deals with the robust control problem for networked uncertain semi‐Markov jump systems over digital communication channel, where some complicated factors are considered in this framework, such as false data injection attacks, incomplete sojourn‐time information, and actuator fault. In network environment, these problems frequently occurred: (1) Data must be quantified before it is transmitted via digital communication channels, and (2) there is always the risk of cyber‐attack. Traditional controllers are not effective to solve the robust control design issue of uncertain semi‐Markov jump systems since the signal quantization and cyber‐attack will degrade control performance evidently. Then, a resilient controller is designed to guarantee the stable running of system with incomplete sojourn‐time information and the system resiliency to unsecure shared data. With the help of Lyapunov stability theory, sufficient conditions are derived in the form of linear matrix inequality, which can determine the gains of the resilient controller. Finally, the simulation examples about single‐machine infinite‐bus power system are given to explain the effectiveness and feasibility of the proposed control approach. [ABSTRACT FROM AUTHOR]

This paper studies the trajectory tracking of a constrained mobile robot under slippery conditions. The goal is to propose a controller for real‐time operations of time‐varying dynamics with insignificant execution time. Therefore, a Laguerre‐based model predictive control (LMPC) is designed, and robustness is provided with an linear matrix inequality (LMI)‐feedback controller. Moreover, a recursive least square (RLS) algorithm with a forgetting factor is utilized to identify the required parameters of the LMI‐based controller. LMPC and LMI‐based controller stability is achieved with suboptimal theory and Lyapunov function, respectively. This algorithm separates the nominal system and introduces new dynamics containing uncertainties. Furthermore, LMPC is removed from the online calculation, which dramatically reduces computation burden and time; consequently, online computation is dedicated to determining the LMI feedback. Simulations are provided to compare the proposed robust controller to its not robust counterpart. Finally, it is demonstrated that this controller diminishes the execution time considerably, making it incomparable to previous robust MPC strategies. [ABSTRACT FROM AUTHOR]

A novel scheme of fault‐tolerant control (FTC) and fault estimation (FE) for the stochastic distribution control (SDC) system with disturbance is investigated. The output probability density function (PDF) is modelled by the weight vector of the B‐spline neural network with the given basis function, and control of output probability density function can be converted to control of the weight vector of the B‐spline neural network. A k‐step fault estimation algorithm aiming at enhancing the accuracy of fault estimation is first applied to the stochastic distribution control system. Subsequently, a dynamic output feedback fault‐tolerant control algorithm is constructed by using the k‐step fault estimation information to guarantee that the target weight vector can be still approximated by the output weight vector in case of actuator fault. A simulation example is used to confirm the availability of the presented method. [ABSTRACT FROM AUTHOR]

The presence of uncertainty in the converter model and controller parameters affects the system's stability and dynamic performance. This paper presents a comparative analysis of robust non‐fragile control based on (i) the Kharitonov method and (ii) the linear matrix inequality (LMI) technique so that the controller can cope with the effect of both uncertainties. The first approach based on Kharitonov theorem determines the robust performance region with guaranteed gain margin and phase margin under parametric uncertainty. The second approach (LMI technique) is based on devising a control law that can quadratically stabilize the closed‐loop system subject to uncertainties and satisfy the H∞ norm bound constraint on disturbance attenuation. Based on these two approaches, a robust non‐fragile PI controller is designed for voltage mode control of dc‐dc buck converter. The effectiveness of the control approaches is evaluated based on (i) robustness against large plant parameter perturbations and load disturbance and (ii) fragility against controller parameter perturbations. The performance of the designed controllers (using the Kharitonov method and the LMI technique) has been thoroughly evaluated and validated through simulation and experimental results. [ABSTRACT FROM AUTHOR]

