Event-Triggered Output-Feedback Adaptive Control of Interconnected Nonlinear Systems: A Cyclic-Small-Gain Approach.

This article proposes a novel output-feedback event-triggered control protocol for a class of interconnected parametric nonlinear systems. Different from most existing works where event-triggering mechanisms are considered for only the controller-to-actuator channel or the sensor-to-controller channel, this work adopts event-triggering mechanisms for both channels as well as adaptive laws. An adaptive states observer is designed to estimate the unavailable system state and then a novel adaptive event-triggered controller is proposed based on the celebrated backstepping technique. By utilizing the cyclic small-gain theorem and Lyapunov theory, it is shown that the proposed control scheme ensures that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB), and the Zeno behavior is successfully excluded. Finally, a practical example is provided to illustrate the effectiveness and advantages of the proposed approach.

Fuzzy Adaptive Event-Triggered Consensus Control for Nonlinear Multiagent Systems Under Jointly Connected Switching Networks.

This article studies the fuzzy adaptive event-triggered (ET) consensus control issue of nonlinear multiagent systems (NMASs) under jointly connected switching networks. Since the leader and its high-order derivatives are unknown under jointly connected switching networks, a novel distributed ET reference generator equipped with an ET mechanism is constructed to estimate them. Meanwhile, the continuous information transmission among agents is avoided and the network channel utilization is optimized. Subsequently, fuzzy logic systems (FLSs) are employed to approximate unknown dynamics, and a fuzzy adaptive ET consensus control algorithm only using intermittent communication is designed by backstepping control methodology. It is demonstrated that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB), with the tracking errors converging to a small neighborhood around zero. Finally, we apply the developed fuzzy adaptive ET consensus control algorithm to unmanned surface vehicles (USVs), and the simulation results verify the effectiveness of the proposed ET consensus control algorithm.

Hierarchical Robust Generalized Nash Equilibrium Seeking of High-Order Uncertain Nonlinear Systems.

This article investigates the distributed generalized Nash equilibrium (GNE) seeking problem of noncooperative games (NGs) for high-order strict-feedback nonlinear multiagent systems (MASs). In particular, the feasible action set of each agent is not only subject to local set and inequality constraints but also coupled through an equality constraint with other agents. This constraint structure is more general and covers most of the constraints in the GNE seeking literature. To accomplish the concerned GNE seeking objective, we propose a novel hierarchical GNE seeking approach in this article to decouple the distributed GNE seeking algorithm design into two layers. First, we construct a distributed primary-dual GNE estimator to generate virtual reference signals that converge to the GNE. Then, with the output of the estimator as the reference signal, we develop an adaptive tracking controller to solve the resultant tracking problems under output constraints. To overcome the negative effects of the disturbances, novel compensating terms associated with smooth functions and positive integrable time-varying functions are incorporated in the controller design, which thereby realizes the exact GNE seeking in the presence of nonvanishing mismatched disturbances. At last, an example is given to support the theoretical analysis of the proposed algorithms.

Nonsingular Fixed-Time Asymptotic Consensus for Nonlinear Nonstrict-Feedback MASs.

In this article, a fuzzy adaptive fixed-time asymptotic consistent control scheme is developed for a class of nonlinear multiagent systems (NMASs) with a nonstrict-feedback (NSF) structure. In the control process, a fixed-time consistency control method without control singularity is proposed by combining fuzzy logic systems (FLSs) with good approximation capability, fixed-time stability theory, and plus power integration techniques. Then, by using Barbalat's Lemma, the asymptotic stability of tracking errors and the boundedness of the controlled systems are successfully achieved, which means that the tracking errors can converge to zero in a fixed time. Finally, the effectiveness of the designed control scheme is demonstrated by a simulation example.

FTC Design for Switched Fractional-Order Nonlinear Systems: An Application in a Permanent Magnet Synchronous Motor System.

In this article, an adaptive fault-tolerant control (FTC) method and a fractional-order dynamic surface control (DSC) algorithm are jointly proposed to deal with the stabilization problem for a class of multiple-input-multiple-output (MIMO) switched fractional-order nonlinear systems with actuator faults and arbitrary switching. In each MIMO subsystem and each switched subsystem, the neural networks (NNs) are utilized to identify the complicated unknown nonlinearities. A fractional filter DSC technology is adopted to conquer the issue of "explosion of complexity," which may occur when some functions are repeatedly derived. The common Lyapunov function method is used to restrain arbitrary switching problems in the system, and the actuator compensation technique is introduced to tackle the failure faults and bias faults in the actuators. By combining the backstepping DSC design technique and fractional-order stability theory, a novel NN adaptive switching FTC algorithm is proposed. Under the operation of the proposed algorithm, the stability and control performance of the fractional-order systems can be guaranteed. Finally, a simulation example of a permanent magnet synchronous motor (PMSM) system reveals the feasibility and effectiveness of the developed scheme.

