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• 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]

This paper investigates the consensus problem for nonlinear multiagent systems (MASs) with unknown time-varying measurement sensitivity and infinite communication delays. Unlike existing works, the output measurement sensitivity is described as time-varying, and an infinite communication delay is considered between the agents. Under this condition, a novel output feedback control algorithm is developed. First, based on the hierarchical technique and Lyapunov-based time-domain method, the high-gain compensator and observer are constructed to tolerate the effect of infinite communication delays and accurately estimate the state of the leader. Subsequently, a new distributed k-filter and output feedback controller are proposed, which not only further relax the traditional Lipschitz conditional conservatism but also greatly simplify the design process. It is proved that the closed-loop system is globally stable and all agents can achieve consensus. Finally, the effectiveness of the proposed method is verified through the simulation of the single-link manipulators. [ABSTRACT FROM AUTHOR]

This paper investigates the optimal backstepping control strategy for strict-feedback nonlinear systems subject to input saturation and time-varying partial output constraints. Compared with the existing results on output constraints, the time-varying partial output constraint is a more general constraint that can start and end at any time during the system operation, or remain unconstrained, which can be called as output constraints occurring in a limited time interval (OCOLT). A special barrier function is embedded into the optimal performance index function to satisfy the OCOLT condition under the optimal control framework, and a shift function is introduced to address the function discontinuity caused by the OCOLT problem. Then, an auxiliary system and a disturbance observer are respectively constructed to handle the influence of the input saturation and compounded disturbances. Meanwhile, the simplified reinforcement learning algorithm, employing the identifier-critic-actor architecture, is developed to achieve the optimal control objective within the framework of the backstepping technology. Moreover, the proposed optimal control method ensures the semi-globally uniformly ultimately bounded of all signals within the closed-loop system. Finally, two simulation examples are given to further prove the effectiveness of the presented optimal control approach. [ABSTRACT FROM AUTHOR]

The adaptive tracking problem for a class of strict-feedback switched nonlinear systems with output constraints, quantization input, distributed time-varying delays and external disturbances is studied in this paper. Firstly, we introduce the hyperbolic tangent function to handle the quantized signal in the design of the controller. For the nonlinear term and distributed time-varying delay of the system, the integral term is introduced into the candidate functional to compensate it. Secondly, based on Dynamic Surface Control (DSC) technique and Barrier Lyapunov function (BLF) method, an adaptive controller is designed to guarantee the stability of the controlled closed-loop system, and the system tracking error can converge to the origin without violating the constraints. Finally, simulation results verify the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper studies the problem of event-triggered adaptive control for a class of strictly-feedback stochastic nonlinear systems. The output dead zone and time-varying full-state constraints are considered in the controller. Firstly, time-varying barrier Lyapunov functions (TVBLFs) are introduced to address problems of time-varying state constraints. Then, the Nussbaum-type function is used to compensate for the influence of the output dead zone. The problem of state constraint is well solved when the system's output signal is affected by the dead zone, which satisfies a wider application space. In addition, a new relative threshold of the event-triggered control (ETC) scheme is considered to save communication resources, and the Zeno behavior is excluded. This scheme makes the trigger interval more flexible and optimizes the performance of the controller. Moreover, the error compensation signals reduce the filtered errors and simplify the algorithm. Simultaneously, an adaptive tracking controller with the backstepping technique is designed so that all signals in the closed-loop system are bounded and the tracking error converges to a small residual set of the origin. Finally, two simulation examples are given to demonstrate the effectiveness of the control method. [ABSTRACT FROM AUTHOR]

This paper deals with state estimation for a class of Lipschitz nonlinear systems under a time-varying disconnected communication network. A distributed observer consists of some local observers that are connected to each other through a communication network. We consider a situation where a communication network does not remain connected all the time, and the network may be caused by intermittent communication link failure. Moreover, each local observer has access to a local measurement, which may be insufficient to ensure the system's observability, but the collection of all measurements in the network ensures observability. In this condition, the purpose is to design a distributed observer where the estimated state vectors of all local observers converge to the state vector of the system asymptotically, while local observers exchange estimated state vectors through a communication network and use their local measurements. According to theoretical analysis, a nonlinear and a robust nonlinear distributed observer exist when in addition to the union of all communication topologies being strongly connected during a time interval, the component of each communication graph is also strongly connected during each subinterval. The existence conditions of the distributed observers are derived in terms of a set of linear matrix inequalities (LMIs). Finally, the effectiveness of the presented method is numerically verified using some simulation examples. [ABSTRACT FROM AUTHOR]

