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This paper presents a new control synthesis methodology for nonholonomic mobile robots subjected to time-varying delays and input saturation constraints. The proposed control method is based on smooth static nonlinear functions, leading to a simpler structure than other available control strategies for this class of systems. In addition, the convergence to a certain target position with guaranteed exponential decay rate can be proved for any orientation error. To this end, a nonlinear Lyapunov-Krasovskii functional has specifically been designed to deal with the inherent discontinuity of the kinematics model as well as the presence of time-varying delays. Thus, the control design can efficiently be addressed by means of Linear Matrix Inequalities (LMIs). Finally, the effectiveness of the proposed control design algorithm is validated through simulation and experimentally using a two-wheeled mobile robot.

This paper presents a fault estimation technique based on the decentralized fuzzy observer for nonlinear large-scale systems, which are considered to be consisted of fuzzy subsystems and uncertain interconnections. Based on a Takagi–Sugeno fuzzy model for the subsystems of the large-scale system and the decentralized fuzzy observer, the $H_{\infty }$ performance of the fault estimation problem is established by using the estimation error model. By using $H_{\infty }$ performance inequalities to address the fault estimation problem, the decentralized fuzzy observer design techniques are proposed to guarantee the fault estimation conditions. Also, sufficient conditions of observer design are converted into the linear matrix inequality formats. Finally, an example is provided to verify the effectiveness of the proposed decentralized fuzzy observer design techniques for fault estimation.

In this study, a sampled-data fuzzy fault estimation observer design problem is considered for nonlinear systems. The main idea of this study is to solve the sampled-data output problem by using two approaches of approximate discretization and exact discrete-time design. Especially, in the exact discrete-time design approach, the discretization error problem is solved, and the estimation error is minimized over whole time interval. Based on the above idea, the fuzzy fault estimation observer uses the Takagi–Sugeno fuzzy model to address the fuzzy fault estimation technique, and the fault estimation conditions with an $H_{\infty }$ performance are guaranteed. Next, sufficient conditions of the proposed fault estimation techniques are converted into linear matrix inequality formats. Finally, two examples of circuit and oscillator systems are provided, and the effectiveness of the proposed fault estimation techniques is verified from results of the simulation.

In this paper, we propose a control approach for the robust stabilization of linear time-invariant (LTI) systems with non-negligible sensor and actuator dynamics subject to time-delayed signals. Our proposition is based on obtaining an augmented model that encompasses the plant, sensor, and actuator dynamics and also the time-delay dynamic effect. We make use of the Padé Approximation for modeling the time-delay impact on the feedback loop. Since the actual plant state variables are not available for feedback, the sensor outputs, which represent a subset of the augmented system state variables, are used for composing a static output-feedback control law. The robust controller gains are computed by means of a two-stage strategy based on linear matrix inequalities (LMI). For obtaining less conservative conditions we consider the use of homogeneous-polynomial Lyapunov functions (HPLF)– and other decision variables– of arbitrary degree. In our proposition, we also take into account the inclusion of a minimum decay rate criterion in order to improve closed-loop system transient response. Disturbance rejection is also addressed through extensions to $\mathscr {H}_{2}$ guaranteed cost minimization. The effectiveness of the proposed strategy is attested in the design of a controller for the lateral axis dynamics of an aircraft and other academic examples.

The introduction of the switched affine system opens new perspectives for the control design of dc–dc converters. In order to overcome the drawbacks of the continuous-time switching control methods, several sampled-data-based switching control approaches have been proposed in the literature. However, in these works, the solution of control parameters involves a nonlinear optimization problem. In addition, the designed switching laws are nonlinear functions about the system state, which require higher computational resources. In this article, a periodic time-triggered hybrid control is proposed based on a new design framework. All the design conditions are in linear matrix inequality formulations, which can be conveniently solved by common semidefinite programming software. Moreover, the proposed switching law is a linear function about the state, reducing the online computing burden. Finally, a unified view of the classical continuous-time switching scheme and the proposed method is established. Simulation and experiment tests on a buck–boost converter demonstrate the good performance of the proposed control strategy. [ABSTRACT FROM AUTHOR]

In this article, we address the distributed event-triggered leader–follower formation tracking control problem of general linear multiagent systems with a dynamic leader in sampled-data settings. A novel locally computable state-estimate-based event generator is established for each follower agent to regulate the interagent communication at each sampling instant. Then, we propose a distributed formation tracking protocol based on the triggered sampled information such that the formation tracking control problem can be formulated as a stability-analysis problem of the closed-loop formation error dynamics. The event generator and formation tracking controller gains can then be co-designed using the feasible linear matrix inequality conditions that are derived from Lyapunov-based stability-analysis methods that guarantee the ultimate boundedness of the closed-loop formation error dynamics. Finally, numerical simulations along with experiment implementations were conducted for a group of linearized unicycle-type mobile robots to demonstrate the effectiveness and advantages of the proposed method. [ABSTRACT FROM AUTHOR]

This study focuses on the quasisynchronization problem for reaction–diffusion neural networks (RDNNs) in the presence of deception attacks. Under deception attacks, a time–space sampled-data (TSSD) control mechanism is proposed for RDNNs. Compared with traditional control strategies, the proposed control mechanism can not only save network bandwidth but also improve the cybersecurity of communications. Inspired by Halanay’s inequality, a new inequality is proposed, which can be effectively applied to the quasisynchronization problem for dynamical systems. Then, by using this inequality and the Lyapunov functional approach, quasisynchronization criteria are set for RDNNs. The desired control gain is gained from solving a group of linear matrix inequalities. Moreover, in the absence of deception attacks, the exponential synchronization problem is studied for RDNNs. In the end, simulation results are given to demonstrate the usefulness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This article addresses the dynamic positioning control problem of a nonlinear unmanned marine vehicle (UMV) system subject to network communication constraints and deny-of-service (DoS) attack, where the dynamics of UMV are described by a Takagi–Sugeno (T-S) fuzzy system (TSFS). In order to save limited communication resource, a new intelligent event-triggering mechanism is proposed, in which the event triggering threshold is optimized by a $Q$ -learning algorithm. Then, a switched system approach is proposed to deal with the aperiodic DoS attack occurring in the communication channels. With a proper piecewise Lyapunov function, some sufficient conditions for global exponential stability (GES) of the closed-loop nonlinear UMV system are derived, and the corresponding observer and controller gains are designed via solving a set of matrix inequalities. A benchmark nonlinear UMV system is adopted as an example in simulation, and the simulation results validate the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

