This article deals with periodic event-triggered control (PETC) of nonlinear systems, considering an equivalent quasi-linear parameter-varying (quasi-LPV) polytopic representation of the nonlinear plant and a gain-scheduled controller for stabilization. Although gain-scheduling approaches allow one to improve the results and extend the set of feasible solutions to the co-design problem, the event-based sampling induces the so-called asynchronous scheduling functions, which void the gain-scheduling advantages, leading to conservative results, especially in the PETC framework. The dominant approaches for dealing with this issue consider a bounding assumption on the mismatched scheduling functions, but do not guarantee that those bounds cannot be violated during the closed-loop operation. To properly manage the asynchronous phenomenon, we propose a novel PETC scheme. Based on the looped-functional approach and a nonquadratic Lyapunov function, we derive linear matrix inequality (LMI)-based conditions to co-design the event-triggering mechanism and the gain-scheduled controller. These conditions are incorporated into a multiobjective optimization problem to maximize the estimate of the region of attraction of the origin and minimize the number of transmissions of the PETC scheme. We prove that the closed-loop trajectories initiated in the estimated region of attraction converge toward the origin without violating the boundedness of the mismatched scheduling functions during operation. Two numerical examples are provided to illustrate the methodology.

This article presents a strategy for estimating deception false data injection (FDI) attacks on sensors and actuators in cyber–physical systems (CPSs) described by a class of linear parameter-varying (LPV) systems. Gain-scheduled intermediate-variable-based estimators (GSIVBEs) are proposed to reconstruct both the system states and the attack sequences, ensuring bounded estimation errors even in cases where such attacks evade detection by conventional threshold-based methods. A convex design condition is derived to ensure that the estimation error dynamics are input-to-state stable with respect to variations in the attack sequences. To improve the accuracy of the estimators, an optimization problem is formulated to minimize the estimation error under these conditions. In addition, different strategies are proposed to mitigate the effects of the attack sequences on the system by using the estimated attack sequences as part of an attack-tolerant control framework. The proposed approach demonstrates its effectiveness in enhancing system resilience, contributing to the security and reliability of CPSs under adversarial scenarios.

This article investigates the event-triggered leaderless consensus control problem for fractional-order multiagent systems (FOMASs), where both the agent-to-agent communication channel and the controller-to-actuator communication channel are based on the events. A filter is introduced to transform the original high-order system into a first-order one, greatly simplifying the complexity of controller design compared to the traditional backstepping. Further, the convergence of filtered output signals is proved to be consistent with that of the outputs of agents themselves. Superior to the traditional event-triggered scheme, two dynamic variables are designed for the triggering conditions of the communication among agents and the controller update, respectively. Via elaborately constructing the dynamic variables, zero-error leaderless consensus can be achieved instead of only ultimately uniformly bounded result. It is proved that the proposed control strategy can guarantee better control performance of leaderless consensus under limited communication resources, and Zeno behavior is excluded. Finally, two examples are provided to verify the effectiveness of our proposed control approach.

This paper investigates the dynamic memory eventtriggered (DMET) fuzzy optimized consensus control for nonlinear multi-agent systems (MASs) with quantized reference signal. To alleviate the communication burden, a dual communication channels DMET scheme is proposed, which encompasses eventdriven communication for interactions among followers and communication between controllers and actuators. In comparison to the traditional dynamic event-triggered (DET) scheme, the devised DMET scheme incorporates historical information of the dynamic variable, resulting in longer triggering time intervals. Note that the problem of non-differentiability in backstepping method is generated by the event-triggered communication and quantization. To address this challenge, a smooth signal generator is introduced to reconstruct the step signals into the differentiable new one. Meanwhile, a reinforcement learning (RL) approach is employed to optimize the controllers, which utilizes an identifiercritic-actor architecture with fuzzy logic system (FLS) approximations at each step of backstepping method. The effectiveness of the proposed control method is demonstrated through simulations, confirming its capabilities in achieving optimized consensus control while mitigating communication loads.