This paper is devoted to the problem of event‐triggered consensus for a class of singular multi‐agent systems with nonlinear dynamics. Firstly, in consideration of the impossibility to reach all agents in some case, an observer is designed to access these agents' states. Secondly, a novel adaptive event‐triggered scheme is proposed based on asynchronous data sampling. In this scheme, the trigger parameter can be adjusted dynamically in order to reduce information transmissions among agents. Thirdly, by employing Lyapunov stability theory, a sufficient condition on the consensus of singular multi‐agent systems is obtained. Then, the control protocol and event‐triggering scheme are designed by solving a linear matrix inequality condition. Finally, an example is given to illustrate the proposed results. [ABSTRACT FROM AUTHOR]

This paper develops a nonlinear Discrete-Event (DE) model for Intersecting Lines (ILs) of a Subway Network (SN). A class of Monte Carlo (MC) methods based on repeated random values is employed to validate the model. Model validation is performed by generating random values for delay rates and external disturbances. After model validation, a Robust State Feedback (RSF) controller is designed to compensate the delays caused by disturbances. Simulations are performed based on the characteristics and actual data of lines 2 and 4 of the Tehran subway to demonstrate the effectiveness of the proposed approach. Simulation results show the accuracy and proper performance of the proposed model. In addition, the closed-loop responses demonstrate the effectiveness of the proposed RSF controller for centralized and decentralized control configurations. • A nonlinear discrete-event state-space model of two intersecting metro lines is introduced by considering the effect of the transfer stations. • The introduced model is validated using repeated random sampling based on the Monte Carlo method. • A robust state feedback controller using a linear matrix inequality is designed to compensate any delays. • Two centralized and decentralized control structures are considered to evaluate and compare the performance of the control structures in metro traffic regulation. [ABSTRACT FROM AUTHOR]

The focus of this article is to present a sawtooth-characteristic-based free-matrix integral inequality and to discuss its application to sampled-data systems (SDSs). Firstly, the free matrix, which is associated with the sawtooth characteristic of the input delay, is presented and incorporated into the integral inequality. In the development of inequality techniques, this is the first time that a free matrix has been associated with the sawtooth characteristic. On this basis, a corresponding sawtooth-characteristic-based free-matrix integral inequality is established, enabling estimation of the integral quadratic terms of the Lyapunov–Krasovskii functional (LKF) derivative. To overcome the challenges posed by second-order terms resulting from the proposed integral inequality, augmented system variables associated with the sawtooth characteristic are also introduced. Thus, the complicated calculation arising from second-order terms and the conservatism caused by the quadratic estimation of the LKF can be avoided. Finally, through the utilization of the sawtooth-characteristic-based free-matrix integral inequality, stability criteria with less conservatism are derived for the SDSs in the form of linear matrix inequalities. The superiority of the proposed approach is illustrated through two numerical examples and a simplified sampled-data based power market. • A sawtooth-characteristic-based free-matrix integral inequality is proposed for the first time. The novelty of this inequality technique is that the commonly used constant free matrix is set to be input delay, i.e., d k 1 (t) -dependent matrix. This is the first time that a free matrix has been associated with the sawtooth characteristic. • Some augmented system variables associated with the input delay d k 1 (t) and the corresponding free-weighting-matrix are introduced to reduce the high-order terms of d k 1 (t). Thanks to the introduction of augmented system variables, the complicated calculation arising from d k 1 (t) 2 -related terms as well as the conservatism caused by the quadratic estimation of the LKF, can be avoided. Meanwhile, some high-order LKF that have been abandoned by scholars because of cumbersome calculations can also be selected as LKF candidates without quadratic treatment. • The proposed sawtooth-characteristic-based free-matrix integral inequality is employed for sampled-data system. The integral quadratic terms of the LKF derivative can be converted into some sawtooth-characteristic-dependent terms by the proposed integral inequality, and less conservative stability criteria for SDSs are obtained. [ABSTRACT FROM AUTHOR]