A dual-loop robust control scheme and its property of performance separation are presented in this article. The dual-loop control scheme consists of two degrees of freedom for nominal and robust performances, with the nominal controller being any stabilizing controller in the observer-based state-feedback form and robust controller being a standard $H_{\infty }$ controller. When there is model error and/or disturbance, the robust controller is activated to compensate the nominal controller; otherwise, the dual-loop control returns to a single-loop nominal controller. We also show that the nominal and robust performances of the dual-loop control are independent of one another. As a result, the nominal and robust controllers can be designed separately offline, and then, online coordinated in the dual-loop control. Furthermore, the state-space realization and controller implementation are also provided. Finally, a two-wheeled robot with varying slip effect is considered as an illustrative example. Both simulation and experimental results show that the dual-loop control outperforms the classical robust control methods. [ABSTRACT FROM AUTHOR]

This article presents a learning-based controller to solve the cooperative formation control problem for multiagent system (MAS) with collision avoidance. First, the consensus problem of first-order MAS is mostly solved by linear matrix inequality (LMI) without consideration of energy loss. To overcome these difficulties, an adaptive dynamic programming (ADP) technique is fit to solve the consensus problem and similar formation control problem for second-order MAS by the establishment of a performance index function. Besides, we introduce the generalized policy iteration (GPI) algorithm as a kind of ADP technique without the problem of low convergence speed and high computational complexity. Combined with previous works, it can be found that our proposed structure can be extended to high-order cases based on the structure of local neighborhood formation error and algorithm. Afterward, the convergence analysis, optimality analysis, and stability analysis are given. Neural networks (NNs) are also implemented to approximate the iterative control policies and value functions, respectively. Moreover, we realize that many collisions may occur in the formation control problem. Inspired by the idea of the artificial potential field (APF) technique, the concept of the repulsive force field is introduced based on our proposed learning-based structure to avoid collisions simply and efficiently. Finally, a simulation is provided to demonstrate the effectiveness of our proposed method. [ABSTRACT FROM AUTHOR]

In this article, the control approach based on structured input–output finite-time stability (IO-FTS) is extended to tackle the reference tracking problem. IO-FTS was originally introduced to deal with the disturbance rejection problem. By applying the finite-time stability control to a properly augmented system, we show that it is possible to enforce a set of specific requirements on the response of the closed-loop system during the transients, taking also into account saturation constraints on the actuators. Adding IO-FTS constraints to classic-state-feedback control law leads to a feasibility problem with bilinear matrix inequality (BMI) constraints. Herein, we show how the original BMI problem can be relaxed to a linear matrix inequality (LMI) one, which comes at a price of more conservatism, but turns out to be computationally more efficient. To prove the effectiveness of the proposed approach, we consider the case of the longitudinal control of a missile. [ABSTRACT FROM AUTHOR]

The entropy power inequality (EPI) and the Brascamp-Lieb inequality (BLI) are fundamental inequalities concerning the differential entropies of linear transformations of random vectors. The EPI provides lower bounds for the differential entropy of linear transformations of random vectors with independent components. The BLI, on the other hand, provides upper bounds on the differential entropy of a random vector in terms of the differential entropies of some of its linear transformations. In this paper, we define a family of entropy functionals, which we show are subadditive. We then establish that Gaussians are extremal for these functionals by adapting a proof technique from Geng and Nair (2014). As a consequence, we obtain a new entropy inequality that generalizes both the BLI and EPI. By considering a variety of independence relations among the components of the random vectors appearing in these functionals, we also obtain families of inequalities that lie between the EPI and the BLI. [ABSTRACT FROM AUTHOR]

This brief dedicates to addressing the robust fault estimation (FE) problem for a class of T-S fuzzy singular systems (TSFSSs) subject to faults and disturbances. A dissipativity-based FE observer design scheme is proposed to realize fault reconstruction, by which the FE performance can be improved in contrast to the existing one. With the help of the Lyapunov approach, dissipativity theory and matrix transformation technique, a brand-new condition is established to ensure observation error dynamics to be strictly $(\mathscr {Q}, \mathscr {U}, \mathscr {R})-\iota -$ dissipative. It is worth mentioning that different from some previous studies, our method can solve observer gains simultaneously in a strict linear matrix inequality (LMI) framework rather than determine some of them artificially. Moreover, to bring extra degrees of freedom, slack scalars and matrices are added in FE observer design. The superiority of our method is fully illustrated via simulations. [ABSTRACT FROM AUTHOR]

This article addresses the delay-dependent Takagi–Sugeno (T–S) fuzzy state feedback control and exponential admissibility analysis for a class of T–S fuzzy singular uncertain systems. First, the T–S fuzzy model is employed to approximate the singular uncertain system with time-varying delay, saturation input, and unmatched disturbance. Second, the delay-dependent T–S fuzzy state feedback controller is designed by employing the T–S fuzzy model. Third, the free-weighting matrices and delay-dependent Lyapunov–Krasovskii functional with multiple integral terms are employed to derive the delay-dependent exponential admissibility conditions and prescribed H-infinity performance is guaranteed. Compared with previous works, the delay-dependent T–S fuzzy state feedback controller is designed for the T–S fuzzy singular uncertain system to relax system design conditions. The convex hull lemma is employed to convert the closed-loop system with saturation input into the closed-loop system without saturation input to enhance controller design flexibility. The Schur complement lemma and Gronwall Bellman lemma are employed to derive the less conservative delay-dependent stability conditions for determining controller gain matrices. The exact invariant set with less conservativeness is employed to convert the controller design problem into linear matrix inequalities (LMIs) optimization constraints to reduce computation complexity of solving LMIs. Finally, simulation examples are presented to show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