Numerous previous findings on the synchronization of fractional-order networks have been conducted through event-triggered control (ETC) or intermittent control (IC), separately. Motivated by the benefits of IC and ETC, this article designs an effective event-triggered intermittent control (ETIC) to investigate the bipartite synchronization of fractional-order fuzzy signed networks. The system dynamics are constructed to describe the nonlinear signed networks via the fuzzy logic and the short-memory performance. Notably, this article represents the first attempt to design the ETIC for fractional-order networks in the sense of exponential convergence. This approach avoids the constantly updating states of IC and the uninterrupted input of ETC. By employing the Lyapunov method, some sufficient conditions for the synchronization of the considered networks are obtained. In addition, the Zeno phenomenon is eliminated so that the infimum of interval length is positive, which ensures the feasibility of the designed controller. Finally, two numerical experiment examples of the fractional-order Chua's circuits model and the fractional-order power system without load disturbance are carried on to illustrate the effectiveness and practicability of our theoretical analysis.

This article adopts a novel homogeneous polynomial parameter-dependent (HPPD) codesign method to deal with the security control problem of the Takagi–Sugeno fuzzy system of cyber-physical dc microgrid under hybrid attacks. A new fuzzy control scheme and state estimation scheme, i.e., a function whose homogeneous polynomial parameters depend on the fuzzy membership function normalized at the current time, is proposed to achieve the combined goal of relaxed control and accurate estimation. Relaxed exponential stability conditions are then derived with less conservatism than the existing conditions. In addition, an HPPD codesign method is further proposed. The effectiveness and superiority of the results in this article are illustrated through simulation examples.

A method to design plug-and-play (PnP) distributed controllers for large-scale nonlinear systems represented by interconnected Takagi-Sugeno fuzzy models with nonlinear consequent is presented in this article. From the combination of techniques to use multiple fuzzy summations and to explore the chordal decomposition of the interconnection graph associated with the large-scale nonlinear system, sufficient conditions for distributed stabilization are derived in terms of linear matrix inequalities (LMIs). Conditions specially designed to allow seamless subsystems plugging-in and unplugging operations from the large-scale system, without requiring the redesign of all previously tuned distributed controllers, are provided. The approach can be used together with fault detection and isolation (FDI) systems, and also in the context of mixed distributed and decentralized controllers operating in a network of interconnected systems. To illustrate the effectiveness of the proposed PnP approach, a network of nonlinearly coupled and heterogeneous Van der Pol oscillators is used in the numerical experiments.

This article presents a novel secure-control framework against sensor deception attacks. The vulnerability of cyber-physical systems with respect to sensor deceptive attacks makes that all sensor measurements are not reliable until the system security is assured by an attack detection module. Most of the active attack detection strategies require some time to assess the system security, while injecting a watermark signal to ease the detection. However, the injection of watermark signals deteriorates the performance and stability of the plant. The proposed control framework consists of a dual-rate control (DRC) that is able to stabilize the plant using: 1) a model predictive controller that operates at a slower sampling time; 2) a state-feedback predictor-based controller that operates in the nominal sampling time disregarding the use of the untrustworthy measurements until the attack detector is able to certify the security; and 3) a reconfiguration block (RB) for palliating the effect of the watermarking. Simulation results indicate the efficacy of the proposed DRC framework to defend the system from cyber-attacks and the ability of the RB to improve the closed-loop performance during the watermark injection.

