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This paper analyzes a discrete-time Cournot competition model with time delays taking into consideration the dynamics of market interactions involving one public firm and multiple private firms. The model assumes that the production output of the public firm is influenced by the past output levels of the private firms. The output levels of the private firms are affected by the past production outputs of both the public firm and their private competitors. The study identifies two equilibrium states within the nonlinear system: a positive equilibrium and a boundary equilibrium. Through a stability analysis, it is established that the boundary equilibrium is a saddle point. In the absence of time delays, the stability region for the positive equilibrium is determined. The research explores various specific delay scenarios, finding conditions under which the positive equilibrium is asymptotic stability. Additionally, the occurrence of flip and Neimark–Sacker bifurcations are examined. In order to illustrate the complex dynamics, the paper provides a series of numerical examples. • We explore Cournot competition with delays, involving both public and private firms. • Two equilibria are found: positive and boundary, with boundary as a saddle point. • Stability of positive equilibrium is analyzed, with and without time delays. • Flip/Neimark–Sacker bifurcations are investigated supported by numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates a robust anti-disturbance interval type-2 (IT2) fuzzy control for interconnected nonlinear partial differential equation (PDE) systems subject to parameter uncertainties by the conjunct observer. First, an IT2 fuzzy model is adopted to remodel the target system. Second, a state observer with mismatched premise variables is constructed to solve the problem that the original system and the observer do not share a uniform premise variable. Moreover, a disturbance observer is designed to estimate the unknown external disturbances, which can be modeled by exogenous PDE systems. Then, utilizing the conjunct observation information, an anti-disturbance IT2 fuzzy control strategy is proposed to attenuate the effect of disturbances on the system performance while ensuring that the closed-loop system is stable. Finally, simulation results verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this paper, the issue of sliding-mode surface (SMS)-based fixed-time adaptive tracking control under the framework of critic network is considered for the zero-sum game of switched nonlinear systems. Firstly, the tracking error and reference trajectory are combined to construct an augmented system, which transforms the optimal tracking control issue into a basic optimal regulation issue. Meanwhile, sliding mode control technology is introduced to improve the robustness and response speed of the system. Subsequently, a special cost function associated with SMS is developed to find a series of optimal control strategies. Besides, the numerical solution of a Hamilton-Jacobi-Isaacs equation is acquired based on a single-critic network architecture. Then, convergence of the tracking error in fixed time and boundedness of the closed-loop signals are strictly proved via the fixed-time stability theory. Finally, the feasibility and optimality of the developed control scheme are verified by two simulation examples. [ABSTRACT FROM AUTHOR]

This paper presents a mathematical model to examine the effects of the coexistence of predators on single prey. Based on fractal–fractional Atangana–Baleanu (AB) and Caputo operators, we present a newly developed system of differential equations for the predator–prey system. Our study utilized the fixed point postulate to investigate the uniqueness and existence of solutions. Additionally, Ulam's type of stability of the proposed model is established with the help of nonlinear functional analysis. Further bifurcation diagrams, as well as phase portraits, have been used to study the proposed system numerically and to analyze its behavior. The generalized non-linear system with fractal–fractional Atangana–Baleanu (AB) and Caputo non-integer operators have been solved numerically via the Toufik–Atangana (TA) scheme respectively. We have demonstrated the applicability and effectiveness of these methods by analyzing numerical simulations for the fractal–fractional predator–prey ecological model and the numerical simulation has been calculated by MATLAB programming. [ABSTRACT FROM AUTHOR]

In this paper, we present a technique aimed at the implementation of high accuracy iterative procedures in nonlinear systems. The main result of this research is a general proof that guarantees an increase in the order of convergence to order p + 3 units for any method of order p. This methodology has as its main objective not only this increase, but also the optimization in the use of resources by requiring only one additional functional evaluation per iteration, thus keeping a tight control over the computational cost. Although there are previous proposals in the literature that approach this goal, in this work we consider such approaches as particular cases of our general proposal. This approach encompasses many methods described by other authors and can be applied to any p -order scheme to increase it by three units. Numerical evaluations, supported by a rigorous theoretical framework, validate the robustness of the proposal, highlighting its advantage over conventional techniques and demonstrating its effectiveness in the face of numerical challenges of considerable magnitude. Summing up, with this research, we offer a substantial contribution to the field of numerical methods, proposing a paradigm that consistently enhances the convergence order of iterative methods. [ABSTRACT FROM AUTHOR]

In this paper, a model with spatial diffusion and mixed delays is presented to describe the spread of echinococcosis between dogs and livestock. Firstly, the local stability is investigated using the Routh–Hurwitz criterion. Furthermore, when considering time delays as bifurcation parameters, the conditions for the occurrence of Hopf bifurcation are discussed based on the linear approximation of the nonlinear system. Lastly, the fixed-time stability is studied under the implementation of appropriate control measures. Numerical simulations are provided to give a better understanding of the theoretical results. [ABSTRACT FROM AUTHOR]

• For the fast-varying delay, an improved analytical method based on Lyapunov-Krasovskii (LK) functionals is given by introducing and proving a new lemma, which is not only independent of the upper bound of time-varying delay, but also independent of the derivative of the time-varying delay. Hence, the developed analytical method greatly expands the application range of the LK functional. • For unknown nonconstant control coefficients, an output feedback control strategy based on the compensated system is proposed. As an intermediate link, the adaptive fuzzy system is introduced into the controller indirectly by the compensation system, so as to avoid the algebraic-loop problem. Hence, the cooperative design of the compensation system, the state observer and the controller is one of the innovations in this paper. • Considering the problems of state immeasurability and time-varying delay comprehensively, an adaptive fuzzy output-feedback control law is proposed based on an improved average dwell time, which relaxes the constraints between the LK functional of each subsystem in switched large-scale interconnected nonlinear systems. In this paper, an adaptive fuzzy decentralized output-feedback control is developed for the uncertain switched large-scale interconnected nonlinear system, which contains fast time-varying delays and unknown nonconstant control coefficients. By introducing and proving a new lemma, an improved analysis method is given based on the Lyapunov-Krasovskii (LK) functional, and it gets rid of the dependence of LK functional design on the bound of the derivative of the delay. Immeasurable states are estimated by co-designing the decentralized state observer and the innovative compensation system, which eliminates a widely adopted but strict assumption that the unknown control coefficient must be constant. By comprehensively designing the state observer, the compensation system and LK functionals, a novel adaptive fuzzy decentralized output-feedback control law is proposed, and stability of the closed-loop system is guaranteed theoretically based on an improved average dwell time. Finally, the effectiveness is further verified by complete simulation experiments. [ABSTRACT FROM AUTHOR]