This paper addresses the distributed control of delayed interconnected nonlinear systems with time-varying delays in both the local subsystems' dynamics and the physical interconnections among the subsystems. The Takagi–Sugeno fuzzy model with nonlinear consequent parts (N-TS), which is capable to provide less complex representations than standard T–S fuzzy models, is considered to efficiently deal with this class of complex systems. Then, based on Lyapunov–Krasovskii stability arguments, a synthesis condition is proposed to design a distributed control law such that the origin of the closed-loop interconnected system is locally asymptotically stable together with a guaranteed set of admissible initial conditions for which the validity of the N-TS fuzzy model is ensured. Moreover, a quasi-convex optimization procedure is formulated to enlarge the set of admissible initial conditions. The effectiveness of the proposed synthesis condition is validated in two numerical examples, including an interconnected power network with seven generators. [ABSTRACT FROM AUTHOR]

The problems of guaranteed cost control and H ∞ control are studied in this paper for nonlinear uncertain Itô's stochastic systems with time-varying delays in finite-time. It is assumed that the nonlinear function in the systems satisfies the quasi-one-sided Lipschitz nonlinear constraint condition, which is weaker and less conservative than the one-sided Lipschitz condition. Some novel sufficient conditions for the existence of guaranteed cost control strategies are derived by using the Gronwall's inequality, Dynkin's formula, and Lyapunov–Krasovskii functional. The state and output feedback's controllers based on event-triggered control guarantee that the closed-loop system is finite-time stochastically bounded and the given quadratic cost function has an upper bound. Finally, the effectiveness of the suggested method is illustrated by numerical simulation. [ABSTRACT FROM AUTHOR]

This paper studies the prescribed-time input-to-state stabilization problem of normal nonlinear systems. With the help of some key properties of a class of parametric Lyapunov equations, the prescribed-time input-to-state stabilization problem of normal nonlinear systems under matched uncertainties is studied. Some bounded time-varying controllers are proposed. It is shown that the closed-loop systems are prescribed-time input-to-state stable. Finally, the effectiveness of the established methods is illustrated by two physical systems. [ABSTRACT FROM AUTHOR]

In this paper, the l 2 − l ∞ state estimation problem of discrete-time nonlinear systems (DTNSs) with time-varying delay is studied. The main objective of this paper is to design a state estimator that guarantees not only the global h -stability of the error system in the absence of interference, but also that the output peak value of the error system remains within a certain range under the zero initial conditions. A direct analysis method based on the system solutions is presented, which gives a sufficient condition to decide whether the designed state estimator satisfies the expectation. The method does not follow the construct of any Lyapunov–Krasovskii functional (LKF), thus greatly reducing the workload and complexity of calculation. Finally, three simulation examples are presented to illustrate the applicability of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we consider a regulation problem for a class of feedforward nonlinear systems with unknown control coefficients and unknown growth rate. More specifically, the unknown control coefficients are assumed to be time-varying and belong to ranges with unknown upper and lower bounds. Due to the described control coefficients with uncertain feedfoward nonlinearities, our considered system is the natural extension of the related existing results. In solving our control problem, a new adaptive controller is derived by constructing a Lyapunov function in backstepping-like procedure and utilizing appropriate parameters based on the gain scaling technique and Nussbaum function. The uniquely designed exponents of a dynamic gain overcome the difficulties caused from the unknown sign and unknown ranges of the control coefficients and uncertain nonlinearities and thus play a key role in system regulation. We give the rigorous system analysis and simulation results of the numerical example to certify our control method. [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 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]

The core objective of this paper is to investigate the problem of robust nonlinear observer-based controller design for one-sided Lipschitz (OLS) switched systems. This work considers nonlinear switched systems with norm-bounded uncertainties, time-varying delays, and external disturbances. By selecting appropriate Lyapunov-Krasovskii functions and applying the OSL condition together with the quadratic inner boundedness property, we drive certain necessary and sufficient conditions for the observer-based control of the underlying system that assure the exponential convergence of the system states, the observer states, and the error states to zero, in respect of linear matrix inequalities via average dwell-time approach. The devised scheme offers necessary robustness against L 2 -norm bounded perturbations. In the end, the proposed scheme has been validated a suitable practical example. [ABSTRACT FROM AUTHOR]

This paper deals with the finite-time state bounding problem of homogeneous nonlinear positive systems with disturbance. Based on a technique used in positive systems, explicit conditions are established such that all solutions of homogeneous nonlinear positive systems with degree 0 < p < 1 converge to a ball in finite time. The approach used in this paper is different from the usual Lyapunov-Krasovskii functional method. We also extend the main result to the general nonlinear time-varying systems. Finally, two numerical examples are given to show the effectiveness of our results. [ABSTRACT FROM AUTHOR]