This article presents a new approach to design static output-feedback (SOF) controllers for constrained Takagi-Sugeno fuzzy systems with nonlinear consequents. The proposed SOF fuzzy control framework is established via the absolute stability theory with appropriate sector-bounded properties of the local state and input nonlinearities. Moreover, both state and input constraints are explicitly taken into account in the control design using set-invariance arguments. Especially, we include the local sector-bounded nonlinearities of the fuzzy systems in the construction of both the nonlinear controller and the nonquadratic Lyapunov function. Within the considered local control context, the new class of nonquadratic Lyapunov functions provides an effective solution to estimate the closed-loop domain of attraction, which can be nonconvex and even disconnected. The convexification procedure is performed using specific congruence transformations in accordance with the special structures of the proposed SOF controllers and nonquadratic Lyapunov functions. Consequently, the fuzzy SOF control design can be reformulated as an optimization problem under strict linear matrix inequality constraints with a linear search parameter. Compared to existing fuzzy SOF control schemes, the new structures of the control law and the Lyapunov function are more general and offer additional degrees of freedom for the control design. Both theoretical arguments and numerical illustrations are provided to demonstrate the effectiveness of the proposed approach in reducing the design conservatism.

This paper is concerned with a new control method for path tracking of autonomous ground vehicles. We exploit the fuzzy model-based control framework to deal with the time-varying feature of the vehicle speed and the highly uncertain behaviors of the tire-road forces involved in the nonlinear vehicle dynamics. To avoid using costly vehicle sensors for feedback control while favoring the simplest control structure for real-time implementation, a new fuzzy static output feedback (SOF) scheme is proposed. In particular, though the robust set-invariance property and Lyapunov-based arguments, the physical constraints on the steering input saturation and the vehicle state can be taken into account in the control design to improve the driving safety and comfort. The theoretical development relies on the use of fuzzy Lyapunov functions and the non-parallel distributed compensation control concept to reduce the design conservatism. Exploiting some specific convexification techniques, the control design is reformulated as an optimization problem under linear matrix inequalities with a single line search, which are efficiently solved via semidefinite programming techniques. The proposed fuzzy path tracking controller is evaluated through various dynamic driving tests conducted with high-fidelity CarSim/Matlab co-simulations. Moreover, to emphasize the advantages of the new fuzzy SOF controller, a performance comparison with the CarSim driver model is also performed.

This article deals with the problem of designing nonlinear distributed control laws for continuous-time networked nonlinear heterogeneous systems with bounded sector nonlinear interconnections. The networked system is a combination of interconnected Takagi–Sugeno (TS) fuzzy systems with nonlinear consequent subject to state and control input constraints. The new sufficient conditions, taking into account state constraints and actuators saturation, are derived in terms of linear matrix inequalities. Further, it is shown that the closed-loop system can be made asymptotically stable while reducing the conservatism over decentralized and linear distributed control laws derived following the same method. At the same time, the maximization of the estimate of the domain of attraction (DoA) for the closed-loop system is pursued. Finally, two cases are presented to illustrate the effectiveness of the proposed design approach: 1) an electrical power system composed of two-machine subsystems and 2) a network of multiple inverted pendulums connected by nonlinear springs.

This paper presents a new control method for path tracking of autonomous vehicles. Takagi-Sugeno fuzzy control is used to handle the time-varying vehicle speed and the uncertain tire-road forces involved in the nonlinear vehicle dynamics. To avoid using costly vehicle sensors while keeping a simple control structure, a new fuzzy static output feedback (SOF) scheme is proposed. Moreover, robust set-invariance is exploited to take into account the physical limitations on the steering input and the vehicle state in the control design for safety and comfort improvement. Based on Lyapunov stability arguments, a non-parallel distributed compensation SOF controller is designed for autonomous driving with reduced conservatism. The control design is reformulated as an optimization problem under linear matrix inequalities, easily solved with available numerical solvers. The path tracking performance of the proposed fuzzy controller is evaluated via dynamic driving tests conducted with high-fidelity CarSim/Simulink co-simulations.

Dealing with uncertain data requires effective methods to properly describe their real meaning in terms of a tradeoff between interpretability and generality on the process of knowledge formation based on data abstraction. This article proposes an online granulation process based on evolving ellipsoidal fuzzy information granules (EEFIG) and the principle of justifiable granularity (PJG) for data streams parameterization. The granulation process consists in the information granule development taking into consideration the data stream with a simplified optimal granularity allocation. In the sequel, an evolving Takagi-Sugeno fuzzy model based on the ellipsoidal granules is proposed for data reconstruction and one-step ahead prediction from past data numerical evidence. Experimental studies concerning clustering, data granulation, and time-series forecasting are performed to illustrate the effectiveness of the proposed method.