An analysis and controller design of double-input dc–dc converter (DIDDC) is introduced in this article. This converter is integrated with buck and boost converters at the front-end and a charge pump on the back-end. Salient features of this topology are as follows: (i) ripple content is low in source currents, (ii) both the dc sources are connected through an inductor, which gives rise to a smooth source current waveform, (iii) both the sources supply power to load either in standalone or simultaneously together, and (iv) two control–loops (one for source current regulation, while the second one for load voltage regulation) are sufficient enough to ensure power transfer/management from dc sources to load. To ensure power management on the input dc sources while keeping a stable closed-loop converter system, a multivariable diagonal controller is designed. The first diagonal controller performs the load voltage regulation task, while the second controller regulates input of source-2 dc current. From the control point of view, the double-input single-output converter becomes a two-input two-output control problem and exhibits control–loop interactions due to the power flow from two different sources to load through common elements. The impact of off-diagonal elements’ interactions is accounted by using decouplers. The H∞ robust control theory and linear matrix inequality (LMI) principles are adopted to design reliable controllers. The structured controller of fixed order (PID) is designed by enforcing the necessary type LMIs. To demonstrate the feasibility and effectiveness of multivariable controllers of the DIDDC, a 60/24 V to 48 V, 150 W, 50 kHz topology prototype is constructed, and the power management aspects are investigated experimentally. Load voltage regulation, source current regulation, load sharing on the input dc sources, and power management aspects of LMI-based controllers were tested extensively for all possible disturbances. In all these test cases, the closed-loop double-input converter system is stable and robust in rejecting a variety of disturbances created. [ABSTRACT FROM AUTHOR]

This article proposes a physics-based control-oriented model and observer design for the state-of-charge (SoC) estimation of lithium-ion cells for applications involving high magnitude fluctuating current profiles. The physics-based single-particle model (SPM) provides enhanced accuracy due to the inclusion of electrolyte dynamics and addresses the issue of nonobservability associated with it. The computationally efficient physics-based model is utilized to design a robust observer-based SoC estimator in the framework of linear matrix inequality to guarantee fast convergence despite parametric uncertainty in the state and output equations, and unknown initial conditions. The observer performance is validated using FTP75 and US06 dynamic tests at different temperatures, and the results are compared with the standard unscented Kalman filter (UKF). The mean SoC estimation error and the integral square error of the estimated SoC for the proposed observer are at least one order of magnitude smaller than that of UKF. Furthermore, robustness to ±30% parametric uncertainty, measurement noise, and unknown initial conditions is demonstrated through Monte Carlo simulations at different temperatures. [ABSTRACT FROM AUTHOR]

This article investigates the admissibility analysis for Takagi–Sugeno fuzzy singular systems (T–S FSSs) with time-varying delays. First, according to the decomposed state vectors, a state decomposition Lyapunov–Krasovskii functional (LKF) is constructed, which possesses fewer decision variables. And, the LKF is augmented by considering more features of the second-order Bessel–Legendre inequality (BLI). Then, the second-order BLI and the generalized reciprocally convex matrix inequality are employed to dispose the derivative of the LKF, where the $d^{2}(t)$ -dependent term exists. Meanwhile, by setting an adjustable parameter, the $d^{2}(t)$ -dependent term of the condition is handled by a relaxed quadratic function negative-determination condition. As a result, a less conservative admissibility criterion for T–S FSSs is obtained. And, the relationship between the conservatism and the numerical burden is better considered. Finally, a numerical example is given to demonstrate the reduced conservatism and computational complexity. [ABSTRACT FROM AUTHOR]

This article considers the reachable set estimation problem and membership function dependent $H_\infty$ performance analysis for a class of fuzzy Markov jump systems (FMJSs) with mode-dependent time-varying delays and bounded external disturbances via sampled-data control. First, mode-dependent sampled-data control for the FMJS is designed using the Takagi–Sugeno (T–S) fuzzy method. Then, a novel stochastic Lyapunov–Krasovskii functional (LKF) is constructed in mode-dependent augmented form by taking full advantage of the variable characteristics related to the actual sampling pattern. At the same time, a membership function dependent $H_\infty$ performance index is introduced for the first time to attenuate the impact of disturbances on the closed-loop FMJS. Based on the novel $H_\infty$ performance index and LKF, new delay-dependent conditions are derived in the framework of linear matrix inequalities to ensure stochastic stability of the closed-loop system and its reachable set is bounded by an ellipsoid in the presence of bounded disturbances. Finally, two illustrated application problems validate theoretical results with less conservatism in the sense of enlarging the sampling period and minimizing the disturbance attenuation level. [ABSTRACT FROM AUTHOR]

This article is concerned with the stability and stabilization of delayed discrete-time T–S fuzzy systems. The purpose is to develop less conservative stability analysis and state-feedback controller design methods. First, a matrix-separation-based inequality is proposed, which can provide a tighter estimation for the augmented summation term. Then, by constructing a delay-product-type Lyapunov–Krasovskii functional, using the proposed inequality to estimate its forward difference and using a cubic functional negative-determination lemma to handle nonconvex conditions with respect to the delay, a delay and its variation-dependent stability criterion are obtained. Moreover, the corresponding controller design method for closed-loop delayed fuzzy systems is derived via parallel distributed compensation scheme. Finally, two examples are given to demonstrate the effectiveness and merits of the proposed approaches. [ABSTRACT FROM AUTHOR]