This paper investigates the adaptive resilient containment control for nonlinear multiagent systems (MASs) with time-varying delay, unmodeled dynamics and sensor faults. To solve the coupling problem of unknown state delays and sensor faults in a nonlower triangular structure, we develop an effective method by using a new lemma and the Lyapunov-Krasovskii functional. Then, to reduce the negative impact of unknown sensor faults, a novel adaptive resilient containment control method is designed based on a distributed sliding-mode estimator, which can effectively improve the transient performance of the MASs. Moreover, by using a dynamic signal, the problem of unmodeled dynamics is solved. The proposed control scheme can not only drive all followers suffering from sensor faults to converge to the convex hull formed by the leaders but also relatively reduce the undesired chattering phenomenon. Finally, a comparative simulation example is given to illustrate the effectiveness of the proposed strategy. [ABSTRACT FROM AUTHOR]

This paper studies the finite-time guaranteed cost control problem for switched nonlinear stochastic systems with parameter uncertainties and time-varying delays. By choosing a model-dependent and delay-dependent Lyapunov-Krasovskii functional, applying the average dwell time approach and the Gronwall inequality, some novel sufficient conditions are derived to ensure that the switched nonlinear stochastic closed-loop system is finite-time stochastically stable and an upper bound is given on the performance index. The obtained nonlinear matrix is transformed into a linear matrix form, and then the feedback controller gains of the switched nonlinear stochastic systems with time-varying delay are obtained. Finally, two simulation examples are designed to verify the effectiveness of the suggested approach. [ABSTRACT FROM AUTHOR]

In this study, the probabilistic-constrained $\mathcal {H}_{\infty }$ tracking control problem is addressed for a class of stochastic nonlinear systems subject to measurement outliers, stochastic nonlinearities and DoS attacks. The considered systems have the following characters: 1) an unequal redundant-channel communication protocol is adopted to resist the DoS attacks and enhance the reliability of packet transmission. Different from some existing redundant-channel approaches, the considered two channels have different transmission abilities. 2) The measurement outliers (e.g., some unexpected large amplitude disturbances) are concerned and a saturation-function-based observer is proposed to avert the side effects from measurement outliers. 3) The DoS jamming attacks are considered in this paper, and an aperiodic DoS model is utilized. 4) Both sector-bounded nonlinear function and stochastic nonlinear function are involved in the considered systems, which makes the considered systems more general. To compensate the negative effect of the DoS jamming attacks and enhance the reliability of the packet transmission, a novel redundant-channel-based switching protocol is proposed to schedule data transmission when the plant suffers malicious cyber attacks. The primary objective of the present study is to design tracking controller such that the prescribed $\mathcal {H}_{\infty }$ control performance is reached and probabilistic constraints on the tracking error are satisfied simultaneously. To achieve this objective, a probabilistic-constrained $\mathcal {H}_{\infty }$ tracking control algorithm is established to obtain tracking controller gains and minimize the prescribed set of the constraint. Finally, two simulation examples are used to validate the practicability of our devised strategy. [ABSTRACT FROM AUTHOR]

This paper mainly focuses on the stabilization of a class of parabolic systems with time-varying delay, external disturbance and nonlinear periodic time-varying parameter (NPTVP). Firstly, combined with Fourier series expansion (FSE) method and neural networks (NNs) approximation technology, a NNs approximator is designed to approximately describe the uncertain dynamic term with NPTVP. Then, based on adaptive control theory, NNs approximation technology and reparameterization method, two robust adaptive neural network control (RANNC) algorithms are designed to make the parabolic systems with time-varying delay, external disturbance and NPTVP achieve asymptotic stability and meet a prescribed adaptive H ∞ performance of disturbance attenuation. Sufficient conditions of the asymptotical stability while satisfying the prescribed adaptive H ∞ performance index for the resulting closed-loop systems are also derived. Finally, several simulations are carried out to verify the effectiveness of the designed RANNC algorithms. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive finite-time command filtered control scheme is investigated for a class of nonlinear systems with asymmetric time-varying full state constraints and input quantization. Firstly, by fusing the backstepping control method and command filter technique, a novel adaptive neural networks (NNs) command filtered control approach is proposed. Moreover, a modified error compensation mechanism is constructed to compensate for the filtering error. Secondly, a smooth nonlinear transformation is constructed to eliminate the influence brought by the actuator subject to input quantization. Based on the constructed asymmetric time-varying barrier Lyapunov function (TVBLF), the strict constraints are guaranteed not to be violated and the stability of the closed-loop system is achieved in finite-time. Finally, simulations are carried out to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, the problem of finite-time state bounding for homogeneous nonlinear positive systems with time-varying delay and bounded disturbance is studied for the first time. By exploiting an approach presented in positive systems which is different from the Lyapunov–Krasovskii functional technique, an explicit criterion is formulated for the existence of a special ball such that all the state trajectories of homogeneous nonlinear positive systems with degree 0 < α < 1 converge within it in finite time. We then extend the main result to the general nonlinear time variant systems. Finally, a numerical example is presented to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper investigates global fuzzy leader-follower consensus problem of mixed-order nonlinear multi-agent systems (MAS) with partially unknown direction control. The follower system is described by a first-order or second-order unknown nonlinear system model with partially unknown direction control and the leader system is described by a second-order time-varying nonlinear system model. Leader can share its position or velocity information with some followers. Due to the different distribution of agents in the network topology, a new hybrid distributed adaptive control protocol is presented in this study. Compared with the asymptotic consensus bounded result, this paper obtains the asymptotic consensus result. The global consensus result is obtained in the paper, which adopts the design method that the fuzzy logic systems (FLSs) acts as a feedforward compensator to approximate the unknown nonlinear dynamics. In the end, a simulation example is given to show the effectiveness of the proposed consensus control protocol. [ABSTRACT FROM AUTHOR]