This paper presents a new method to design non-parallel distributed compensation (non-PDC) laws for Takagi- Sugeno fuzzy systems with local nonlinear models subject to actuator saturation. Based on specific congruence transformations, the local stabilization conditions are derived using Lyapunov stability theorem. The local design framework is established through an effective treatment of the sector-bound conditions for the input-saturation phenomenon and the nonlinearities in the consequents of the fuzzy systems. Using a non-quadratic Lyapunov function candidate, the control design is reformulated as an LMI-based optimization problem with a line search over a parameter, which can be effectively solved with convex optimization techniques. In particular, we theoretically prove that the new control method is less conservative compared to that derived from a standard non-PDC controller. Illustrative examples are provided to point out the interests of the proposed control method.

This paper is concerned with the reduction of conservatism on stabilization conditions of discrete-time Takagi-Sugeno fuzzy models via delayed nonquadratic Lyapunov functions. A fruitful approach recently appeared in the literature, which, despite its benefits, dramatically increases the number of linear matrix inequalities needed to synthesize a controller. The two sets of sufficient conditions hereby proposed tackle this numerical problem while reducing conservatism and increasing the stabilization domain of existing conditions in literature, as illustrated in several examples.

Many of the recent advances on control and estimation of systems described by Takagi-Sugeno (TS) fuzzy models are based on matrix inversion, which could be a trouble in the case of real-time implementation. This paper is devoted to the development of alternative solutions to this matrix inversion problem in the discrete-time case. Two different methods are proposed: The first one relies on replacing the matrix inversion by multiple sums and the second methodology is based on an estimation of the matrix inversion by an observer structure. For the first methodology, a new class of controllers and observers are introduced which are called, respectively, the counterpart of an advanced TS-based (CATS) controller and the replica of an advanced TS-based (RATS) observer. Instead of relaxations for the linear matrix inequalities conditions, an original use of the membership functions is presented. In the second methodology, it is proposed the estimation-based control law for approximating TS-based (ECLATS) controller that uses a fuzzy state observer. The Lyapunov theory is used to ensure stability conditions for either the closed-loop system as well as the estimation error. Numerical examples and comparisons highlight the efficiency of the procedures that can be used to replace any inverted matrix in any advanced fuzzy controller or observer. Finally, advantages and drawbacks of the proposed method are discussed.

A verification methodology is described and evaluated to formally determine uncertain linear systems stability in digital controllers with considerations to the implementation aspects. In particular, this methodology is combined with the digital-system verifier (DSVerifier), which is a verification tool that employs Bounded Model Checking based on Satisfiability Modulo Theories to check the stability of digital control systems with uncertainty. DSVerifier determines the control system stability, considering all the plant interval variation set, together with the Finite Word-length (FWL) effects in the digital controller implementation; DSVerifier checks the robust non-fragile stability of a given closed-loop system. The proposed methodology and respective tool are evaluated considering non-fragile control examples from literature. Experimental results show that the approach used in this study is able to foresee fragility problems in robust controllers, which could be overlooked by other existing approaches due to underestimating of FWL effects.

This paper aims to present a systematic methodology for designing a Replica of an Advanced Takagi-Sugeno (RATS) discrete observer. Advance observers for nonlinear systems under Takagi-Sugeno representation have been designed for years using efficient structure such as non-PDC (Parallel Distributed Compensation), which it is powerful and, in some cases, it is the only observer able to estimate an unknown value. However, in spite of these advantages, this observer strategy presents an inconvenient: The use of matrix inversion. This paper will present the RATS observer which is equivalent an observer using the non-PDC structure without matrix inversion. By a stability analysis, not only the efficiency is proved but also its validity. Finally, some simulation results will emphasize the originality and the power of the proposed RATS observer.