The fixed-time tracking control issue is investigated for a class of high-order nonlinear delayed systems subject to mismatched disturbances in this paper. Wherein, the fuzzy logic system is applied in dealing with the nonlinear functions and the power integrator technique is appropriately introduced to address the high-order terms in the considered system. Different from the conventional methods of using the Lyapunov-Krasovskii functional approach to cope with the delayed terms in the previous work, the adaptive backstepping method is utilized in this paper. The main purpose of the addressed control problem is to design a suitable adaptive fuzzy fixed-time controller such that the closed-loop system is stable and guaranteed to be bounded in a fixed-time interval. Subsequently, the specific control law is deduced through the inductive method, and the upper bound on the settling time for the fixed-time control is given. Finally, the simulation examples are given to illustrate the feasibility and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive fixed-time tracking control problem for a class of stochastic nonlinear systems with constrained states and input saturation. By utilizing a barrier Lyapunov function (BLF), the issue caused by constrained states is settled. Simultaneously, a smooth function is constructed to approximate input saturation and the unknown nonlinear function is approximated by neural networks (NNs). In view of the fixed-time tracking control problem of stochastic nonlinear systems, a fixed-time stability lemma for stochastic nonlinear systems has been established and proved. Under the designed controller, the closed-loop system is semi-globally fixed-time stable in probability (SGFSP), and all the states are constrained within a compact set. Moreover, the controlled system in this paper achieves equilibrium within a fixed-time internal. Lastly, the presented method is verified by a simulation example. [ABSTRACT FROM AUTHOR]

In this paper, the stabilization is studied for a complex dynamic model which involves nonlinearities, uncertainty, and Lévy noises. This paper also discusses the controller discretization and presents a new algorithm to obtain the upper bound for the sample interval through which the exponential stability of the discrete system can still be guaranteed. Firstly, an integral sliding surface is designed to obtain the sliding mode dynamics for the considered stochastic Lévy process. By using Lyapunov theory, generalized Itô formula and some inequality techniques, the exponential stability is proved in the sense of mean square for sliding mode dynamics. The reachability of the sliding mode surface is also ensured by designing a sliding mode control law. Secondly, the continuous-time controller is discretized from the point of control cost, and the squared difference is analyzed for the states before and after the discretization. Different from those classical stochastic differential equations driven by Brownian motions, the noise is supposed to be Lévy type and the squared difference is analyzed in different cases. Furthermore, we obtain the largest sampling interval through which the discretized controller can still stabilize the Lévy process driven stochastic system. Finally, a simulation for a drill bit system is given to demonstrate the results under the algorithms. [ABSTRACT FROM AUTHOR]

This paper investigates the prescribed-time containment control problem for multi-agent systems with high-order nonlinear dynamics under a directed communication topology. Firstly, in view of the fact that only some follower agents can directly access the state information of multiple leader agents, a prescribed-time distributed observer is put forward to estimate the convex hull spanned by these leaders. Then, with the help of the distributed observer, a novel containment control method is developed for each follower based on a time-varying scaling function, so that all followers can converge to the convex hull spanned by the states of multiple leaders within a prescribed time. The comparison with the finite-time and fixed-time control methods differs in that the convergence time of the method proposed in this paper is independent of the initial conditions and control parameters and can be arbitrarily preassigned according to actual needs. Finally, an example is given to demonstrate the usefulness of the prescribed-time containment control method. [ABSTRACT FROM AUTHOR]

This paper proposes a novel algorithm twice optimization for interval type-2 fuzzy neural networks with asymmetric membership functions (TOIT2FNN-AMF), for nonlinear system identification problems. The proposed TOIT2FNN-AMF uses an asymmetric Gaussian interval type-2 membership function to enhance the network's ability to describe and solve nonlinear and uncertain problems. The twice optimization algorithm consists of structure learning and parameter learning. Firstly, this paper proposes a multi-strategy adaptive differential evolution (MSADE) algorithm as the first optimization algorithm, which is used to determine the structure and the initial values of the parameters of the TOIT2FNN-AMF. It applies the root mean square error (RMSE) of the TOIT2FNN-AMF as the fitness function to determine the structure (number of rules) and initial parameters of the IT2FNN by searching for the RMSE values under different structures. When the fitness value reaches the minimum, that is, the RMSE value of the TOIT2FNN-AMF, the corresponding number will become the optimal one of fuzzy rules of the TOIT2FNN-AMF. Then, the second optimization algorithm of the TOIT2FNN-AMF turns into a hybrid optimization algorithm composed of an adaptive moment estimation (Adam) algorithm and recursive least squares (RLS) algorithm. Adam is used to optimize the antecedent parameters of TOIT2FNN-AMF rules, so as to maintain rapid convergence without generating oscillation during the training process; RLS is used to optimize the consequent parameters of TOIT2FNN-AMF rules, so that the network parameters can be optimized rapidly. In this way, the problems of excessive parameters to be adjusted and excessive slow convergence of the network can be solved. Finally, this paper evaluates the proposed TOIT2FNN-AMF by testing on problems of nonlinear system identification and chaotic time-series prediction. The simulation results are compared with those of similar methods in the existing literatures, which demonstrates that the proposed TOIT2FNN-AMF model yields a lower RMSE value and a simpler network structure than the other type-2 fuzzy neural networks (T2FNNs). [ABSTRACT FROM AUTHOR]

In this paper, a temporal second order two-grid difference scheme is proposed for the two-dimensional nonlinear time-fractional partial integro-differential equations with a weakly singular kernel. The first-order backward difference and L 1 formula are used in the temporal direction to estimate the first level of time, the L 2 − 1 σ formula and L 1 -type formula are used in the temporal direction for later time steps, and the central difference formula is used in the spatial directions. To improve the computational efficiency of nonlinear system, an efficient time two-grid algorithm is proposed. This algorithm firstly solves a nonlinear system on the coarse grid, and then the Lagrangian linear interpolation is applied on the coarse grid to estimate the function values on the fine grid. The stability and convergence of the two-grid difference scheme are analyzed by the energy method. The convergence order of the two-grid difference scheme is O (τ F 2 + τ C 4 + h x 2 + h y 2) , where τ F and τ C are the time step sizes of fine grid and coarse grid respectively, while h x and h y are the space step sizes. Numerical experiments show that the accuracy of the theoretical analysis and the efficiency of the two-grid algorithm. [ABSTRACT FROM AUTHOR]