In this paper, we propose a convex programming based method to address a long-standing problem of inner-approximating backward reachable sets of state-constrained polynomial systems subject to time-varying uncertainties. The backward reachable set is a set of states, from which all trajectories starting will surely enter a target region at the end of a given time horizon without violating a set of state constraints in spite of the actions of uncertainties. It is equal to the zero sublevel set of the unique Lipschitz viscosity solution to a Hamilton–Jacobi partial differential equation (HJE). We show that inner approximations of the backward reachable set can be formed by zero sublevel sets of its viscosity supersolutions. Consequently, we reduce the inner-approximation problem to a problem of synthesizing polynomial viscosity supersolutions to this HJE. Such a polynomial solution in our method is synthesized by solving a single semidefinite program. We also prove that polynomial solutions to the formulated semidefinite program exist and can produce a convergent sequence of inner approximations to the interior of the backward reachable set in measure under appropriate assumptions. This is the main contribution of this paper. Several illustrative examples demonstrate the merits of our approach. [ABSTRACT FROM AUTHOR]

One often wishes for the ability to formally analyze large-scale systems—typically, however, one can either formally analyze a rather small system or informally analyze a large-scale system. This paper tries to further close this performance gap for reachability analysis of linear systems. Reachability analysis can capture the whole set of possible solutions of a dynamic system and is thus used to prove that unsafe states are never reached; this requires full consideration of arbitrarily varying uncertain inputs, since sensor noise or disturbances usually do not follow any patterns. We use Krylov methods in this paper to compute reachable sets for large-scale linear systems. While Krylov methods have been used before in reachability analysis, we overcome the previous limitation that inputs must be (piecewise) constant. As a result, we can compute reachable sets of systems with several thousand state variables for bounded, but arbitrarily varying inputs. [ABSTRACT FROM AUTHOR]

This paper studies an adaptive neural network (NN) tracking control method for a class of uncertain nonlinear strict-feedback systems with time-varying full-state constraints. As we all know, the states are inevitably constrained in the actual systems because of the safety and performance factors. The main contributions of this paper are that: 1) in order to ensure that the states do not violate the asymmetric time-varying constraint regions, an adaptive NN controller is constructed by introducing the asymmetric time-varying barrier Lyapunov function (TVBLF) and 2) the amount of the learning parameters is reduced by introducing a TVBLF at each step of the backstepping. Based on the Lyapunov stability analysis, it can be proven that all the signals in the closed-loop system are the semiglobal ultimately uniformly bounded and the time-varying full-state constraints are never violated. Finally, a numerical simulation is given, and the effectiveness of this adaptive control method can be verified. [ABSTRACT FROM AUTHOR]

This paper studies the high-order sliding mode (HOSM) control for a general class of uncertain nonlinear systems. Firstly, the standard sliding mode system is extended to a new sliding mode system subject to mismatched terms. The use of the new sliding mode system can reduce the system uncertainties in the control channel and relax the well defined relative degree assumption. Secondly, the conventional constant upper bounds assumption is relaxed to time-varying positive functions, which enables us to obtain a global result. For the new sliding mode system under the new global assumption, a novel HOSM controller, that has a simple relay polynomial form, is then proposed. By introducing a new continuous component in the controller, the discontinuous component of the controller only needs to be selected to suppress the uncertainties and thus a controller with minimal discontinuous component magnitude can be implemented. Finally, strict Lyapunov analysis is provided to show the globally finite-time stability of the closed-loop sliding mode system and an application to Buck converter is presented. [ABSTRACT FROM AUTHOR]

