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This article develops a neuro‐adaptive observer for state and nonlinear function estimation in systems with partially modeled process dynamics. The developed adaptive observer is shown to provide exponentially stable estimation errors in which both states and nonlinear functions converge to their true values. When the neural approximator has an approximation error with respect to the true nonlinear function, the observer can be used to provide an H∞$$ {H}_{\infty } $$ bound on the estimation error. The article does not require assumptions on the process dynamics or output equation being linear functions of neural network weights and instead assumes a reasonable affine parameter dependence in the process dynamics. A convex problem is formulated and an equivalent polytopic observer design method is developed. Finally, a hybrid estimation system that switches between a neuro‐adaptive observer for system identification and a regular nonlinear observer for state estimation is proposed. The switched operation enables parameter estimation updates whenever adequate measurements are available. The performance of the developed adaptive observer is shown through simulations for a Van der Pol oscillator and a single link robot. In the application, no manual tuning of adaptation gains is needed and estimates of both the states and the nonlinear functions converge successfully. [ABSTRACT FROM AUTHOR]

The classical PID (proportional‐integral‐derivative) control is the most basic and widely used control algorithm in engineering systems by far. Whether PID control can effectively deal with coupled multiagent uncertain nonlinear dynamics is well worth investigating. In this article, a class of PID controlled multiagent stochastic systems with coupled uncertain dynamics is considered, where the control input is nonaffine. Each agent has its own regulation objective, and only has access to its own regulation error information for PID feedback. First, a PID parameter set will be constructed explicitly based on some prior knowledge about the nonlinear functions, such that the overall multiagent system can be stabilized globally in the mean square sense, as long as the PID parameters are chosen from the constructed set. Moreover, the regulation error will be proven to have an upper bound proportional to the noise intensity along the reference signal. Furthermore, it will be shown that the regulation error of each agent can be arbitrarily small by choosing the PID parameters suitably large. Finally, the theoretical results will be verified by simulations. [ABSTRACT FROM AUTHOR]

Summary: An impedance control scheme is proposed for a Stewart‐structure‐based wheel‐legged robotic system to strengthen the dynamic attitude adjustment stability in wheel motion. The wheel‐leg, which is driven by electrical cylinders in the Stewart structure, is analyzed in kinematics and dynamics. The rotation in the axial direction of every electric cylinder is calculated to improve the accuracy of the kinematic model. To fulfill the impedance demands, a passive structure with 6 degrees of freedom (DOF) is modeled. The mass of the mechanism has a coupling effect on the impedance model for each DOF, which is a nonlinear function. As motion decoupling in the workspace has been completed for the Stewart structure, an impedance control strategy with inner‐loop position tracking is employed. An extended state observer (ESO) is designed to estimate the disturbances arising from the nonlinear coupling effects. Based on the ESO observation outputs, an active disturbance rejection control that explicitly handles the workspace limit is designed with guaranteed practical stability. By reducing force interaction and body vibration, the wheel‐legged robotic system keeps wheel motion stability on uneven roads. Multiple comparative experimental results are presented to validate the stability and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, the distributed containment control schemes are presented for a class of nonlinear heterogeneous high‐order fully actuated multi‐agent systems. First, for each follower, the reference trajectory generator is constructed by using the output information of the neighbor agents. Then, the distributed containment controllers are designed for the system with known nonlinear system function matrices and control gain matrices. Further, since the existence of modeling errors and other uncertain factors, the obtained system model is often not accurate enough, that is, the system function matrix and control gain matrix are actually unknown nonlinear matrices. To tackle these obstacles, we employ the radial basis function neural network method to approximate the unknown nonlinear system function matrices and skillfully construct the controllers combined with the adaptive technology to eliminate the effects of the unknown control gain matrices. The developed control strategies can guarantee that the containment control can be realized and the containment errors can be adjusted to arbitrary precision. In the end, the simulation results on the electromechanical system and robotic system demonstrate the availability and effectiveness of the provided schemes. [ABSTRACT FROM AUTHOR]

An adaptive event‐triggered control issue based on command filter and dynamic surface control is studied for switched nonlinear systems with full state time‐varying constraints in this article. To handle state constraints, the nonlinear mapping conversion technique is used. Radial basis function neural networks (RBFNNs) are utilized to approximate unknown nonlinear continuous functions. Adaptive control algorithm is designed based on command filtered backstepping technology. Novel even triggered control is constructed for two different cases in the switching interval. Furthermore, all signals in the switched system are proved to be semi‐globally uniformly ultimate bounded (SGUUB) by the aid of dynamic surface control method under arbitrary switching. Meanwhile, all states do not violate the preset constraints and Zeno phenomenon is avoided. The validity of the presented approach is confirmed through a numerical simulation result. [ABSTRACT FROM AUTHOR]