Resonance and bifurcation are prominent and significant features observed in various nonlinear systems, often leading to catastrophic failure in practical engineering. This paper investigates, under an analytical and numerical perspective, the dynamical characteristics of a fractional Rayleigh oscillator with distributed time delay. Firstly, through the application of the multiple scales method, we derive approximated analytical solutions and amplitude–frequency equations for the regions near both primary and secondary resonances. The stability conditions of steady-state motions and the existence region of the subharmonic response are also obtained. Furthermore, to validate the accuracy of the approximated solutions, the results are compared with numerical solutions derived from the Caputo scheme, revealing a high concordance between them. Then, a comprehensive study on response curves is conducted for the system under different nonlinear damping, fractional parameters and delay strength. Finally, we identify and discuss the presence of the forked bifurcation within the system. [ABSTRACT FROM AUTHOR]

In this paper, we propose a fault diagnosis (FD) approach for a class of nonlinear uncertain systems based on the deterministic learning approach (DLA). Specifically, an adaptive learning observer is constructed, in which the adaptive neural networks (NNs) are constructed to approximate the unknown system dynamics under normal and fault modes. Based on the strictly positive real (SPR) condition, the convergence of the state estimation can be guaranteed. When the system is undergoing a periodic or periodic-like (recurrent) motion, the states of the observer will also become recurrent. Thus through DLA, the partial persistent excitation (PE) condition of the associated subvectors of NNs is satisfied. By utilizing the partial (PE) condition, the uniformly completely observable (UCO) property of the identification system is analyzed and the exponential convergence condition of the identification system is derived. Under this condition, the unknown dynamics under normal and fault modes can be accurately identified along the system trajectory. And by utilizing the knowledge obtained in the identification phase, the fault can be detected in the diagnosis phase. The main attraction of this paper lies in the analytical result, which shows that the exponential convergence condition of the learning observer not only depends on the observer gain matrix, but also depends on the PE level of the regressor subvector of NN. Simulation results are included to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we present a connectivity-preserving performance function approach for the distributed output-feedback synchronized tracking of uncertain heterogeneous nonlinear multiagent systems in a nonstrict-feedback form. Compared with existing output-feedback cooperative control results using neural networks, this paper contributes to developing a universal output-feedback synchronized control methodology that uses a connectivity-preserving performance function to ensure both initial network connectivity and preselected synchronization performance with a designable convergence time. To this end, a neural-network-based adaptive observer for each follower is designed to ensure the boundedness of estimation errors of unmeasurable states. Then, local event-triggered synchronized trackers using only relative output information and the connectivity-preserving performance function are constructed to guarantee the closed-loop stability in a low-complexity sense, where no adaptive neural networks and command filters are not required in the local trackers. Finally, a purely academic example and a practical platoon-control problem of multiple uncertain vehicular systems are considered to clarify and verify the proposed connectivity-preserving performance function approach in the simulation. [ABSTRACT FROM AUTHOR]

• In the framework of finite-time command filter control, this paper constructs a quadratic function in the controller. Compared with [23, 24, 25], the presented adaptive finite-time control algorithm not only solves the "explosion of complexity" problem effectively, but also circumvents the singularity problem. • In contrast to the literatures on finite-time control [43, 44, 45], the cases of faults happening during transmission phase of system are rarely considered. Moreover, nonlinear faults may exist in many real systems, which necessitates the design of fault-tolerant controllers to enhance the system reliability and guarantee consistent control performance. In this paper, nonaffine nonlinear faults are taken into account, which is more complex than linear faults studied in [37, 39, 46]. • Different from the results [28, 29, 47] which used the trial-and-error method to validate the observation gain matrix, this paper skillfully introduces the differential mean value theorem and the convex combination theorem to transform the acquisition of the observation gain matrix from solving a nonlinear matrix inequality to solving a set of LMIs. Meanwhile, the solvability of LMIs guarantees the stability of the observer and simplifies the algorithm. The present work deals with the consensus issue for nonlinear multiagent systems (MASs) subject to nonaffine nonlinear faults and unmeasurable states. First, the Butterworth low-pass filter (BLPF) is exploited to eliminate the algebraic loop problem arising from nonaffine nonlinear faults. In light of the convex combination theory, a neural observer is established to estimate the unmeasured states, which improves the efficiency of solving the observer gain. Then, with the help of the adaptive backstepping algorithm, an observer-based neural finite-time control protocol is proposed in which a quadratic function is constructed to circumvent the singularity problem. The finite-time stability criterion and Lyapunov stability theorem are utilized to demonstrate that all signals of the closed-loop system are bounded in finite time. Finally, a simulation experiment is applied to show the effectiveness of the present method. [ABSTRACT FROM AUTHOR]

This paper studies the fault-tolerant control (FTC) problem of a class of strict-feedback nonlinear systems. First, we put forward a key theorem which shows that type-B Nussbaum functions can be extended to the cases containing multiple Nussbaum functions in the same Lyapunov inequality under certain conditions. Then, by using the techniques of Nussbaum functions and adaptive control, a new fault-tolerant control scheme is proposed. Compared with the previous work, this paper considers unknown time-varying control coefficients and unknown time-varying fault coefficients of actuators. It is proved that all the signals of the closed-loop system are globally bounded and the tracking error converges to zero asymptotically. Finally, simulations are provided to verify the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper is concerned on the event-triggered practical tracking control for a class of uncertain high-order nonlinear systems with output-constraint. Remarkably, the system under investigation not only considers output constraint, but also involves more serious uncertainties which are reflected from unknown control directions and input powers. Such two distinguished features make the traditional method technically more difficult to apply, and consequently a novel switching event-triggered control scheme is proposed in this paper. Specifically, a switching time-triggered controller is first designed based on certain critical event, in which an event-triggered mechanism is chosen to tune the controller parameters via switching in two families of predefined sequences, and in turn to compensate the serious uncertainties. Combining the event that used for switching mentioned above with another new one that is carefully chosen by incorporating the compensation of unknown input power into the sampling error of control input, an event-triggered mechanism is designed and then brings a switching event-triggered controller. Finally, it is shown that the designed controller guarantees that, along with the stopping of the switching of controller parameters, all the signals of the resulting closed-loop system are bounded while system output practically tracks the reference signal without any violation of the output constraint, and moreover, Zeno phenomenon is excluded by showing all the sampling intervals are lower bounded by certain positive constant. Two simulation examples are provided to validate the effectiveness of the proposed theoretical results. [ABSTRACT FROM AUTHOR]