This article studies the finite-time composite antidisturbance control problem for nonhomogeneous Markovian jump systems (MJSs) subject to multiple disturbances via the Takagi–Sugeno (T–S) fuzzy control scheme. The designed two-gains disturbance observer (DO) and the considered MJSs are supposed to switch the different Markovian chains, which are depicted by a hidden Markovian model. Herein, an asynchronous DO design is explored for the first time, providing new insight into the construction of asynchronous DO. First, the $H_\infty /L_{2}-L_\infty$ finite-time boundedness of the augmented system is guaranteed. Second, based on the Finsler lemma, the linearization issue in calculating observer/controller gain is addressed. Finally, two illustrations are presented to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article addresses the stabilization of the nonlinear reaction–diffusion equation with an unknown but bounded delay. Based on Takagi–Sugeno (T–S) fuzzy rules, a T–S fuzzy partial differential equation (PDE) model is constructed to describe the nonlinear distributed parameter system. More importantly, we contribute to the large delay compensation and the future state prediction by introducing a chain of subpredictors for the T–S fuzzy PDE model, and the convergence of observation errors is guaranteed as well. Different from the conventional approaches, the proposed observer can compensate a larger delay. To stabilize the system, for the first time, a new subpredictor-based T–S fuzzy control law is suggested by using the proposed observer, which is composed of elementary observers connected in series. The implementation of the subpredictor feedback is simpler than the classical methods that only one of the elementary observers is employed. Via Lyapunov–Krasovskii approach, sufficient exponential stability conditions are established in the framework of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness of theoretical results. [ABSTRACT FROM AUTHOR]

In this article, the backstepping control scheme is designed for a class of systems with multisource disturbances, actuator saturation, and nonlinearities in the domain of discrete time. To address the multisource disturbances, we put forward a novel discrete-time hybrid observer, which can deal with both modeled and unmodeled disturbances. In virtue of the radial basis function neural networks, the unknown nonlinearities are approximated. In addition, the anti-windup technique is adopted to cope with the actuator saturation phenomenon, which is pervasive in engineering practice. Bearing all the adopted mechanisms in mind, the composite control strategy is designed in a backstepping manner. Sufficient conditions are established to guarantee that the states of the system ultimately converge to a small range with linear matrix inequalities. Finally, the effectiveness of the presented methodology is verified for the spacecraft attitude system. [ABSTRACT FROM AUTHOR]

This article deals with the problems of stability and control of the interconnected system (IS) with unknown time-varying delays via decentralized time-delay control using partial variables with measurable states. First, the model of the IS with time delays is established, and the relevant control scheme is proposed. The control scheme just needs to control all or partial state variables corresponding to the elements on the main diagonal of the gain matrices, which can reduce the control cost and improve the flexibility of control. In addition, there are no additional restrictions in the process of designing the controller. Second, relevant lemmas are derived. The exponential boundedness and stability analysis of the IS with time delays are presented, respectively, by stability theory, and related results are derived. Meanwhile, the stability domain of the IS is estimated. Besides, the obtained results can also be used for many practical systems, such as the interconnected power system, the multislave teleoperation systems, the brushless dc motor (BLDCM) system, and the chaotic system. Finally, the effectiveness and application of the obtained results are verified by several examples. [ABSTRACT FROM AUTHOR]

In harsh environments, tracking is organized assuming disturbances, initial errors, and data errors that requires robust algorithms. In this article, we develop, in discrete-time state space, a robust a posteriori $H_{2}$ optimal finite impulse response ($H_{2}$ -OFIR) filter of disturbed systems under initial and measurement errors. The derivation is provided using a novel $H_{2}$ finite impulse response ($H_{2}$ -FIR) state estimation approach by minimizing the squared Frobenius norm of the weighted transfer function. The robust $H_{2}$ -OFIR filter is designed for full block error matrices, and its recursive forms are shown for diagonal error matrices. Also presented is the suboptimal $H_{2}$ -FIR filtering algorithm using the linear matrix inequality. It is shown that, in global-positioning-system-based tracking of moving vehicles, the $H_{2}$ -OFIR filter outperforms the Kalman and unbiased FIR filters in terms of accuracy and robustness. Moreover, the ability to operate on short horizons makes the $H_{2}$ -OFIR filter computationally efficient. [ABSTRACT FROM AUTHOR]

This article presents a novel dynamic event-triggered scheme for the load frequency regulation with periodic denial-of-service (DoS) attacks and deception attacks via decentralized output-based control algorithm. Compared with the existing event-triggered strategy, the proposed one automatically changes the parameters of the triggered condition by detecting the frequency trend of the DoS attack to change the release frequency, which can ensure the stability of the power system while increasing the probability of effective transmission subject to DoS attack and thus, reducing network bandwidth usage. First, the proposed dynamic event-triggered strategy combined with the decentralized output-based controller is presented in a unified framework to deal with deception attacks and DoS attacks in the multiarea power system. Then, we utilize the Lyapunov stability theory to analyze the exponential stability in the mean-square sense and the robustness of the power system. By solving a set of linear matrix inequalities (LMIs), a procedure is given for the design of output-based load frequency controllers. Finally, a three-area power system is exploited as a simulation to verify the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This article focuses on the design problem of fault detection (FD) observer for a class of continuous-time nonlinear systems. The $\mathcal {H_{-}}$ index is employed to measure the worst cast fault sensitivity. First, the nonlinear systems are represented by the Takagi–Sugeno (T–S) fuzzy dynamic models. Then, a novel fuzzy Lyapunov function (FLF) analyzing approach is proposed to reduce the conservatism in stability analysis and $\mathcal {H_{-}}$ index estimation for the T–S fuzzy model. In particular, employing this new type of the FLF, the stability analysis of the T–S fuzzy systems perfectly overcomes the difficulty of evaluating the upper bound of the time derivative of the membership function. Based on the descriptor system approach, some new sufficient conditions on the existence of fuzzy FD observers are obtained in terms of linear matrix inequalities (LMIs). Finally, illustrative examples are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article proposes a unified framework to investigate the leader-following and leaderless consensus problem of general linear multiagent systems under the directed communication topology only containing a spanning tree. To further reduce the use of resources for the control objective, an energy-saving control algorithm is introduced composed of double dynamic event-triggered mechanisms that work independently: one intends to control the communication of agents with their neighbors and the other to decide the update of controllers. It is shown that the control algorithm performs well compared to most existing control algorithms in terms of the communication cost between agents and the update cost of controllers. In addition, a new procedure to choose parameters is obtained by the developed Lyapunov stabilty method, with the potential of achieving less conservative parameters than related results. Finally, the effectiveness of the proposed control scheme is verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This article investigates the problems of state bounding description and reachable set estimation for discrete-time delayed genetic regulatory networks with bounded disturbances. A novel delay-dependent sufficient condition composing several simple linear matrix inequalities is first given to guarantee that the state trajectories converge globally exponentially into a Cartesian product of two polytopes. Furthermore, equivalent sufficient conditions directly represented by the system parameters are derived. As applications, it is shown that these sufficient conditions are exactly global exponential stability criteria of the zero equilibrium when the disturbances vanish, and the Cartesian product of two polytopes can be viewed as a reachable set estimation of the states when the initial functions are limited into a certain range. The effectiveness of the proposed approach is illustrated by two numerical examples. Compared with the existing results, it is worthy to stress that the presented method does not need to construct any Lyapunov–Krasovskii functional and can be easily realized. [ABSTRACT FROM AUTHOR]