Adaptive Neural Network Event-Triggered Output-Feedback Containment Control for Nonlinear MASs With Input Quantization.

This article investigates the adaptive neural network (NN) event-triggered containment control problem for a class of nonlinear multiagent systems (MASs). Since the considered nonlinear MASs contain unknown nonlinear dynamics, immeasurable states, and quantized input signals, the NNs are adopted to model unknown agents, and an NN state observer is established by using the intermittent output signal. Subsequently, a novel event-triggered mechanism consisting of both the sensor-to-controller and controller-to-actuator channels are established. By decomposing quantized input signals into the sum of two bounded nonlinear functions and based on the adaptive backstepping control and first-order filter design theories, an adaptive NN event-triggered output-feedback containment control scheme is formulated. It is proved that the controlled system is semi-globally uniformly ultimately bounded (SGUUB) and the followers are within a convex hull formed by the leaders. Finally, a simulation example is given to validate the effectiveness of the presented NN containment control scheme.

Fuzzy Adaptive Consensus Control for Nonlinear Multiagent Systems With Intermittent Actuator Faults.

This article addresses the distributed adaptive fuzzy consensus fault-tolerant control (FTC) problem for a class of nonstrict-feedback nonlinear multiagent systems (NMASs) with intermittent actuator faults. The NMASs contain unknown nonlinear dynamics, and actuator faults are the type of intermittent faults. Unknown nonlinear functions have been handled based on fuzzy-logic systems (FLSs) approximation, and the distributed virtual controllers together with their parameter adaptive laws are first designed by combining the adaptive backstepping algorithm and the bounded estimation algorithm. To compensate for the intermittent actuator faults, the novel adaptive fuzzy consensus fault-tolerant controllers are then developed by co-designing the last virtual controllers. On the basis of the Lyapunov theory, the stability analysis of the closed-loop system are given, in which the tracking errors converge to zero asymptotically under the directed communication topologies theory. Finally, the proposed FTC scheme is carried on a group of one-link robotic manipulator systems, and its practicability and effectiveness are verified.

Observer-Based Fixed-Time Adaptive Fuzzy Consensus DSC for Nonlinear Multiagent Systems.

This article studies the output-feedback fixed-time fuzzy consensus control problem for nonlinear multiagent systems (MASs) under the directed communication topologies. Since the controlled systems contain the unmeasurable states and unknown dynamics, the unmeasurable states are reconstructed via linear state observers, and fuzzy logic systems are utilized to identify the unknown internal dynamics. By constructing the integral type Lyapunov function, a fixed-time adaptive fuzzy consensus control scheme is developed by introducing the nonlinear filter technique into the backstepping recursive technique adaptive control algorithm. The presented consensus control method can not only guarantee the controlled system is semi-global practical fixed-time stable (SGPFTS), but also avoid the singular problem in existing backstepping recursive control design methods. Finally, an application of unmanned surface vehicles is provided to verify the effectiveness of the presented fixed-time fuzzy consensus control method.

Finite-Time Fuzzy Adaptive PPC for Nonstrict-Feedback Nonlinear MIMO Systems.

This article addresses the issue of the fuzzy adaptive prescribed performance control (PPC) design for nonstrict feedback multiple input multiple output (MIMO) nonlinear systems in finite time. Unknown nonlinear functions are handled via fuzzy-logic systems (FLSs). By combining the adaptive backstepping control algorithm and the nonlinear filters, a novel dynamic surface control (DSC) method is proposed, which can not only avoid the computational complexity issue but also improve the control performance in contrast to the traditional DSC control methods. Furthermore, to make the tracking errors have the prescribed performance in finite time, a new Lyapunov function is constructed by considering the transform error constraint. Based on the designed Lyapunov functions, it is proved that all the signals of the controlled systems are semiglobal practical finite-time stability (SGPFS). Finally, a simulation example is provided to illustrate the feasibility and validity of the put forward control scheme.

Neural Network Output-Feedback Consensus Fault-Tolerant Control for Nonlinear Multiagent Systems With Intermittent Actuator Faults.

In this article, the distributed adaptive neural network (NN) consensus fault-tolerant control (FTC) problem is studied for nonstrict-feedback nonlinear multiagent systems (NMASs) subjected to intermittent actuator faults. The NNs are applied to approximate nonlinear functions, and a NN state-observer is developed to estimate the unmeasured states. Then, to compensate for the influence of intermittent actuator faults, a novel distributed output-feedback adaptive FTC is then designed by co-designing the last virtual controller, and the problem of "algebraic-loop" can be solved. The stability of the closed-loop system is proven by using the Lyapunov theory. Finally, the effectiveness of the proposed FTC approach is validated by numerical and practical examples.