This paper proposes particle filtering for state estimation considering Round-Robin protocol for discrete-time nonlinear cyber–physical systems with non-Gaussian noise affecting the channels and multiple complex sensor phenomena, including missing measurements (MMs) and randomly occurring sensor saturations (ROSSs). A novel energy harvesting sensor is applied to ensure uninterrupted measurement transmission, and a simplified energy-transfer recursive algorithm is proposed to further calculate the measurement transmission probability of energy harvesting sensors. In addition, considering actual engineering scenarios, two sequences of Bernoulli-distributed random variables with known probability distributions are employed to describe the characteristics of MMs and ROSSs. During the design process of the filtering scheme, we construct a modified likelihood function to compensate for the impact of MMs, ROSSs, and energy harvesting sensors in cyber–physical systems. Subsequently, based on the mathematical characterisation of the likelihood function, we propose a particle filtering algorithm that can address the difficulty in obtaining the likelihood function when MMs and ROSSs occur simultaneously. Finally, the usefulness of the proposed particle filtering method is validated using two tracking examples. • This paper proposes a nonlinear and non-Gaussian cyber–physical systems model using Round-Robin protocol scheduling and energy-harvesting sensors, and fully considers issues like randomly occurring sensor saturations and missing measurements. • This paper optimises the energy transfer probability formula of the energy harvesting sensors and designs a new calculation formula to determine the transmission ability of the sensor, simplifying the calculation process. • This paper proposes a new likelihood function based on Round-Robin protocol and a particle filtering algorithm for nonlinear, non-Gaussian cyber–physical systems with energy harvesting sensors, addressing the problem of state estimation when randomly occurring sensor saturations and missing measurements occur simultaneously. [ABSTRACT FROM AUTHOR]

A practical predefined-time control of multi-agent nonlinear systems with full-state constraints is studied in this paper, where the multiple agents are driven to reach consensus. Compared with existing related research, this predefined-time control can directly constrain all states instead of constraining tracking and virtual errors and ensure the practical predefined-time stability of closed-loop multi-agent systems. A new full-state constrained control framework is proposed to convert the dynamic model under full-state constraints into an unconstrained dynamic model. Fuzzy logic systems are applied to estimate the unknown nonlinear terms present in the transformed dynamic model. Combining the back stepping control framework and the predefined-time control theory, the predefined-time fuzzy adaptive consensus tracking control approach is proposed. The designed control technique ensures that the controlled multi-agent systems achieve stability within a predesignated time and maintain all system states within the desired range. Finally, a simulation example of attitude consensus tracking of multiple quadrotor unmanned aerial vehicles is provided to validate the effectiveness of the proposed control approach. • This paper proposes a novel fuzzy adaptive consensus tracking control method capable of preserving full-state constraints and ensuring practical predefined-time stability. • The proposed method allows the direct constraints of all states of the controlled system. • The proposed full-state constrained control framework is more suitable for practical engineering applications compared to existing methods. [ABSTRACT FROM AUTHOR]

The issue of fault-tolerant cooperative output regulation (COR) for nonlinear uncertain multiagent systems (MASs) under communication link faults (LFs) and actuator faults is investigated in this paper. This is the first attempt to study the fault-tolerant COR problem for the aforementioned MASs under directed graphs. To handle unknown LFs and avoid using global information, adaptive event-triggered (ET) observers are designed to estimate the exosystem state. That is, resilience against communication LFs is translated to distributed observer design. To overcome the "explosion of complexity" and obtain asymptotically stable results, dynamic surface control (DSC) techniques are introduced. Unlike existing linear DSC techniques that generate boundary layer errors, this paper introduces nonlinear filters with compensation terms into dynamic surfaces to eliminate boundary layer errors. Adaptive control laws that can achieve asymptotically regulated output are then developed based on the improved DSC techniques. It is shown that the developed control strategy can achieve fault-tolerant COR for the considered MASs. Additionally, the implemented dynamic event-triggered mechanism (ETM) ensures strictly positive minimum event-triggered intervals (ETIs) and avoids Zeno behavior. Finally, a practical simulation example reveals the effectiveness of the suggested scheme. [ABSTRACT FROM AUTHOR]

This paper is concerned with the small-controllability problem of state-affine nonlinear systems, where the control inputs can be sufficiently small. By proposing the characteristic equation, a necessary condition for small-controllability of discrete-time state-affine nonlinear systems is first given, which covers the classical results for bilinear systems. The proposed characteristic equation is also generalized to continuous-time state-affine nonlinear systems. Then, two classes of sufficient conditions for small-controllability of discrete-time state-affine nonlinear systems are formulated by algebraizing the local rank condition. In this way, not only the classical sufficient results applied for the degenerate systems are improved, but also the scope is extended to more general state-affine nonlinear systems. Finally, the sufficient conditions are generalized to the multi-input case and the continuous-time case. Examples are given to illustrate the small-controllability results of this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the scenario of remote state estimation using multi-rate asynchronous sampling sensor data for perturbed nonlinear systems. The sensors are categorized into N groups with different sampling rates according to the designed event-triggered mechanism. Subsequently, the measurement data from each sensor group is transmitted to the remote state observer through independent scheduling protocols and communication networks at the sampling instants. To address this problem, this paper introduces a novel multi-rate continuous-discrete observer framework with a dynamic event-timing-triggered mechanism. The multi-rate continuous-discrete observer framework fuses sampled outputs from different rates into continuous output signals, enabling the derivation of continuous state estimation. The dynamic event-timing-triggered mechanism presents a versatile and unified framework for both time-triggered and event-triggered mechanisms. Through the utilization of a hybrid system framework, it is proven that the state estimation error remains input-to-state stable concerning measurement noise and disturbance inputs. The proposed multi-rate continuous-discrete observer is applicable to design a new type of event-triggered high-gain observer. Numerical simulations are conducted to demonstrate the efficacy of the proposed methodology. [ABSTRACT FROM AUTHOR]