This paper delves into the problem of fixed-time neural network adaptive prescribed performance control for a category of nonstrict-feedback systems with time-varying unknown control coefficients (UCCs). Firstly, two key technical lemmas are proposed. One is to put forward a novel fixed-time stability lemma with a more precise upper-bound estimate of the settling time. The other is to present a new lemma based on a category of type-B Nussbaum functions (TBNFs), which can effectively address the time-varying UCCs in the systems. Secondly, neural networks are employed to approach the uncertain nonlinear terms, and a fixed-time performance function and a nonlinear shifting function are constructed to eliminate the restriction of tracking error in terms of initial condition. Then, to overcome the singularity problem, the switched virtual controllers are designed with the help of the novel fixed-time stability lemma and dynamic surface control technique. It turns out that the tracking error converges to a predefined asymmetric constraint region within a fixed time and the closed-loop system is practically fixed-time stable. Finally, a numerical example and a mass-spring-damper system are provided to verify the effectiveness of the presented design method. [ABSTRACT FROM AUTHOR]

In this work, the finite-time extended dissipativity of the interval type-2 (IT2) fuzzy systems with probabilistic time-varying delay is discussed via resilient memory sampled-data control. To enable the stability analysis and control combination, an IT2 fuzzy model is employed to represent the dynamics of nonlinear systems of which the parameter uncertainties are taken by IT2 membership functions distinguish by the lower and upper membership functions. The main objective of this paper is to design a resilient memory sampled-data controller such that the resulting closed-loop system is finite-time bounded and satisfies extended dissipative performance. Moreover, the solvability of the derived conditions not only depends on the size of the delay but also on the probabilistic distribution of the delay taking values in some interval, thus probabilistic delay protocol is encountered in the IT2 fuzzy model. By employing suitable Lyapunov-Krasovskii functional (LKF) along with Wirtinger-based inequality, a set of sufficient conditions ensuring the finite-time extended dissipative performance for IT2 fuzzy systems are derived in terms of linear matrix inequalities (LMIs). Finally, two numerical simulations are presented to reveal the effectiveness of the developed technique. [ABSTRACT FROM AUTHOR]

This paper studies the consensus problem for a class of nonlinear multi-agent systems with asymmetric time-varying output constraints and completely unknown non-identical control directions. Firstly, in order to deal with the problem of asymmetric time-varying output constraints, the original output-constrained multi-agent systems are transformed into new unconstrained multi-agent systems by constructing the state transformation for each agent. Secondly, the emergence of multiple Nussbaum-type function terms is avoided by introducing novel sliding-mode-esque auxiliary variables and consensus estimate variables, which allows the control directions to be completely unknown non-identical. Thirdly, a novel control strategy is proposed by combining novel variables with state transformation method for the first time, which makes the design of distributed consensus protocol more concise. Through Lyapunov stability analysis, the proposed distributed protocol ensures that the output constraints are never violated and the consensus can be achieved asymptotically. Finally, a practical simulation example is given to demonstrate the effectiveness of the proposed distributed consensus protocol. [ABSTRACT FROM AUTHOR]