Distributed Estimator-Based Event-Triggered Neuro-Adaptive Control for Leader-Follower Consensus of Strict-Feedback Nonlinear Multiagent Systems.

This article investigates the leader-follower consensus problem for strict-feedback nonlinear multiagent systems under a dual-terminal event-triggered mechanism. Compared with the existing event-triggered recursive consensus control design, the primary contribution of this article is the development of a distributed estimator-based event-triggered neuro-adaptive consensus control methodology. In particular, by introducing a dynamic event-triggered communication mechanism without continuous monitoring neighbors' information, a novel distributed event-triggered estimator in chain form is constructed to provide the leader's information to the followers. Subsequently, the distributed estimator is utilized to consensus control via backstepping design. To further decrease information transmission, a neuro-adaptive control and an event-triggered mechanism setting on the control channel are codesigned via the function approximate approach. A theoretical analysis shows that all the closed-loop signals are bounded under the developed control methodology, and the estimation of the tracking error asymptotically converges to zero, i.e., the leader-follower consensus is guaranteed. Finally, simulation studies and comparisons are conducted to verify the effectiveness of the proposed control method.

Observer-Based Decentralized Control for Non-Strict-Feedback Fractional-Order Nonlinear Large-Scale Systems With Unknown Dead Zones.

This article addresses the output-feedback decentralized control issue for the fractional-order nonlinear large-scale nonstrict-feedback systems with states immeasurable and unknown dead zones. The unknown nonlinear functions are identified by neural networks (NNs), and immeasurable states are estimated by establishing an NNs' decentralized state observer. The algebraic loop issue is solved by using the property of NN basis functions and designing the fractional-order adaptation laws. In addition, the fractional-order dynamic surface control (FODSC) design technique is introduced in the adaptive backstepping control algorithm to avoid the issue of "explosion of complexity." Then, by treating the nonsymmetric dead zones as the time-varying uncertain systems, an adaptive NNs' output-feedback decentralized control scheme is developed via the fractional-order Lyapunov stability criterion. It is proven that the controlled fractional-order systems are stable, and the tracking and observer errors can converge to a small neighborhood of zero. Two simulation examples are given to confirm the validity of the put forward control scheme.

Event-Triggered Adaptive Fuzzy Asymptotic Tracking Control of Nonlinear Pure-Feedback Systems With Prescribed Performance.

This article considers the problem of fixed-time prescribed event-triggered adaptive asymptotic tracking control for nonlinear pure-feedback systems with uncertain disturbances. The fuzzy-logic system (FLS) is introduced to deal with the unknown nonlinear functions in the system. By constructing a new type of Lyapunov function, the restrictive requirement that the upper bounds of the partial derivative of the unknown system functions need to be known is relaxed during the controller design process. At the same time, by developing a novel fixed-time performance function (FPF), the fixed-time prescribed performance (FPP) can be achieved, that is, the tracking error can converge to the neighborhood of the origin in a fixed time and finally converges to zero asymptotically. In addition, the event-triggered strategy is developed to reduce the waste of communication resources. The proposed control law can ensure that all the signals of the system are bounded. Meanwhile, the Zeno behavior can be effectively avoided. Finally, an example is provided to prove the effectiveness of the proposed scheme.

Adaptive Output Feedback Fuzzy Fault-Tolerant Control for Nonlinear Full-State-Constrained Switched Systems.

In this article, an output feedback adaptive fuzzy tracking control method for a class of switched uncertain nonlinear systems with actuator failures and full-state constraints is proposed under an arbitrary switching signal combining the dynamic surface technique. Since the state variables of the system under study are not measurable, a fuzzy observer is constructed to identify the unmeasured states. The actuator failures are considered in the system. To compensate this failure, a fault-tolerant controller is proposed. Moreover, each state needs to be kept within the constraints, so the tangent Barrier Lyapunov function is selected to solve the full-state constraint problem, and the unknown nonlinear function is approximated by fuzzy-logic systems (FLSs). We also proved that all signals in the closed-loop system are bounded. Furthermore, the states can be kept within the predetermined range even if the actuator fails. Finally, a simulation example is given to verify the effectiveness of the proposed control strategy.

Neural-Network-Based Adaptive Constrained Control for Switched Systems Under State-Dependent Switching Law.

This article addresses the adaptive tracking control problem for switched uncertain nonlinear systems with state constraints via the multiple Lyapunov function approach. The system functions are considered unknown and approximated by radial basis function neural networks (RBFNNs). For the state constraint problem, the barrier Lyapunov functions (BLFs) are chosen to ensure the satisfaction of the constrained properties. Moreover, a state-dependent switching law is designed, which does not require stability for individual subsystems. Then, using the backstepping technique, an adaptive NN controller is constructed such that all signals in the resulting system are bounded, the system output can track the reference signal to a compact set, and the constraint conditions for states are not violated under the designed state-dependent switching signal. Finally, simulation results show the effectiveness of the proposed method.