The paper introduces a novel 2-dimensional 2 × 2 space-invariant cellular neural network (CNN) architecture, employing a current-controlled memristor to replace the resistor in one cell's output. The CNN system is defined by space-invariant cloning templates and modeled as a fifth-order nonlinear system. Within the CNN system, non-symmetric double-wing chaotic attractors are exhibited, owing to the presence of two non-symmetric unstable equilibrium points, alongside one unstable equilibrium point located at the origin. Additionally, the paper delves into its nonlinear dynamics, ultimately determining that by adjusting the parameters of the memristor, the system exhibits chaotic and periodic attractors. Moreover, a locally sustained chaotic state is demonstrated across different initial conditions. The theoretical results are substantiated through circuit implementation. Furthermore, global fixed-time synchronization for the proposed CNN system with unmodeled dynamics and external disturbance is proposed by sliding mode control. The synchronization of the master–slave CNN system is achieved within a fixed converge time, independent on the initial conditions, and possesses a degree of robustness, as the synchronization times for CNNs with and without unmodeled dynamics and disturbances are nearly indistinguishable. The synchronization time can be manipulated by adjusting parameters of the sliding mode surface and the controller. The new discoveries pave a way for its applications to secure communications. [ABSTRACT FROM AUTHOR]

Predefined time performance control has been widely used in practical applications due to its ability in improving the system's transient performance. However, imprecise feedback information from faulty sensors will make this control strategy ineffective and seriously compromise the system performance. This paper concentrates on addressing predefined time tracking control for non-strict feedback nonlinear systems while considering sensor faults. First, a fault-tolerant performance function combined with the settling time regulator is constructed to handle the output constraints in the presence of system faults. Second, in spite of the output feedback information being imprecise, the designed adaptive neural network observer can still obtain the real state information. Third, the designed control scheme can efficiently counteract the negative influences of unknown nonlinearities and faulty sensors, which makes the system achieve asymptotic tracking with predefined time performance. Finally, the acquired control algorithm's applicability is demonstrated through numerical simulations. • The designed flexible performance boundary achieves a trade-off between stability and transient performance. • The proposed control strategy can estimate the fault parameters well even using inaccurate feedback information; meanwhile, the limitation on initial values is further relaxed. • The designed controller makes the tracking error converge to a predefined residual set at a user-specified time and asymptotically converge to zero as the time goes to infinity. The convergence time in this paper can be set directly, rather than relying on a complex implicit formulation. [ABSTRACT FROM AUTHOR]

This paper conducts a new study on fuzzy approximation-based reparametrization and adaptive control design of non-canonical nonlinear aircraft dynamics, with particular focus on emphasizing the expansion of linearization-based adaptive flight control designs from local to semi-global scopes. The linearization-based adaptive control method has been employed for managing non-canonical nonlinear aircraft systems, owing to its capability in handling the complexity of aircraft system dynamics. To enhance the operational range of the linearization-based approach, this paper focuses on the aircraft longitudinal dynamic model in general non-canonical forms. A semi-global linearization-based adaptive control method is developed for this kind of system. Firstly, a new reparametrization is devised, leveraging local linearized models and a concept of relative degree. Subsequently, adaptive controllers are designed to guarantee stable and asymptotic output tracking for aircraft systems with various relative degrees. The efficiency of the newly developed adaptive control approach is validated through simulation outcomes. [ABSTRACT FROM AUTHOR]

This paper addresses the observer-based controller design problem for nonlinear time-delayed systems under input saturation. The nonlinearities are supposed to satisfy the quasi-one-sided Lipschitz condition, which is less conservative than the one-sided Lipschitz condition. Based on the nonlinear matrix inequalities, control law for nonlinear systems subject to input saturation, time delays, and unavailable states, some sufficient conditions have been developed for an augmented system containing the system state vector and the error vector to ensure the convergence of all states to zero. The paper used a decoupling approach to reduce the complexity of the corresponding observer and controller gain computations. Finally, the effectiveness of the developed results is validated using suitable examples. • This work studies observer-based control for input-saturated nonlinear systems. • Nonlinearities are assumed to satisfy the quasi-one-sided Lipschitz condition. • Initially, conditions are developed using nonlinear matrix inequalities. • Later, a decoupling approach transforms these conditions into solvable LMIs. • Finally, suitable examples validate the effectiveness of the proposed results. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of finite-time adaptive fuzzy event-triggered control for a class of uncertain nonlinear systems with input quantization. The nonlinear systems under consideration contain unmodeled dynamics and time-varying delays. Fuzzy logic systems are used to handle unknown nonlinear terms. Additionally, finite-time filters are introduced to solve the problem of "explosion of complexity" as well as to ensure that the derivative of the virtual controller can be approximated in finite time. The Lyapunov–Krasovskii function is used to handle time-varying delays. The hysteresis quantizer is used to ensure adequate precision when there is a low transmission rate requirement. The control strategy combines event-triggered mechanisms and quantization technology to ensure that all signals of the closed-loop system remain bounded in finite time. Finally, two examples are included to demonstrate the effectiveness of the proposed controller. This paper considered a class of more general nonlinear systems with time-varying delays and unmodeled dynamics, the adaptive fuzzy event-triggered controller with quantization technology was constructed to ensure that all signals of the closed-loop system converge to the neighborhood in finite time. [ABSTRACT FROM AUTHOR]

• The RODAs and DETM are both considered in FTFD problem of conic-type nonlinear systems. • A finite-time fault detection filter is proposed to handle conic-type nonlinearity and RODAs. • New sufficient criterion is given to achieve the finite-time stochastic stability with H ∞ requirements. The paper is concerned with the finite-time fault detection (FTFD) problem for a class of delayed networked systems subject to conic-type nonlinearity and randomly occurring deception attacks (RODAs) via dynamic event-triggered mechanism (DETM). The nonlinear function with the conic-type constraint is limited to a known hypersphere with uncertain center. Moreover, a variable governed by Bernoulli distribution is introduced to characterize the RODAs phenomenon. In order to reduce unnecessary communication transmissions, a DETM is considered in the design of finite-time fault detection filter (FTFDF) for the addressed networked systems with time-delays. This paper focuses on the design of an FTFDF via the DETM to ensure the finite-time stochastic stability of error dynamics system with satisfactory the prescribed H ∞ performance. Moreover, the desired FTFDF parameter matrices are obtained by solving linear matrix inequalities. In the end, a simulation example is employed to illustrate the validity of the proposed FTFD method. [ABSTRACT FROM AUTHOR]