• The annulus-event-based communication scheme is introduced for the purpose of avoiding unnecessary transmission of measurement outputs. • A new fault detection scheme is given for saturated nonlinear systems with state saturations and time-varying delays. • A new iterative linear matrix inequality algorithm is presented to deal with the obtained nonlinear matrix inequalities. In this paper, the annulus-event-based fault detection method is proposed for a class of nonlinear systems subject to state saturation and time-varying delays. In particular, in order to save the network resources, a novel communication strategy called annulus-event-based triggering mechanism is considered. That is to say, the measurement output is sent to the filter only when the error between the measured value at the current moment and the data at the last transmission moment is within the prescribed triggering-annulus. Moreover, the system states at each instant are bounded by the convex hull via introducing a free matrix whose infinite norm is less than or equal to 1. Subsequently, sufficient conditions are obtained to ensure the global asymptotic stability and the H ∞ performance of the filtering error dynamics system, which are expressed in line with some nonlinear matrix inequalities that can be handled via the given iterative linear matrix inequality method. Finally, two numerical simulations are employed to illustrate the validity of the developed fault detection filtering algorithm. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of fixed-time stabilization for a class of high-order nonlinear systems with time-varying output constraint (also known as p -normal form systems). Compared with the existing results, the order of the systems can be less than 1, which is more relaxed. Moreover, each subsystem is with the dead-zone input and interconnected nonlinearity. We design a new decentralized fixed-time controller based on the recursive design method by revamping the technique of adding a power integrator and using the tan-type barrier Lyapunov function. The proposed controller is also effective for the systems with asymmetric output constraints. Based on Lyapunov stability theory, it is proved that the decentralized controller can realize that the outputs are strictly constrained within predefined boundaries and all state variables converge to zero in a fixed time, where the bound of reaching time is independent of the initial conditions. Finally, simulation examples are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper proposes a fuzzy adaptive event-triggered control (ETC) design method for nonlinear systems with time-varying state constraints. Fuzzy logic systems (FLSs) is adopted to approximate the unknown smooth functions and the constraints are satisfied by using an appropriate asymmetric time-varying barrier Lyapunov function (BLF). The communication burden from the controller to the actuator is reduced by designing an appropriate ETC scheme. Finally, it is shown that the full-state constraints are not violated at any step of the backstepping design and the signals in the closed-loop system are bounded. The effectiveness of the proposed adaptive ETC scheme is verified by two simulation examples. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to report on the global practical uniform h-stabilization for certain classes of nonlinear time-varying systems and its application in a separately excited DC motor circuit. Design/methodology/approach: Based on Lyapunov theory, the practical h-stabilization result is derived to guarantee practical h-stability and applicated in a separately excited DC motor. Findings: A controller is designed and added to the nonlinear time-varying system. The practical h-stability of the nonlinear control systems is guaranteed by applying the appropriate controller based on Lyapunov second method. Another effective controller is also designed for the global practical uniform h-stability on the separately excited DC motor with load. Numerical simulations are demonstrated to verify the effectiveness of the proposed controller scheme. Originality/value: The introduced approach is interesting for practical h-stabilization of nonlinear time-varying systems and its application in a separately excited DC motor. The original results generalize well-known fundamental result: practical exponential stabilization for nonlinear time-varying systems. [ABSTRACT FROM AUTHOR]

In this paper, the global output feedback tracking control is investigated for a class of switched nonlinear systems with time-varying system fault and deferred prescribed performance. The shifting function is introduced to improve the traditional prescribed performance control technique, remove the constraint condition on the initial value, and make the constraint bounds have more alternative forms. To estimate the unmeasured state variables and compensate the system fault, the switched dynamic gain extended state observer is constructed, which relaxes the traditional Lipschitz conditions on the nonlinear functions. Based on the proposed observer, by constructing the new Lyapunov function and using the backstepping method, the global robust output feedback controller is designed to make the output track the reference signal successfully, and after the adjustment time, the tracking error enters into the prescribed set. The stability of the system is analyzed by the average dwell time method. Finally, simulation results are given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article investigates adaptive state-feedback stabilization problem for a class of stochastic high-order nonlinear systems with unknown time-varying powers and stochastic inverse dynamics for the first time. The existence of stochastic inverse dynamics, unknown parameters, and time-varying powers makes stochastic high-order nonlinear systems essentially different from the related papers, which brings a series of obstacles to achieve the control objective. By virtue of the parameter separation principle, adaptive technique and some flexible algebraic methods, a novel adaptive state-feedback controller is designed to guarantee that the equilibrium of the closed-loop system is globally stable in probability. Finally, a simulation is provided to demonstrate the effectiveness of the control scheme. [ABSTRACT FROM AUTHOR]

The problem of dissipativity-based filtering for switched time-delayed Takagi–Sugeno (T–S) fuzzy nonlinear systems is investigated. Stochastic perturbation and state-dependent switching are taken into consideration simultaneously. Firstly, the characterized T–S fuzzy systems and designed fuzzy filtering error dynamic system should be mean-square exponential stability with a (ℵ, ℏ, ℓ)- δ -dissipative. This paper dedicates effort to stabilization analysis of continuous T–S fuzzy systems, diminishing the conservatism of stability conditions by means of constructing non-common Lyapunov–Krasovskii functional and employing linear matrix inequalities (LMIs). Secondly, the dissipative control problem for T–S fuzzy stochastic system with time-varying delay and uncertainties via state-dependent switching will be dealt with. Thirdly, Sufficient conditions are proposed to guarantee that the filter-based dynamical error system with time delays and uncertainties is mean-square exponentially stable through dissipativity analysis. Numerical simulation results demonstrate availability and effectiveness of the developed design scheme. [ABSTRACT FROM AUTHOR]