This article is concerned with the leader-following output consensus problem in the framework of distributed nonlinear observers. Instead of certain hypotheses on the leader system, a group of geometric conditions is put forward to develop a novel distributed observers strategy, thereby definitely improving the applicability of the existing results. To be more specific, the improved distributed observers can precisely handle consensus problems for some nonlinear leader systems, which are invalid for the traditional strategies with a certain assumption, such as elastic shaft single linkage manipulator (ESSLM) systems and most of the first-order nonlinear systems. We prove the sufficient conditions for the exponential stability of our distributed observers’ error dynamic by proposing two pioneered lemmas to show the relationship between the maximum eigenvalues of two matrices appearing in Lyapunov type matrices. Then, a partial feedback linearization method with zero dynamic proposed in differential geometry is employed to design the purely decentralized control law for the affine nonlinear multiagent system. With this advancement, the existing results can be regarded as a specific case owing to that the followers can be chosen as an arbitrary minimum phase affine smooth nonlinear system. At last, the novel distributed observers and the improved purely decentralized control law are applied in the distributed control framework to construct a closed-loop system. We also prove the stability of the closed-loop system to achieve leader-following consensus. Our method is illustrated by the ESSLM system and Van der Pol system as leaders. [ABSTRACT FROM AUTHOR]

In this article, we present an innovative approach, i.e., horizonwise model-predictive control (H-MPC), to solve the model-predictive control (MPC) problem of a linear time-varying (LTV) system. In H-MPC, we regard the time-varying parameters as time invariant within the prediction horizon. To solve the MPC problem of the time-varying system, the decision variable is decomposed into two terms: one for linear time-invariant optimization and the other for compensating LTV uncertainties with an introduction to a uniform compensation condition. The proposed H-MPC solves the time-varying problem by removing the uncertainty due to the future parameter variations within the horizon and by updating the time-invariant MPC at each sampling time. To validate the usefulness of the proposed H-MPC, it is applied to lane tracking control for an autonomous driving vehicle. From a comparative study of the H-MPC and conventional MPCs in lane tracking control, it is confirmed that the proposed H-MPC has a competitive performance compared to LTV-MPC despite its much simpler structure. [ABSTRACT FROM AUTHOR]

This paper studies the distributed consensus protocol for the connected vehicle platoon with heterogeneous time-varying delays and switching topologies. A third-order dynamics model with powertrain inertial lag is proposed to characterize the node longitudinal dynamics of vehicles in platoon. A novel distributed adaptive consensus protocol considering the time-varying delays and the random switched inter-vehicular communication topologies is designed to stabilize the heterogeneous vehicle platoon in the presence of external disturbance. The delay-range-dependent approach is used to deal with the system heterogeneous time-varying delays by considering the characteristics of the heterogeneous platoon. Directed graphs are adopted to describe the accessible information flow among vehicles. The necessary and sufficient conditions for the unified closed-loop vehicle platoon system are derived by using matrix analysis and Lyapunov-Krasovskii approach. Numerical simulations demonstrate the proposed method is effective. [ABSTRACT FROM AUTHOR]

In order to ease the online computational burden of fuzzy model-predictive control for the Takagi–Sugeno model with bounded disturbance, a lookup table containing the possible mappings from the state to the input is usually constructed offline so that the online computational burden is reduced to searching in this lookup table. However, with the increase in the problem size, the computational burden of the online search in the lookup table can be large enough to influence the real-time implementation. In this article, we propose a novel offline approach to solve this problem, where the control law is online searched in a receding horizon cache, which is only a small portion of the lookup table. The cache is refreshed in a one-step-ahead fashion to guarantee that the proper one-step-ahead state-to-input mapping can be found in the cache. The recursive feasibility and stability hold. The effectiveness and the efficiency of the proposed approach are verified through two examples. [ABSTRACT FROM AUTHOR]

This article investigates the nonfragile guaranteed cost (GC) control problem of discrete-time impulsive switched Takagi–Sugeno (T–S) fuzzy systems with input quantization and asynchronous switching. The model-dependent dynamic quantizers are applied to obtain the quantized input signal. To deeply study the GC performance analysis and GC control problems in the presence of quantization, asynchronous switching, and impulses, a novel piecewise cost function containing the quantized input instead of normal input is applied in this article. By using the mode-dependent average dwell time approach and introducing a class of Lyapunov-like functions allowing to increase during the asynchronous period, new sufficient conditions are established to guarantee the asymptotical stability with the GC performance index for the impulsive switched T–S fuzzy systems with quantized control input and asynchronous switching. Then, new design conditions about the nonfragile GC controllers and dynamic quantizers of impulsive switched T–S fuzzy systems are obtained in the form of linear matrix inequalities. Finally, a numerical example and a practical example are provided. [ABSTRACT FROM AUTHOR]