• Our paper shows how to stabilize an unstable nonlinear delay hybrid SDEs with Lévy noise. • We design a feedback control in both drift and diffusion parts based on discrete-time observations. • We prove the existence and boundedness of the unique global solution under a new set of suitable conditions. • We discuss several kinds of stability for the controlled system using Lyapunov functions. • Our findings improve and generalize some works done in the stabilization theory. There are many hybrid stochastic differential equations (SDEs) in the real-world that don't satisfy the linear growth condition (namely, SDEs are highly nonlinear), but they have highly nonlinear characteristics. Based on some existing results, the main difficulties here are to deal with those equations if they are driven by Lévy noise and delay terms, then to investigate their stability in this case. The present paper aims to show how to stabilize a given unstable nonlinear hybrid SDEs with Lévy noise by designing delay feedback controls in the both drift and diffusion parts of the given SDEs. The controllers are based on discrete-time state observations which are more realistic and make the cost less in practice. By using the Lyapunov functional method under a set of appropriate assumptions, stability results of the controlled hybrid SDEs are discussed in the sense of p th moment asymptotic stability and exponential stability. As an application, an illustrative example is provided to show the feasibility of our theorem. The results obtained in this paper can be considered as an extension of some conclusions in the stabilization theory. [ABSTRACT FROM AUTHOR]

This paper focuses on the fault detection (FD) problem for nonlinear continuous-time multi-agent systems (MASs) with external disturbances and random time-varying delay. The communication topology is assumed to be undirected and connected. Firstly, a stochastic variable satisfying the Bernoulli distribution is utilized to describe the random time-varying delay and transfer the random time-varying delay to a deterministic time-varying delay. To avoid the constraints of the rank conditions for unknown input observer (UIO), the external disturbances and faults from other agents are treated as the unknown inputs which are partitioned into the decoupled part and the non-decoupled part. Sufficient conditions composed of linear matrix inequalities (LMIs) are derived to ensure the stochastic stability of the augmented system with a desired H ∞ performance index and extra freedom of design. By utilizing the properties of UIOs properly, the method proposed in this paper can detect multiple faulty nodes simultaneously. Finally, a numerical example demonstrates the effectiveness and feasibility of the proposed approach. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the numerical analysis of Fitzhugh–Nagumo (FHN) reaction–diffusion equations. The properties of numerical solutions of a semi-discrete and fully-practical piecewise linear finite element technique are provided. Moreover, for a semi-discrete and fully discrete finite element approximation, we establish a priori estimates and error bounds. We also introduce the results of some numerical examples in one and two dimensions, which confirm the theoretical findings of this paper. [ABSTRACT FROM AUTHOR]

The helicopter is a highly unstable nonlinear non-minimum phase multiple-input multiple-output (MIMO) system with strong coupling between degrees of freedom. Therefore, its modeling will cause many problems such as control complexity. In addition, hover and forward flight modes are one of the most widely used helicopter flight modes used in many operations. To achieve and stay in these situations, you need very precise settings and timely manual control of the bird. This paper seeks to provide an L 1 adaptive-hybrid control method to solve helicopter control problems in the Koppler system. In this regard, three channels in the coupler system are considered for the design of this controller. The proposed controller also proves the stability of the system during switching between channels. The helicopter that is modeled in this research and its data is used to implement and simulate the Coupler system control is the SA330 Puma helicopter, which is a medium-sized twin-engine support helicopter, in the category of 6 tons, built by Eurocopter France (ECF), and is in service several domestic operators and the armed forces, including the British Air Force. This device is a completely unstable dynamic system. In addition to the inherent instability of this bird, by adding an external load hanging to this system, the challenge of controlling this system is doubled hence, it is necessary to maintain its stability by using a suitable control system. In the meantime, the modeling of the hanging load should be done in three dimensions and two planes, and like most of the work done, only the movement of the plane should not be considered. For this purpose, an L 1 adaptive-hybrid control method is proposed and fully developed in the paper, then it is properly designed for the Coupler system, which contains three channels: Pitch, Roll, and Collective, taking into account the load hanging on the helicopter. Finally, by simulating the results, it can be seen that the main goals, even in the presence of various disturbances, have the desired, efficient, and very good performance. [ABSTRACT FROM AUTHOR]

Although conventional dynamic surface filters can eliminate the issue of complexity explosion in backstepping design, the convergence of filter errors significantly influences the overall control performance. This paper proposes a unified design framework of an event-triggered adaptive fuzzy design scheme with fixed-time performance for unmodeled strict-feedback nonlinear systems, where the tracking performance, filter error, and parameter learning convergence are considered simultaneously. The unified framework guarantees the smoothness of all the closed-loop signals. A novel dynamic surface filter is designed to avoid the repeated differentiation of recursive virtual control while the filter error converges in fixed time. Compared with the conventional backstepping design, the proposed adaptive fuzzy controller design in this paper can guarantee fixed-time tracking performance. An event-triggered condition with intermittent feedback is developed to decrease the computational and communication burden. Two simulation examples are provided to validate the effectiveness of the unified fixed-time framework. [ABSTRACT FROM AUTHOR]

This paper researches the observer-based exponential stabilization problem for switched Takagi–Sugeno (T–S) fuzzy systems with unmeasurable premise variables and local nonlinearities. The local nonlinear parts that satisfy the incremental quadratic constraint exist in the systems and observers, which have the merit of being able to contain many common nonlinearities in a unified framework. Because the premise variables are not measurable, the performance of the observers in estimation is critical. Different from existing observer-based control strategies, the strategy of this paper not only depends on the current outputs of the systems but also relates to the past outputs of the systems which can provide a way to improve performance. In order to tackle the difficulties caused by introducing the past outputs and design a set of non-fragile fuzzy controllers to stabilize the systems, a new augmented state vector is constructed. Then, the conditions for designing the observer-based controller are derived by using auxiliary scalars, projection Lemma and S -procedure. Finally, the effectiveness of the control strategy obtained in this paper is proved by two examples. [ABSTRACT FROM AUTHOR]

This paper introduces a distributed adaptive fault-tolerant control scheme for nonlinear multi-agent systems afflicted by actuator failures. The proposed scheme ensures that the consensus-tracking errors of the systems meet the prescribed performance requirements. First, in the backstepping design process, a barrier function is constructed based on the proposed scalar function and normalization function to address the prescribed performance issue. Next, both multi-dimensional Taylor network (MTN) control and robust control techniques are utilized to address unknown nonlinear functions. Continuous switching functions are devised to transition from MTN control to robust control whenever the arguments of the unknown functions surpass the operating range of MTN. This effectively resolves the global problem of the system. Furthermore, a boundary estimation method is proposed to handle actuator failures that may occur infinitely. Stability analysis confirms that all signals in the closed-loop system are globally uniformly ultimately bounded. Additionally, the consensus-tracking errors can always be constrained within prescribed boundaries, achieving global convergence to a prescribed accuracy within a prescribed time. Users can flexibly and independently choose the desired settling time and accuracy, without being restricted by any initial conditions. Simulation results provide evidence of the efficacy of the proposed control method. • This paper considers the possibility of each actuator in each agent of NMASs experiencing an in finite number of failures. • The proposed scheme not only ensures a deterministic settling time but also allows for the flexible design of the settling time based on specific requirements. • The challenge of achieving global tracking in NMASs by redirecting escaping transients back into the active region of the MTN. [ABSTRACT FROM AUTHOR]