In stabilization of a Large-Scale System (LSS), the decentralized nature of the controller is a significant issue, because centralized controllers are difficult and impractical for real-time implementation. The designing procedure for decentralized controllers should guarantee the stability of the overall LSS and at the same time, allow limited information exchange in the LSS. In this paper, a decentralized controller for a nonlinear LSS modeled by a Linear Parameter Varying (LPV) model is designed. The controller design procedure is formulated as a convex feasibility problem which can be solved by finding a feasible answer to some Linear Matrix Inequalities (LMIs). The solution to this feasibility problem assures a fully decentralized controller where information exchange among local controllers is forbidden and, only data transfer among each controller and its corresponding subsystem is allowed. In the proposed approach, the Lyapunov function of the LSS equipped with local controllers is considered as the sum of the Lyapunov functions of all subsystems. Then, the stability conditions are derived to assure the stability of the LSS. After designing a decentralized controller to ensure LSS stability, the same approach is exploited for H ∞ and H 2 performance improvement of the LSS in the presence of disturbances. To verify the efficacy of the designed controller, a large-scale power system which is a practical example is considered, and the proposed approach is applied on it. The simulation results prove the appropriateness of the designed local controllers. • A decentralized controller is designed for a large-scale linear parameter varying system. • A fully decentralized controller with limited information exchange among subsystems is designed. • The controller is designed in three cases; stabilization, H ∞ and H 2 performance improvement. • The stabilization design procedure is formulated as a convex feasibility problem. • The H ∞ and H 2 design procedures are formulated as convex optimization problems. [ABSTRACT FROM AUTHOR]

The existing impulsive consensus algorithms for second-order Lipschitz nonlinear multi-agent systems require to apply the impulsive control to both position and velocity vectors at the same time. Such a requirement cannot be met in most of the real-world applications. To overcome the limitations of these impulsive algorithms, two kinds of new second-order impulsive consensus algorithms using only velocity regulation are proposed. Through developing a weighted discontinuous Lyapunov function-based approach that is able to leverage the spectral property of Laplacian matrix, impulse-dwell-time-dependent sufficient conditions for solving second-order impulsive consensus are derived in the form of linear matrix inequalities. Further, it is shown that if the impulsively controlled velocity subsystems are globally exponentially stable, the impulsive static consensus algorithm is able to ensure that all agents tend to an agreed position. Based on the consensus conditions, two convex optimization problems are formulated, by which the impulsive gain matrices for ensuring a prescribed exponential convergence rate can be designed. Finally, the effectiveness of the proposed distributed impulsive consensus algorithms is certified through numerical simulations. • Impulsive consensus algorithms based on velocity regulation are proposed for vector second-order Lipschitz nonlinear MASs. • The relationship between impulsive dynamical consensus and impulsive static consensus is analyzed. • A convex framework is proposed to design impulsive consensus gain matrices with guaranteed convergence rate. [ABSTRACT FROM AUTHOR]

This study utilizes the Takagi–Sugeno fuzzy model to represent a subset of nonlinear systems and presents an innovative adaptive approach for optimal dynamic terminal sliding mode control (TSMC). The systems under consideration encompass bounded uncertainties in parameters and actuators, as well as susceptibility to external disturbances. Performance evaluation entails the design of an adaptive terminal sliding surface through a two-step process. Initially, a state feedback gain and controller are developed using Linear Matrix Inequality (LMI) techniques, grounded on H 2 -performance and partial eigenstructure assignment. Dynamic sliding gain is subsequently attained via convex optimization, leveraging the derived state feedback gain and the designed terminal sliding mode (TSM) controller. This approach diverges from conventional methods by incorporating control effort and estimating actuator uncertainty bounds, while also addressing sliding surface and TSM controller design intricacies. The TSM controller is redefined into a strict feedback form, rendering it suitable for addressing output-tracking challenges in nonlinear systems. Comparative simulations validate the effectiveness of the proposed TSM controller, emphasizing its practical applicability. [ABSTRACT FROM AUTHOR]