This paper aims to compare alternative time delay relaxations for a class of nonlinear systems controlled via network and described by Takagi-Sugeno fuzzy models. In this regard, three alternatives were proposed and compared with a very recent relaxation proposed in the literature. Basically, the changes are made at two strategic points. The first point is the Lyapunov functional proposed and the second one is related to the introduction of different integral inequalities conditions. A numerical example of a network-based fuzzy tracking control systems is presented to highligth the advantages of the alternatives relaxations.

International audience

Unknown nonstationary processes require modeling and control design to be done in real time using streams of data collected from the process. The purpose is to stabilize the closed-loop system under changes of the operating conditions and process parameters. This paper introduces a model-based evolving granular fuzzy control approach as a step toward the development of a general framework for online modeling and control of unknown nonstationary processes with no human intervention. An incremental learning algorithm is introduced to develop and adapt the structure and parameters of the process model and controller based on information extracted from uncertain data streams. State feedback control laws and closed-loop stability are obtained from the solution of relaxed linear matrix inequalities derived from a fuzzy Lyapunov function. Bounded control inputs are also taken into account in the control system design. We explain the role of fuzzy granular data and the use of parallel distributed compensation. Fuzzy granular computation provides a way to handle data uncertainty and facilitates incorporation of domain knowledge. Although the evolving granular approach is oriented to control systems whose dynamics is complex and unknown, for expositional clarity, we consider online modeling and stabilization of the well-known Lorenz chaos as an illustrative example.

This paper presents the model identification and the velocity control of an autonomous car. The control system was designed so that the car is controlled at low speeds, where the main applications for the vehicle's autonomous operations include parking and urban adaptive cruise control. A longitudinal model of the car was used in the control loop to compensate the nonlinear behavior of its dynamics. Since the determination of the vehicle's model is a difficult step in the design of model-based controllers, the main contribution of this paper is the use of an empirically determined model to this end. In this paper, the structure of the model was conceived from the car's physics equations, but its parameters were estimated using data-based identification techniques. An important contribution of this paper is the fact that, although the model is strictly linear, we can change its parameters as a function of the operation point of the vehicle to represent the engine's and the transmission's nonlinear behaviors. Moreover, in this paper, we propose a way to include changes in the longitudinal dynamics caused by the automatic gear shifting. The validation of the proposed controller was conducted by computer simulations and real-world experiments.

Improvements of recent stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems are proposed. The key idea is to bring together the so-called local transformations of membership functions and new piecewise fuzzy Lyapunov functions. By relying on these special local transformations, the associated linear matrix inequalities that are used to prove the system's stability can be relaxed without increasing the number of conditions. In addition, to enhance the usefulness of the proposed methodology, one can choose between two different sets of conditions characterized by independence or dependence on known bounds of the membership functions time derivatives. A standard example is presented to illustrate that the proposed method is able to provide substantial improvements in some cases.

In this paper, the stability analysis and control design of Takagi-Sugeno (TS) fuzzy systems subject to uncertain time-delay are addressed. The proposed approach is based on linear matrix inequalities and the Lyapunov-Krasovskii theory, where a new fuzzy weighting-dependent Lyapunov-Krasovskii functional is introduced. By employing the Gu discretization technique and strategies to add slack matrix variables, less conservative conditions are obtained. Numerical experiments are performed to illustrate the effectiveness of the proposed methodology.

This article presents a simple efficient algorithm for the subdivision of a d -dimensional simplex in k d simplices, where k is any positive integer number. The algorithm is an extension of Freudenthal's subdivision method. The proposed algorithm deals with the more general case of k d subdivision, and is considerably simpler than the RedRefinementND algorithm for implementation of Freudenthal's strategy. The proposed simplex subdivision algorithm is motivated by a problem in the field of robust control theory: the computation of a tight upper bound of a dynamical system performance index by means of a branch-and-bound algorithm.