This paper investigates the reinforcement learning (RL) adaptive tracking control design problem for a class of mismatched stochastic nonlinear systems with non-affine structure. The stochastic system studied in this paper is more generally representative due to the presence of non-affine inputs, internal uncertainties, and mismatched external disturbances. Firstly, in order to solve the non-affine structure of stochastic systems, an extended stochastic differential equation is constructed. Based on the actor–critic framework, by generating reinforcement signals, the network is stimulated to evolve more quickly towards the desired direction, while compensating internal uncertainties and induced uncertainties in the stochastic system. Furthermore, aiming at the approximation errors and external disturbances, while satisfying stochastic stability, the adaptive laws for disturbances boundary estimator are established with the usage of higher powers of tracking errors. As a result, a novel non-affine adaptive tracking controller has been proposed by integrating RL, disturbances boundary estimation, and dynamic surface method. Through the stability analysis, it is proved that all closed-loop signals are bounded in probability, and the system output converges to a small neighborhood near the desired trajectory. Numerical simulations demonstrate the effectiveness and superiority of the proposed controller. • Auxiliary integration obtain extended stochastic differential equation systems. • Actor-critic network reduces fitting error and improves environmental adaptability. • All signals Inclosed-loop are bounded in probability. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive fuzzy event-triggered control (ETC) method for a class of time-delay nonlinear multi-agent systems (MASs) with dead zone (DZ) and partial state constraints (PSCs). It should be pointed out that the states considered in this paper are unmeasurable and part of the system states are constrained by time-varying boundary. By utilizing fuzzy logic systems (FLSs) and backstepping design framework, a fuzzy state observer is constructed to estimate the unmeasured states, while the introduction of a time-varying barrier Lyapunov function (BLF) addresses the partial state constrained problem. Furthermore, during the design process of the state observer, compensation for the influence of the unknown DZ input on the system is achieved through utilization of known designed event-triggered input signal and adaptive parameter. Building upon this foundation, employing the Lyapunov stability theory and adaptive backstepping technique with ETC strategy, the developed distributed control mechanism demonstrates that all variables of the closed-loop system are bounded, the consensus error of the system can converge to a small region of origin and Zeno behavior can be ruled out. Finally, two simulation examples further illustrate the proposed control strategy and theorem. • Observer-based adaptive tracking control for nonlinear time-delay MASs is studied. • Dead-zone input and partial state constraints are considered simultaneously. • A novel adaptive ETC scheme is proposed for nonlinear MASs with unknown dead zone. • By constructing a novel fuzzy state observer, a new control method is proposed. • The tracking control problem of MASs with partial state constraints is studied. [ABSTRACT FROM AUTHOR]

A fixed time fuzzy adaptive tracking controller is presented for high-order nonlinear systems, which includes unknown nonlinear functions and satisfies full state constraints. This is a constructive control scheme based on integrator barrier Lyapunov function, unique dominant adaptive parameter related to fuzzy approximation, and complex high-order back-stepping technique, which ensures that the tracking error can be confined to a preassigned neighbourhood including the origin within a fixed time independent of initial values, and all the states remain the given constraints. A practical application to single joint manipulator tracking control is provided, where comparative simulation results are illustrated for two different preassigned tracking errors. Another numerical example is offered to further manifest the feasibility of the theoretical results and the effectiveness of the controller in this paper. • The integrator barrier Lyapunov function is introduced to control high-order tracking systems with full-state constraints and unknown nonlinearities. The scheme proposed in the paper can make the tracking error keep in the preassigned interval including the origin within a fixed time independent of the initial values. Meanwhile all the states stay in the given constrains all the time respectively. [ABSTRACT FROM AUTHOR]

This paper focus on the design issue of event-based dissipative filter for quantized nonlinear singular systems. To save the communication resource, we employ a dynamic quantizer to quantized the measurement output signal prior to transmitting it to the filter via digital communication. Furthermore, the paper also presents an event-triggered mechanism for determining the transmission of the quantized signal. The intention of this paper is to try to propose an event-triggered filter to ensure that the filtering error system (FES) is admissible and satisfies strictly dissipativity performance, in the presence of dynamic quantization and occurring uncertainties. The Lyapunov function is utilized to establish a sufficient condition for the FES to meet the strictly dissipative performance. Depending on the obtained conditions, the required filter parameters are proposed using the standard linear matrix inequality (LMI) technique. Ultimately, the effectiveness of the developed method is verified by an actual circuit simulation. • The problem of dissppativity-based robust filter design for singular systems is investigated. The admissibility and the dissipative performance of the filtering error system are discussed. • The event triggering mechanism, dynamic quantization and parameter uncertainty are also studied in the filtering error system. By introducing strict LMI, the design conditions are given to ensure that the filtering error system is admissible and possesses strictly dissipative performance. • The quantizers dynamic parameter is designed within the quantization range based on the LMI conditions. [ABSTRACT FROM AUTHOR]

This paper mainly investigates the adaptive state feedback control problem for a class of stochastic nonlinear systems with time-delay and unknown control coefficients. The proposed control scheme leverages the dynamic gain technology and Nussbaum function to develop a state feedback controller, aiming to simplify its implementation and eliminate the influence of unidentified time-varying control coefficients. Through the utilization of suitable Lyapunov–Krasovskii (L–K) functionals and stochastic stability theories, it is demonstrated that the designed control mechanism guarantees the boundedness in probability for all closed-loop signals, ultimately regulating the state of the plant to zero. The availability and superiority of the developed adaptive management strategy are further certified through simulation results. • In contrast to traditional backstepping methods, this paper introduces dynamic gain at each step of the virtual controller design, utilizing adaptive laws in a novel recursive manner. This approach enhances the flexibility and adaptability of the control scheme, enabling effective compensation for uncertainties. • Our study extends the dynamic gain methodology from nonlinear time-delay systems to more complex nonlinear time-delay stochastic systems. We further innovate by integrating the Nussbaum function with the dynamic gain technique, effectively addressing the unknown control coefficients. • By selecting appropriate L–K functionals and dynamic gains, we eliminate the adverse effects of uncertainties and effectively regulate the system states to converge to zero. This ensures desirable system behavior and establishes the desired control objectives. [ABSTRACT FROM AUTHOR]