In this paper, two novel methodologies of employing machine learning (here, the type-2 fuzzy system) are presented to control a multiagent system in which the agents are flexible joint robots. In the previous methods, the static mode controller has been investigated, which has little flexibility and cannot measure all the states of the system, but in the method presented in this paper, we can eliminate these disadvantages. The control signal is consisting of feedback from the output and the estimated states of the system. In the first method, the control signal coefficients are calculated from the linear matrix inequality (LMI), followed by a type-2 fuzzy system that adds the compensation signal to the control signal. In the second method, the type-2 fuzzy system is directly used to estimate the control signal coefficients which do not employ LMI. Both methods have their disadvantages and benefits, so in general, one of these two methods cannot be considered superior. To prove the effectiveness of the two proposed methods, a topology with four robots has been considered. Both proposed methods have been evaluated for controlling the angle and speed of the robot link. Also, another simulation was made without using the fuzzy system to verify the importance of our methods. Simulation results indicate the proper efficiency of proposed methods, especially in presence of uncertainty in the system. [ABSTRACT FROM AUTHOR]

This paper is devoted to investigating a class of stochastic neutral-type neural networks with delays. By using the fixed point theorem and the properties of neutral-type operator, we obtain the existence conditions for periodic solutions of stochastic neutral-type neural networks. Furthermore, we obtain the conditions for the exponential stability of periodic solutions using Gronwall-Bellman inequality and stochastic analysis technique. Finally, a numerical example is given to show the effectiveness and merits of the present results. Our results can be used to obtain the existence and exponential stability of periodic solution to the corresponding deterministic systems. [ABSTRACT FROM AUTHOR]

This article investigates the robust cooperative fault-tolerant control problem of multi-agent systems subject to mismatched uncertainties and actuator faults. During the design process of the intermediate variable estimator, there is no need to satisfy fault estimation matching conditions, and this overcomes a crucial constraint of traditional observers and estimators. The feedback term of the designed estimator contains the centralized estimation errors and the distributed estimation errors of the agent, and this further improves the design freedom of the proposed estimator. A novel fault-tolerant control protocol is designed based on the fault estimation information. In this work, the bounds of the fault and its derivatives are unknown, and the considered method is applicable to both directed and undirected multi-agent systems. Furthermore, the parameters of the estimator are determined through the resolution of a linear matrix inequality (LMI), which is decoupled by employing coordinate transformation and Schur decomposition. Lastly, a numerical simulation result is used to demonstrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a learning-based control approach for autonomous vehicles. An explicit Takagi–Sugeno (TS) controller is learned using input and output data from a preexisting controller, employing the Adaptive Neuro-Fuzzy Inference System (ANFIS) algorithm. At the same time, the vehicle model is identified in the TS model form for closed-loop stability assessment using Lyapunov theory and LMIs. The proposed approach is applied to learn the control law from an MPC controller, thus avoiding the use of online optimization. This reduces the computational burden of the control loop and facilitates real-time implementation. Finally, the proposed approach is assessed through simulation using a small-scale autonomous racing car. [ABSTRACT FROM AUTHOR]

In this paper, a novel nonlinear unknown input observer is proposed in order to fault estimation for nonlinear uncertain systems with time delays. By the estimation of the faults, the features are detected such as shape, size occurrence time etc. The time delay is considered a constant and known parameter in the states. The disturbances are investigated in the states and outputs and also, and sensor and actuator faults are considered. The stability of the closed‐loop system is guaranteed by Lyapunov–Krasovskii theory and some feasible Linear matrix inequalities (LMI). The proposed method is simulated on a continuous‐stirred tank reactor (CSTR) with uncertainties and time delay. Simulation results show the appropriate efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