In this work, a robust static output feedback (SOF) design for continuous-time nonlinear systems under norm bounded uncertainties, described as a Takagi–Sugeno (TS) system is proposed. The key features are that a switching control law is used to activate the SOF gains to stabilize the uncertain TS fuzzy system and the SOF design does not require the measurements of all premise variables in real time as in the standard fuzzy parallel distributed compensation design. The main result is given in terms of linear matrix inequalities, which guarantees a ${\mathcal {H}}_{\infty }$ attenuation level of $\gamma$ for the SOF control system. The efficiency of the main results is illustrated with examples, including a nonlinear active suspension system under uncertain driver masses, and compared with other published results from the literature. [ABSTRACT FROM AUTHOR]

This article is dedicated to studying realization issues of the stability performance-based nonlinear fault-tolerant control framework via Takagi–Sugeno (T–S)fuzzy models. To this end, the nonlinear fault-tolerant control strategy with an online fault detection system monitoring the system stability performance degradation induced by faults is first introduced by means of the stable image and kernel representations. On this basis, the T–S fuzzy models are applied to approximate the nonlinear system, and a design approach of the fuzzy observer-based controller is proposed for the system stabilization via the iterative linear matrix inequality method. With the controller gains, the fuzzy-model-based nominal stable image representation of the system is formulated, which leads to the generation of the input and output error signals. Then, with the reference signal and system input and output error signal data, a data-driven algorithm is given to online estimate the evaluation function defined in terms of system uncertainties and faults. By virtue of the $L_{2}$ input–output stability of the controller stable kernel representation, a threshold calculation method is presented and, thus, the stability performance-based fault detection system based on fuzzy models is realized. Furthermore, for fault-tolerant purpose, the fault-tolerant controller design is discussed, which aims to retain the system stability. Two examples are provided in the end to illustrate the proposed results. [ABSTRACT FROM AUTHOR]

This article is concerned with exponential stabilization almost surely for a class of discrete-time switched T–S fuzzy systems (DTSTSFSs), in which each mode switches according to transition probability and evolves with mode-dependent average dwell time. Parallel distributed compensation (PDC) event-triggered dynamic output quantization (ETDOQ) control is considered for the DTSTSFSs, where event-triggered (ET) mechanism without Zeno behavior is designed, which is mode-dependent and does not restrict the dwell time of each mode. By using the mode-dependent Lyapunov function method, two sufficient conditions termed by linear matrix inequalities are provided. Different from most of existing results, no inequality is resorted in dealing with the uncertainties coming from the quantization. It is interesting that the controlled modes are not required to be stable. New algorithm is designed for the control gains of the ETDOQ controller and the parameters of the ET condition, which overcomes the mismatching difficulty of the parameters induced by the PDC. Numerical simulations demonstrate the merits of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This study concerns the stabilization criteria of Takagi–Sugeno (T–S) fuzzy systems under the memory-based sampled-data control. Contrasted to the traditional sampled-data control strategy, a more general control scheme that admits the signal transmission delay and the multiplicative control gain uncertainties is designed. In order to indicate the perturbations of control gain, the Bernoulli sequence is applied to the designed control scheme. At the same time, the membership function dependent $H_{\infty }$ performance index is introduced to attenuate the disturbances of continuous-time T–S fuzzy systems for the first time. By utilizing the novel $H_{\infty }$ performance index together with the appropriate Lyapunov–Krasovskii functional, including the information of sampling period and signal transmission delay, the sufficient conditions are derived in the framework of linear matrix inequalities. These conditions ensure the stabilization of concerned T–S fuzzy systems and enlarging the maximum sampling period. At last, the advantages of the derived results are shown by the numerical examples. [ABSTRACT FROM AUTHOR]

In this study, the robust $H_{\infty }$ fuzzy observer-based fault-tolerant tracking control strategy is proposed for the stochastic polynomial fuzzy system (SPFS) under the effect of external disturbance, measurement noise, system/sensor fault signals and continuous/discontinuous internal random fluctuations. At first, the smoothed models of fault signals are constructed to describe their dynamic behavior. Then, by integrating the SPFS with the smoothed models of fault signals as one augmented system, the state/fault signal estimation problem can be transformed to a state estimation problem of augmented system by the proposed polynomial fuzzy observer. With the utilization of estimated state/fault signals and reference trajectory, a fuzzy polynomial fault-tolerant tracking controller can be implemented. To attenuate the effect of undesired external disturbance and measurement noise on the state/fault signal estimation and tracking control performance, the robust $H_{\infty }$ fuzzy observer-based fault-tolerant tracking control strategy is proposed in this study. By utilizing the homogeneous Lyapunov function and Lipschiz condition, the Itô-Lévy formula is reformulated to relax the compensation terms of stochastic processes during the design. Then, the design conditions are derived in terms of interpolation function-dependent matrix inequality and consequently transformed to a two-step sum of square (SOS) condition design problem for the robust $H_{\infty }$ fuzzy observer-based fault-tolerant tracking control strategy. A simulation example of double lane maneuvering task for autonomous ground vehicle (AGV) is provided to illustrate the effectiveness of proposed method. Index terms: Observer-based tracking control, polynomial fuzzy system, stochastic control, fault-tolerant control, sum of square (SOS).

This paper deals with the design of an energy-to-peak reduced-order filter (also called $L_{2}-L_{\infty }$ filtering) for continuous-time Markov jump linear systems, assuming that the filter has only access to an estimate of the Markov parameter, coming from the output of a detector device. To model this situation we consider that the joint process formed by the Markov parameter and the detector information follows an exponential hidden Markov model. The result is given in terms of Linear Matrix Inequalities (LMI) so that the available numerical package tools can be readily implemented to solve the problem. The paper is concluded with some numerical simulations.