Hammerstein structure is commonly used for describing nonlinear dynamic characteristics, and its identification is a basic premise of nonlinear system analysis and control. This paper investigates online identification methods for a class of Hammerstein nonlinear systems, which consists of a nonlinear memoryless element followed by a linear output-error subsystem. The unmeasurable noise-free output of the linear subsystem makes the model parameters cannot be directly estimated by traditional identification methods. To address this difficulty, by using a series of weighted particles to adaptively approximate the posterior probability density function of the unmeasurable noise-free output, this paper proposes a particle filter-based stochastic gradient algorithm. Moreover, to enhance the data utilization and estimation accuracy, a particle filter-based multi-innovation stochastic gradient algorithm is developed through the innovation expansion technique. The simulation results demonstrate that compared with the existing benchmark algorithms, the proposed algorithms need a little more computational time due to the introduction of the adaptive particle filter, but they have the improved identification accuracies. [ABSTRACT FROM AUTHOR]

This paper investigates the problem of prescribed-time adaptive fuzzy tracking control for pure-feedback stochastic systems with backlash-like hysteresis. To address the non-affine issue, the pure-feedback case is converted into strict-feedback form by introducing the mean value theorem. The key is that a non-scaling transformation method is introduced to decrease the computational burden such that the controller design is under the standard Lyapunov stability theoretical framework. In addition, the unknown nonlinear functions are approximated via fuzzy logic systems. At the same time, a novel prescribed-time tracking control scheme is proposed to ensure that the considered closed-loop systems are prescribed-time stability. Unlike existing results, the salient characteristic of the proposed control schemes is not only unrelated with the design parameters but also is independent of the initial states in this paper. Finally, simulation results are given to reveal the properties of the investigated control strategy. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of distributed optimal coordination over second-order multi-agent systems, where the dynamics are nonlinear and unknown. To solve this problem, a state-based observer is designed to handle the unknown matched and unmatched nonlinear terms. Using this observer and the proportional–integral control concept, a distributed optimal coordination algorithm with fixed control parameters is constructed through the consensus scheme and gradient flow method. With the help of the Routh–Hurwitz stability criterion, the exponential convergence proof is guaranteed under the condition that the nonlinear term and the convex local cost function are all locally Lipschitz. Finally, we present four simulation examples, including the vehicle platoon's cooperative control, to demonstrate the efficiency of our proposed algorithms. • This paper solves distributed consensus problems of nonlinear second-order systems. • A state-based observer is created to solve the matched and unmatched nonlinear item. • The Routh–Hurwitz criterion is used to prove the exponential convergence rate. • The created coordination method has been applied to the distributed vehicle platoon. [ABSTRACT FROM AUTHOR]

This paper develops a practical fixed-time bipartite consensus control framework for the uncertain nonlinear multi-agent systems (MASs) via using a barrier Lyapunov function (BLF)-based approach. Distinguish from the most existing results, the unknown nonlinearities of MASs in this paper are tackled by utilizing the robustness of BLF instead of applying fuzzy logic systems/neural networks approximating. In order to avoid feasibility verification in the traditional BLF method, a piecewise and differentiable function named the shift function is skillfully inserted into the coordination transformation of the controller design process, allowing not only the initial value of MASs states to be chosen arbitrarily, but also the settling time of bipartite consensus errors can be pre-designated. According to the backstepping framework, an approximated-free control algorithm is developed by combining the shift function with BLF, which guarantees that for any initial state of MASs, the outputs of all the agents can achieve the practical fixed-time bipartite consensus tracking, and all the signals in closed-loop systems are bounded. Especially, the settling time and the tracking error accuracy can be appointed by the designer. Finally, simulation results are given to show the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper focuses on stability theorems of random nonlinear time delay systems and their application. On the one hand, some noise-to-state practical stability theorems are improved for random nonlinear systems with time delay in this paper. Compared with the existing stability theorems, some strict constraints have been removed and the existing stability theorems can be viewed as special cases of the new established stability theorems in this paper. On the other hand, the state feedback tracking control problem is investigated to show the applicability of improved stability theorems in this paper. [ABSTRACT FROM AUTHOR]

This paper presents a robust adaptive stabilizing control scheme via partial-state feedback for a class of nonlinear cascaded systems with a time-varying output constraint. Different from the existing achievements, the nonlinear parameterization and unmeasured zero-dynamics are considered in this paper. The notion of input-to-state stability (ISS) and ISS-Lyapunov function are used to describe the zero-dynamics. The time-varying barrier Lyapunov function (TVBLF) is employed to ensure the output constraint satisfaction and the changing supply rates technique is used to deal with the unknown cascaded zero-dynamic states. It is shown that all the signals in the closed-loop system are bounded, and the asymptotic stabilization is achieved without violation of the output constraint. The performance of the proposed control scheme is illustrated through a simulation example. [ABSTRACT FROM AUTHOR]

In the paper, a class of unknown fractional-order nonlinear systems suffering from actuator faults are investigated. Meanwhile, an adaptive finite-time sliding mode control (SMC) approach based on approximation principle of fuzzy logic system (FLS) and backstepping layout is proposed. It is well known that the standard backstepping control has inherent computational complexity. Therefore, a type of fractional-order command filter (CF) is introduced to overcome such a shortcoming, that is, by means of fractional-order CF, the virtual input signal and its fractional derivative can be estimated properly as anticipated. Fractional-order sliding mode surfaces are constructed to diminish the filtering errors such that more better performance is guaranteed. Besides, compared to the conventional backstepping control, the CF-based fuzzy backstepping SMC approach presented in the paper not only shows the superior robustness, but also facilitates to accomplish the desired tracking control objective in finite time. The finite-time stability analysis is established on the basis of fractional-order Lyapunov method. Finally, the effectiveness of the proposed methodology is identified by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, the problem of the predefined-time tracking with time-varying output constraints (TVOC) is investigated for a class of nonlinear strict-feedback systems. First, the sufficient conditions for the studied problem are presented. Then, a recursive design algorithm of the controller is proposed by backstepping technique. A novel stabilizing function is constructed by adding a fractional term, which is capable of decreasing the asymmetric time-varying Barrier Lyapunov Function (BLF) to the origin within any desired settling time. After that, it is shown that under our proposed control, all the closed-loop signals are bounded, and the tracking error converges to zero within any desired settling time and remains zero thereafter without the violation of the output constraint. The settling time in this paper is not only independent of the design parameters, nor does it depend on the initial conditions, and can be set according to per our will. Finally, two examples are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]