Performance Improvement of Active Suspension Constrained System via Neural Network Identification.

A robust adaptive control method for a certain type of quarter active suspension system (ASS) is proposed in this work. The constraint issue of ASS is put into consideration primarily. Due to the limitation of the traditional barrier Lyapunov functions (BLFs), the integral barrier Lyapunov function (iBLF) is introduced to exert direct constraints on state variables in each stage under the backstepping frame, and neural networks (NNs) are applied to identify those unknown functions. Then, an adaptive law based on the projection operator is defined to eliminate the influence caused by the actuator failure. It is widely known that only the vertical displacement and velocity constraints are not violated, can the ASSs become stable and secure. It can be ultimately confirmed that all signals in the closed-loop system are bounded, and the control goals are satisfied. Last but not least, the feasibility of the approach is illustrated directly through a contrast simulation example.

Integral BLF-Based Adaptive Neural Constrained Regulation for Switched Systems With Unknown Bounds on Control Gain.

In this article, an integral barrier Lyapunov-function (IBLF)-based adaptive tracking controller is proposed for a class of switched nonlinear systems under the arbitrary switching rule, in which the unknown terms are approximated by radial basis function neural networks (RBFNNs). The IBLF method is used to solve the problem of state constraint. This method constrains states directly and avoids the verification of feasibility conditions. In addition, a completely unknown control gain is considered, which makes it impossible to directly apply previous existing methods. To offset the effect of the unknown control gain, the lower bound of the control gain is added into the barrier Lyapunov function, and a regulating term is introduced into the controller. The proposed control strategy realizes three control objectives: 1) all the signals in the resulting system are bounded; 2) the system output tracks the reference signal to a arbitrarily small compact set; and 3) all the constraint conditions for system states are not violated. Finally, a simulation example is used to show the effectiveness of the proposed method.

Adaptive Neural Network Control for a Class of Nonlinear Systems With Function Constraints on States.

In this article, the problem of tracking control for a class of nonlinear time-varying full state constrained systems is investigated. By constructing the time-varying asymmetric barrier Lyapunov function (BLF) and combining it with the backstepping algorithm, the intelligent controller and adaptive law are developed. Neural networks (NNs) are utilized to approximate the uncertain function. It is well known that in the past research of nonlinear systems with state constraints, the state constraint boundary is either a constant or a time-varying function. In this article, the constraint boundaries both related to state and time are investigated, which makes the design of control algorithm more complex and difficult. Furthermore, by employing the Lyapunov stability analysis, it is proven that all signals in the closed-loop system are bounded and the time-varying full state constraints are not violated. In the end, the effectiveness of the control algorithm is verified by numerical simulation.

Anti-Attack Event-Triggered Control for Nonlinear Multi-Agent Systems With Input Quantization.

In this article, an anti-attack event-triggered secure control scheme for a class of nonlinear multi-agent systems with input quantization is developed. With the help of neural networks approximating unknown nonlinear functions, unknown states are obtained by designing an adaptive neural state observer. Then, a relative threshold event-triggered control strategy is introduced to save communication resources including network bandwidth and computational capabilities. Furthermore, a quantizer is employed to provide sufficient accuracy under the requirement of a low transmission rate, which is represented by the so-called a hysteresis quantizer. Meanwhile, to resist attacks in the multi-agent network, a predictor is designed to record whether an edge is attacked or not. Through the Lyapunov analysis, the proposed secure control protocol can ensure that all the closed-loop signals remain bounded under attacks. Finally, the effectiveness of the designed scheme is verified by simulation results.

Adaptive Neural Consensus Tracking Control for Nonlinear Multiagent Systems Using Integral Barrier Lyapunov Functionals.

This article presents the adaptive tracking control scheme of nonlinear multiagent systems under a directed graph and state constraints. In this article, the integral barrier Lyapunov functionals (iBLFs) are introduced to overcome the conservative limitation of the barrier Lyapunov function with error variables, relax the feasibility conditions, and simultaneously solve state constrained and coupling terms of the communication errors between agents. An adaptive distributed controller was designed based on iBLF and backstepping method, and iBLF was differentiated by means of the integral mean value theorem. At the same time, the properties of neural network are used to approximate the unknown terms, and the stability of the systems is proven by the Lyapunov stability theory. This scheme can not only ensure that the output of all the followers meets the output trajectory of the leader but also make the state variables not violate the constraint bounds, and all the closed-loop signals are bounded. Finally, the efficiency of the proposed controller is revealed.