In the paper, the exponential synchronisation for delayed Clifford-valued coupled switched neural networks via static event-triggering rule is studied. Firstly, the drive-response systems for delayed Clifford-valued coupled neural network models are established. So as to avoid the non-commutativity issue of Clifford number multiplication, the original n-dimensional Clifford-valued models are decomposed into $ 2 ^mn $ 2 m n -dimensional real-valued models. On this basis, the error dynamics system is constructed, and then some new sufficient conditions are presented of the exponential synchronisation for the considered neural network models by using Lyapunov–Krasovskii (L-K) functional approach and the technique of linear matrix inequality. Finally, the effectiveness of the results are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This article is concerned with the stability and stabilisation of switched time-delay systems (STDSs) with exponential uncertainty. Based on the Hurwitz convex combination and the energy attenuation principle, an improved state-dependent switching strategy is proposed, which switches to the next modes to obey the minimum energy. This approach fully considers the system dynamic of subsystems, which is more general. Considering the complex switching and delay dynamics, a mode-dependent Lyapunov–Krasovskii functional (LKF) that contains a triple integral term is constructed. The generalised free-matrix-based integral inequality (GFMBII) is used to estimate the integral terms in the derivative of the LKF, and an improved delay-dependent stability criterion is established in the form of linear matrix inequalities (LMIs). Further, to guarantee the stability of the STDSs with a large time-varying delay, a controller that considers the time delay and the exponential uncertainty is designed. Under this controller, a less conservative delay-dependent robust stabilisation criterion for STDSs with exponential uncertainty is established. The validity of the proposed methods is validated by two numerical examples and an application in river pollution control. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of event-triggered robust state and fault simultaneous estimation for nonlinear time-delay systems subject to actuator and sensor unknown disturbances. Based on a fault decomposition technique and some basic mathematical transformations, we obtain an augmented system where the state vector consists of the variable of the original system and the fault. Then a novel event-triggered state observer for the augmented system is proposed to robustly estimate the variable of the original system and the fault. We next established a sufficient condition for the existence of such an observer. We translated it into a linear matrix inequality (LMI), which can be effectively solved using the MATLAB LMI Control Toolbox. Finally, an illustrative example is applied to test the proposed method. [ABSTRACT FROM AUTHOR]

The problem of unknown input observer design for discrete-time nonlinear generalized Markov jump systems is studied. First, like a normal system, the whole nonlinear system is transformed into a local linear system, and then a large number of linear system theories can be applied to solve related problems. Second, in the observer design of general discrete-time Markov jump systems, only the unknown input in the state equation is usually considered. In this paper, the unknown input is considered in both the state equation and the output equation. The state estimation error system is derived by defining the error. The non-uniform Lyapunov functional is selected to stabilize the estimation error system using the Lyapunov theory. The sufficient conditions for the stability of the system are obtained and transformed into the feasibility problem of linear matrix inequality. The problem of unknown input observer design for discrete-time nonlinear generalized Markov jump systems is solved using MATLAB software. Finally, a numerical example of two rules and two modes is used to verify the effectiveness and feasibility of the proposed unknown input observer. [ABSTRACT FROM AUTHOR]

A robust dynamic output feedback predictive control approach is developed for a discrete system with time-varying delays, unknown external disturbances, and unmeasurable states. First, the discrete system is transformed into an incremental state deviation model. Based on this model, a novel tracking deviation feedback model is established by extending the output tracking error. Then, a robust predictive control law, possessing more degrees of freedom, is designed. The closed-loop model is further given in conjunction with the feedback model. Second, by using the linear matrix inequality (LMI) method, relaxation technique, and variable transformation method, a less conservative stability condition is given in LMI form, which allows the controller to tolerate a greater range of time-varying delays. The gains of the control law are acquired by solving the stability condition, and the control performance can be significantly enhanced. Finally, by utilizing the TTS20 water tank as a simulation case, the viability and effectiveness of the proposed method are demonstrated. [ABSTRACT FROM AUTHOR]

It is well known that control effort is the key factor considered in formation control of a multi‐agent system (MAS). To reduce the controller effort, an economic event‐triggered super twisting control (STC) protocol for the formation tracking of a nonlinear MAS, which avoids the unnecessary computations and transmission of control inputs among agents. Specifically, a distributed leader‐follower control framework, combing the multi‐input STC with event‐triggered strategy, is proposed to ensure that the followers' states reach an agreement on the leaders state. Then, the sufficient conditions for the selection of controller parameters are formulated in terms of linear matrix inequalities (LMIs). On this basis, the event‐triggered conditions for implementing the STC protocol in the network environment are obtained using Lyapunov stability theory. Simulation study is carried out to demonstrate the effectiveness and merits of the STC in terms of formation construction, trajectory tracking, and robustness to system uncertainties. [ABSTRACT FROM AUTHOR]