This paper investigates the tracking control issue of nonlinear stochastic systems subject to time-varying full state constraints and input saturation. By employing both neural network-based approximator and backstepping technique, an adaptive neural network (NN) control approach is presented on the basis of the time-varying barrier Lyapunov function. To surmount the influence of saturation nonlinearity, a Gaussian error function-based continuous differentiable saturation model is introduced such that the actual control in the final backstepping step can be achieved. The designed controller can not only achieve the tracking control objective, but also surmount the impact of input saturation to stochastic system performance. Meanwhile, the norm of NN weight vector is taken as estimated parameter, and it can alleviate computation burden. The presented controller can ensure that all the signals in the closed-loop system are bounded in probability and all state variables are restricted the predefined regions. Finally, simulation results are given to illustrate the effectiveness of the established controller. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear impulsive observer for a class of Lipschitz nonlinear systems with time-varying uncertainties is investigated. The observer uses discrete time measurements of the system output. A time-varying Lyapunov function is used to show that, under sufficient conditions based on linear matrix inequalities, the estimation error is globally practically stable at the origin. The dynamic observer is tested on an example to demonstrate the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

Stability problem of switched nonlinear time-varying systems (SNTVS) with mixed delays is presented in this paper. Unlike the previous results, by employing the comparison principle and a method developed in positive systems without involving Lyapunov function, stability criteria are derived under average dwell time (ADT) switching. The theoretical results are demonstrated by numerical examples that are not covered in the existing ones. [ABSTRACT FROM AUTHOR]

Persistently excited nonlinear time-varying systems are considered in this paper. Two new quadratic, time-varying, Lyapunov functions are presented, whose time-varying matrices—solutions to suitable linear time-varying matrix differential equations—are causal (nonanticipating) and, thus, differently from related results in the literature, available at runtime. They allow for directly addressing and successfully achieving further adaptation goals, when uncertain parameters affect the system dynamics. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of local stabilization of nonlinear polynomial control systems subject to time-varying input delay and polytopic parameter uncertainty. A linear matrix inequality approach based on the Lyapunov–Krasovskii theory is proposed for designing a nonlinear polynomial state feedback controller ensuring the robust local uniform asymptotic stability of the system origin along with an estimate of its region of attraction. Two convex optimization procedures are presented to compute a stabilizing controller ensuring either a maximized set of admissible initial states for given upper bounds on the delay and its variation rate or a maximized lower bound on the maximum admissible input delay considering a given set of admissible initial states. Numerical examples demonstrate the potentials of the proposed stabilization approach. [ABSTRACT FROM AUTHOR]

This paper employs detectability ideas to decide uniform global asymptotic stability (UGAS) of the trivial solution for a class of switched nonlinear time-varying systems when the trivial solution is uniformly globally stable. Using the notion of limiting behaviors of the state, output, and switching signals, the concept of a limiting zeroing-output solution is introduced. This leads to a definition of weak zero-state detectability (WZSD) that can be used to check UGAS, (uniformly for a set of switched signals). En route to establish this, a number of new stability results are derived. For example, under appropriate conditions, it is feasible to decide UGAS even when the switching signal does not satisfy an averaged dwell-time condition. It is also shown that WZSD of the original switched system can be verified by detectability conditions of much simpler auxiliary systems. Moreover, UGAS can be guaranteed without requiring that in each allowable system (without switching), the trivial solution is attractive. The effectiveness of the proposed concept is illustrated by a few examples including a switched semi-quasi-Z-source inverter. [ABSTRACT FROM AUTHOR]

This paper is concerned with the distributed set-membership filtering problem for a class of general discrete-time nonlinear systems under event-triggered communication protocols over sensor networks. To mitigate the communication burden, each intelligent sensing node broadcasts its measurement to the neighboring nodes only when a predetermined event-based media-access condition is satisfied. According to the interval mathematics theory, a recursive distributed set-membership scheme is designed to obtain an ellipsoid set containing the target states of interest via adequately fusing the measurements from neighboring nodes, where both the accurate estimate on Lagrange remainder and the event-based media-access condition are skillfully utilized to improve the filter performance. Furthermore, such a scheme is only dependent on neighbor information and local adjacency weights, thereby fulfilling the scalability requirement of sensor networks. In addition, an optimization algorithm is developed to minimize the trace of the estimated ellipsoid set, and the effect from the adopted event-triggered threshold is thoroughly discussed as well. Finally, a simulation example is utilized to illustrate the usefulness of the proposed distributed set-membership filtering scheme. [ABSTRACT FROM AUTHOR]

In this paper, we propose continuous-time and sampled-data output feedback controllers for nonlinear multi-input multi-output systems with time-varying measurement and input delays, with no restriction on the bound or serious limitations on the growth of the nonlinearities. A state prediction is generated by chains of saturated high-gain observers with switching error-correction terms and the state prediction is used to stabilize the system with saturated controls. The observers reconstruct the unmeasurable states at different delayed time-instants, which partition the maximal variation interval of the time-varying delays. These delayed time instant depend both on the magnitude of the delays and the growth rate of the nonlinearities. We also design sampled-data stabilizers as zero-order discretization of a hybrid modification (with continuous-time states and discrete-time control and innovations) of the continuous-time stabilizers. [ABSTRACT FROM AUTHOR]