This paper proposes a new LMI-based strategy for designing decentralized control, which is aimed at large-scale systems. A distinguishing feature of this approach is its ability to produce decentralized feedback laws without placing any structural constraints on the Lyapunov function. It also allows the user to control the number of LMI variables, which can significantly reduce the computational effort. The effectiveness of this method is illustrated through applications to interconnected microgrid clusters. Simulation results show that the proposed approach can be used to regulate energy exchanges between the clusters in a way that ensures robust stability.

In this paper, we investigate the interval observer problem for a class of discrete-time nonlinear systems, in absence or presence of external disturbances and parametric uncertainties. The interval observers depend on the design of two preserving order observers, providing lower and upper estimations of the state. The main objective is to apply the stability radii notions and cooperativity property in the estimation error systems in order to guarantee that the lower/upper estimation is always below/above the real state trajectory at each time instant from an appropriate initialization, and the estimation errors converge asymptotically towards zero when the disturbances and/or uncertainties are vanishing. For the disturbed case, the estimation errors practically converge to a vicinity of zero, while the lower/upper estimations preserve the partial ordering with respect to the state trajectory. The design conditions, that are valid for Lipschitz nonlinearities, can be expressed as Linear Matrix Inequalities (LMIs). A numerical simulation example is provided to verify the effectiveness of the proposed method.

A robust algorithm for the extraction of reduced-order behavioral models from sampled frequency responses is proposed. The system under investigation can be any Linear and Time Invariant structure, although the main emphasis is on devices that are relevant for Signal and Power Integrity and RF design, such as electrical interconnects and integrated passive components. We assume that the device under modeling is parameterized by one or more design variables, which can be related to geometry or materials. Therefore, we seek for multivariate macromodels that reproduce the dynamic behavior over a predefined frequency band, with an explicit embedded dependence of the model equations on these external parameters. Such parameterized macromodels may be used to construct component libraries and prove very useful in fast system-level numerical simulations in time or frequency domain, including optimization, what-if, and sensitivity analysis. The main novel contribution is the formulation of a finite set of convex constraints that are applied during model identification, which provide sufficient conditions for uniform model stability and passivity throughout the parameter space. Such constraints are characterized by an explicit control allowing for a trade-off between model accuracy and runtime, thanks to some special properties of Bernstein polynomials. In summary, we propose a method to systematically address the longstanding problem of multivariate stability and passivity enforcement in data-driven model order reduction, which insofar has been tackled only via either over-conservative or heuristic and possibly unreliable methods.

In this study, a robust $H_{\infty }$ networked security observer-based reference tracking control scheme is proposed for the stochastic quadrotor unmanned aerial vehicle (UAV) system under malicious attacks on the actuator and sensor of network control system (NCS). To reduce the computational burden on UAV system, the UAV system is connected with a remote computing unit and the complicated tracking control command can be calculated by remote computing unit. By using the novel discrete smoothed model, the model of attack signals on actuator and sensor can be embedded in system state of UAV and thus the attack signals as well as the quadrotor system state can be simultaneously estimated through a conventional Luenberger observer. Further, the corruption of attack signals on state estimation of UAV is also avoided. To eliminate the effect of unavailable external disturbance and intrinsic fluctuation during the reference tracking control process, a robust $H_{\infty }$ networked security observer-based reference tracking control scheme is introduced to attenuate their effects on the NCS of quadrotor UAV. By using the characteristic of convex Lyapunov function, the design condition of robust $H_{\infty }$ networked security observer-based tracking control is derived in terms of the nonlinear functional inequalities. Since the nonlinear functional inequalities are not easy to be solved analytically or numerically, the Takagi-Sugeno (T-S) fuzzy interpolation technique is employed to interpolate the nonlinear stochastic quadrotor NCS by a set of linear local systems via fuzzy bases. In this case, the nonlinear functional inequalities can be converted to a set of linear matrix inequalities (LMIs) which can be easily solved by the MATLAB LMI TOOLBOX. Simulation results are provided to validate the effectiveness of the proposed method in comparison with conventional robust observer-based T-S fuzzy tracking control scheme.

The team formation of large-scale satellites for communication services of future smart cities in the 5G and 6G era is an important research topic currently. In this study, a robust $H_{\infty }$ tracking control with an event-triggered mechanism is proposed for the formation of large-scale satellites for communication tasks. At first, a satellite in the team formation is described by a nonlinear stochastic system with intrinsic random fluctuation, external disturbance, and coupling from other satellites. The proposed team formation tracking control for each satellite needs to consider the effect of network-induced delay and packet-dropout as well as save communication resources via an event-triggered mechanism. Further, the desired team formation of large-scale satellites can be prescribed by a set of reference models with the desired formation shape embedded in their reference inputs. Therefore, the large-scale team formation design problem can be simplified as an independent $H_{\infty }$ network model reference tracking control design problem for each satellite to efficiently attenuate the worst-effect of external disturbance, coupling of other satellites, intrinsic random fluctuation, network-induced delay, and packet-dropout on the model reference tracking performance. In order to avoid solving a nonlinear partial differential Hamillion-Jacobin inequality(HJI) for the $H_{\infty }$ decentralized network formation control for each satellite in the team the formation, the T-S fuzzy model is employed to interpolate several local linearized systems to approximate nonlinear satellite systems. Then the HJI in the $H_{\infty }$ decentralized network team formation design problem can be transformed into a set of linear matrix inequalities (LMIs) which can be easily solved by LMI TOOLBOX in MATLAB. Finally, a simulation example of team formation composed of ten satellites is given to illustrate the design procedure and to validate the proposed method in comparison with other methods.