In this paper, the unscented Kalman filtering (UKF) problem is investigated for a class of general nonlinear systems with stochastic uncertainties under communication protocols. A modified unscented transformation is put forward to account for stochastic uncertainties caused by modeling errors. For preventing data collisions and mitigating communication burden, the round-robin protocol and the weighted try-once-discard protocol are, respectively, introduced to regulate the data transmission order from sensors to the filter. Then, by employing two kinds of data-holding strategies (i.e., zero-order holder and zero input) for those nodes without transmission privilege, two novel protocol-based measurement models are formulated. Subsequently, by resorting to the sigma point approximation method, two resource-saving UKF algorithms are developed, where the impact from the underlying protocols on the filter design is explicitly quantified. Finally, compared with the protocol-based extended Kalman filtering algorithms, a simulation example is presented to demonstrate the effectiveness of the proposed protocol-based UKF algorithms. [ABSTRACT FROM AUTHOR]

This paper studies the distributed time-varying convex optimization problem for a class of nonlinear multiagent systems. An auxiliary system is first designed to estimate the global optimal state and its high-order derivatives by means of a distributed algorithm. Relying on this auxiliary system, the solution of the distributed time-varying convex optimization problem is converted into that of a tracking problem for a class of nonlinear systems. A tracking control scheme is then proposed based on the back-stepping strategy. Simulations are provided to validate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper is devoted to tracking control for a class of strict-feedback time-varying nonlinear systems with unknown control directions. Currently, most existing control methods for strict-feedback nonlinear systems can realize asymptotic tracking while neglecting the transient performance; or they can guarantee the preassigned transient performance, but merely ultimately bounded tracking error is reached. By introducing smooth compensating terms in a function form of tracking errors, an innovative control algorithm is proposed that can ensure preassigned bounds of overshoot and convergence rate without a priori knowledge of control directions while achieving asymptotic tracking and global uniform boundedness of all the closed-loop signals. Furthermore, the adaptive σ -modification control algorithm for the parameter estimates is developed, which renders smaller parameter estimates and thus results in lower shocks on the control input without compromising the preassigned transient performance and asymptotic tracking convergence. The proposed control algorithms obviate the need for analytic calculation of the partial derivatives of the stabilizing functions (virtual controllers) that is typically employed in controlling of strict-feedback systems, and are therefore more easily derived and implemented. Simulations are provided to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of H ∞ fuzzy filter design in finite frequency intervals for discrete-time nonlinear systems subject to time-varying delays. Fuzzy filters whose order is greater (non-minimal) than the order of the system are synthesized by transforming the original time-delayed system into an equivalent switched nonlinear system. The design conditions are given in terms of sufficient parameter-dependent linear matrix inequalities that can be solved through relaxations based on semi-definite programming. The advantages of the proposed approach are illustrated through numerical examples and comparisons with other available techniques. [ABSTRACT FROM AUTHOR]

In this paper, a learning-based robust tracking control scheme is proposed for a quadrotor unmanned aerial vehicle system. The quadrotor dynamics are modeled including time-varying and coupling uncertainties. By designing position and attitude tracking error subsystems, the robust tracking control strategy is conducted by involving the approximately optimal control of associated nominal error subsystems. Furthermore, an improved weight updating rule is adopted, and neural networks are applied in the learning-based control scheme to get the approximately optimal control laws of the nominal error subsystems. The stability of tracking error subsystems with time-varying and coupling uncertainties is provided as the theoretical guarantee of learning-based robust tracking control scheme. Finally, considering the variable disturbances in the actual environment, three simulation cases are presented based on linear and nonlinear models of quadrotor with competitive results to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, input-to-state stability (ISS) for discrete-time switched nonlinear time-varying (SNTV) systems is investigated. Starting with discrete-time nonlinear time-varying (NTV) systems, some improved sufficient conditions are proposed to verify the ISS of systems by using the weak implication-form ISS (WI-ISS) Lyapunov function, weak dissipative-form ISS (WD-ISS) Lyapunov function, and interval descent technique. Then, the results obtained are extended to study the ISS of discrete-time SNTV systems, several relaxed conditions are given by using piecewise WI-ISS and WD-ISS Lyapunov functions, minimum dwell time, and infinite switching methods, respectively. Comparing with the existing results, the obtained conditions release the requirement on negative definiteness of the differences of (piecewise) Lyapunov functions, moreover, all subsystems are allowed to be unstable in the case of infinite switching. Finally, a numerical example is given to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]