In this study, a robust $H_{\infty }$ network observer-based attack-tolerant path tracking control design is proposed for the autonomous ground vehicle (AGV) under the effect of external disturbance, measurement noise and actuator/sensor attack signals. At first, a more practical AGV system is applied to describe the interaction among the longitudinal speed, lateral speed and yaw rate. Based on Controller Area Network (CAN), the information of local AGV is transmitted to remote control center through wireless channel and then the control command can be calculated from remote control center. To avoid the corruption of actuator/sensor attack signal from insecure CAN, two novel smoothed signal models are introduced to describe these attack signals and are embedded with the AGV dynamics system as an augmented system. Subsequently these attack signals can be simultaneously estimated with the AGV system state by the conventional Luenberger-type observer of the augmented system. By using the estimated state and attack signals, a robust $H_{\infty }$ network observer-based attack-tolerant path tracking controller is constructed to attenuate the effect of unknown disturbance on the energy of path tracking error and eliminate the influence of attacks signals. With the help of convex Lyapunov function, the design conditions of robust $H_{\infty }$ network observer-based attack-tolerant path tracking control design for AGV are derived in terms of a set of nonlinear difference inequalities. To reduce the difficulties in solving these nonlinear difference inequalities, Takagi-Sugeno fuzzy interpolation method is applied to approximate the nonlinear AGV system and the design can be simplified to a set of LMIs, which can be easily solved via LMI TOOLBOX in MATLAB. A double lane change task of AGV in CAN is provided as a simulation example to illustrate the design procedure and validate the effectiveness of proposed design method in comparison with the conventional steering control method.

A synchronization algorithm of nonlinear complex networks composed of nonlinear nodes is designed. The main idea is to apply the exact feedback linearization of every node first, then applying methods for synchronization of linear complex networks. The nodes need not admit full exact feedback linearization, however, they are supposed to be minimum-phase systems. To achieve the synchronization of the observable parts of the nodes, an algorithm based on the convex optimization (to be specific, on linear matrix inequalities) is proposed. Then, it is demonstrated that, using the minimum-phase assumption, the non-observable part of the nodes is synchronized as well. The algorithm for synchronization of the observable parts of the nodes can be used to design a control law that is capable of maintaining stability in presence of certain variations of the control gain. Uncertainties in the parameters are also taken into account. Two examples illustrate the control design.

Due to the uncertainty of vehicle model parameters, modeling errors and external disturbances, the performance of path tracking control system is poor, especially under high velocity and large curvature extreme conditions. To address this issue, this paper presents a novel gain-scheduled robust control strategy based on linear parameter varying system with model predictive control (MPC) and H∞. Firstly, fully considering the influence of the time-varying characteristics of vehicle velocity and tire cornering stiffness on the path tracking system model, a novel linear parameter varying system model is built for path tracking control of autonomous vehicle. Then, a path tracking robust controller is designed based on gain-scheduled approach, and the linear matrix inequality (LMI) is applied to solve optimization problem, in which MPC and H∞ robust control theory are applied to the controller design process. Finally, the simulation experiments have verified that the proposed novel robust control strategy can improve the path tracking accuracy and ensure the vehicle lateral and roll stability, especially under high velocity and large curvature extreme conditions. Meanwhile, the proposed robust controller shows superiority to suppress the parameters uncertainty, modeling error and external disturbance. [ABSTRACT FROM AUTHOR]

In order to ensure that the power system frequency and tie-line power remain at the nominal value when the load fluctuates, while reducing the release number of decentralized sensor, this work presents a novel adaptive event-triggered scheme for the load frequency regulation via designing the decentralized dynamic output feedback controller (DOFC), where the communication delay issue is also considered due to communication constraints. Distinct from the existing ones, the proposed adaptive event-triggered strategy automatically tunes the threshold according to the local extremum of the system output signal, which can significantly reduce the number of unnecessary signal transmissions to ensure system performance. First, the proposed adaptive event-triggered transmission scheme is integrated with the decentralized DOFC and communication delays under the framework of a linear time-delay system. Then, the asymptotic stability of the closed-loop power system is analyzed through the Lyapunov stability theory and a procedure is given for the design of decentralized dynamic output load frequency controllers by solving some linear matrix inequalities (LMIs). Finally, a three-area power system is used to verify the effectiveness and usefulness of the proposed results. [ABSTRACT FROM AUTHOR]

In this work, we study simultaneous reconstructions of sensor fault and actuator fault, as well as fault-tolerant control (FTC) for nonlinear systems approximated by the T–S fuzzy model. By making the sensor fault as part of the state, a rectangular singular system is firstly given, based on which, a proportional-integral observer (PIO) is synthesized to realize the reconstructions of sensor and actuator faults simultaneously. With the support of these estimation information, an FTC scheme is well provided to maintain the stability of the closed-loop system even in the occurrence of faults. Furthermore, by resorting to linear matrix inequalities (LMIs), the stability criteria are formulated via the fuzzy Lyapunov function method. Finally, the performance of the theoretical result is verified through two real dynamics. [ABSTRACT FROM AUTHOR]

This article is concerned with the fault detection and isolation (FDI) problem for a class of nonlinear systems described by the T–S fuzzy models. Based on the concept of minimum unobservability subspace and geometric property of factor space, a set of FDI filters where each residual is only affected by one fault and completely decoupled from other faults is designed. Furthermore, in the decoupling space, the $H_{\infty }/H_{-}$ performance indexes are provided to enhance the sensitivity of residual to faults and robustness to disturbances. In particular, to solve the nonconvex filter design problem caused by introducing the $H_{-}$ index, the Gerschgorin theorem is first used to linearize the corresponding filter design conditions in the outer region of a ball. Then, the FDI filter design problem is converted into a convex optimization one, which is solved via the linear matrix inequality (LMI) control Toolbox, and the advantages and effectiveness of the proposed FDI method are verified through two simulation examples. [ABSTRACT FROM AUTHOR]