This article is concerned with event‐triggered adaptive tracking control design of strict‐feedback nonlinear systems, which are subject to input saturation and unknown control directions. In the design procedure, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. The Nussbaum gain technique is employed to address the issue of the unknown control directions. A predetermined time convergent performance function and a nonlinear mapping technique are introduced to guarantee that the tracking error can converge in the predetermined time with a fast convergence rate and a high accuracy. Then the event‐triggered adaptive prescribed performance tracking control strategy is proposed, which not only ensures the boundedness of all the closed‐loop signals and the convergence of tracking error but also reduces the communication burden from the controller to the actuator. At last, the simulation study further tests the availability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the adaptive control is investigated by switching linear controllers for a class of nonlinear parameterized systems with multiple unknown control directions. Parametric uncertainties entering the state equations nonlinearly can be fast time‐varying or jumping at unknown time instants, the bounds of the parametric uncertainties are not required to know a priori and the multiple control directions are unknown. Our proposed adaptive controller is a switching type controller. First, sufficient conditions for designing an adaptive stabilizer are derived. Then, a switching‐type adaptive controller is designed, in which a linear controller with two undetermined design parameters to be tuned is recursively designed by adding a power integrator, and a switching mechanism is proposed to tune these parameters online for compensating the multiple unknown control directions and the unknown bounds of the parametric uncertainties. The undetermined design parameters are based on the upper bound estimation of the unknown parameters existing not only in the nonlinear functions but also in the control directions functions. The proposed adaptive controller globally asymptotically stabilizes the system in the sense that, for any initial conditions, the state converges to the origin while all the signals of the closed‐loop system are bounded. Finally, an example is given to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article studies the adaptive state‐feedback control problem of output‐constrained stochastic high‐order nonlinear systems with stochastic integral input‐to‐state stability (SiISS) inverse dynamics. A key nonlinear transformation function is constructed to convert the original output‐constrained stochastic nonlinear system into an equivalent form without any output constraint. By subtly using the SiISS small‐gain condition and fully extracting the characteristics of system nonlinearities, two new control design and analysis methods are developed to guarantee that the closed‐loop system has an almost surely unique solution, all the closed‐loop signals are bounded almost surely, and the equilibrium point is stable in probability without the violation of output constraint. A simulation result is provided to show the effectiveness of this control method. [ABSTRACT FROM AUTHOR]

This article investigates the adaptive fault‐tolerant tracking control problem for nonlinear systems with prescribed performance and input dead‐zone. First, a new composite variable is constructed by using the characteristics of actuator fault and input dead‐zone for the modeling purpose. Second, an adaptive neural network observer is designed to estimate the system states in the presence of inaccurate feedback information. Third, the proposed control strategy effectively counteracts the effects of sensor failure and unknown nonlinear functions, which makes the tracking error confined within the performance boundary and all the signals of the closed‐loop system semi‐globally uniformly ultimately bounded. Finally, an application oriented example is provided to demonstrate the effectiveness of the proposed control algorithm. [ABSTRACT FROM AUTHOR]

Distributed observer is an effective tool to deal with leader‐following control problems. This article investigates the fully predefined‐time distributed observer (FPTDO) design problem of a generalized second‐order strict‐feedback nonlinear leader system. Firstly, given the system parameters and the upper bounds of the system nonlinearities, an FPTDO is proposed to provide the state estimates. Secondly, considering that the time‐varying system parameters and nonlinear functions of the leader system are unknown to each follower, an FPTDO is developed to estimate the time‐varying system parameters, nonlinearities and full state of the leader. The proposed FPTDOs exhibit the following advantages: (1) the observation errors converge to zero within a finite time that is predefined by only one design parameter independent of the initial conditions; (2) the designs of the FPTDOs do not require any information of the communication topology (Laplacian matrix); and (3) the exact models of the nonlinear functions are not required by each follower. Finally, simulation examples are given to demonstrate the effectiveness of the proposed FPTDOs. [ABSTRACT FROM AUTHOR]

This note is devoted to the analysis of adaptive sliding mode control of H∞$$ {}_{\infty } $$/passivity of semi‐Markov jump discrete‐time uncertain singular systems. We consider the constraints of parameter uncertainties, unknown nonlinear functions, and external disturbances throughout the model. Firstly, a novel mode‐independent sliding mode surface is constructed, then the sliding mode dynamic equation under the equivalent controller is obtained. Secondly, by introducing virtual points, several sufficiency criteria are derived for the sliding mode dynamic ensuring H∞$$ {}_{\infty } $$/passive performance and stochastic admissibility with linear matrix inequalities form. Thirdly, the state trajectory can be driven into a switching band containing the origin by adaptive sliding mode control techniques. Finally, the effectiveness of our findings is demonstrated by comparing existing strategies with three simulation examples. [ABSTRACT FROM AUTHOR]

This article studies the fault‐tolerant control for linear systems with disturbances through sliding mode scheme. Compared with the existing results, by means of a nonlinear sliding function with an exponential term, a reduced‐order sliding motion can be obtained while the reaching phase of conventional sliding mode control is eliminated. On the other side, with the help of an exponentially decaying barrier Lyapunov functions, a continuous sliding mode algorithm is established. Within the proposed framework, the trajectories of closed‐loop systems can be forced to a prescribed practical sliding surface, and then, both the transient as well as steady‐state performances are guaranteed despite the occurrence of abrupt actuator faults. Under the Lyapunov direct method, a sufficient condition is derived such that the sliding motion is uniformly bounded with time‐varying performance constraints. Finally, an electric amplidyne system is considered to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

This article investigates the robust adaptive guaranteed cost tracking (RAGCT) control problems for two class of high‐order nonlinear systems with time‐varying uncertainties. A special nonlinear function, named as the local smooth nonlinear function, is introduced, which is crucial for our controller design. Then, using the function and the recently proposed high‐order fully actuated (HOFA) system approaches, a novel RAGCT controller for HOFA system with time‐varying uncertainty is designed, which guarantees the global boundedness of the closed‐loop system within finite time. Then, based on the result about the above HOFA system, the RAGCT controller for a class of strict‐feedback systems with high‐order form and time‐varying uncertainties is obtained, which also guarantees that the closed‐loop system is globally bounded within finite time. Most importantly, two designed controllers can preset arbitrarily the upper bounds of cost functions characterizing the tracking performance independent of the system initial values and the time‐varying uncertainties, which optimizes greatly the system tracking performance, and is difficult to achieve by using existing guaranteed cost control methods. Finally, two simulation examples including one‐link manipulator are provided to show the effect and the practicability of our proposed control method. [ABSTRACT FROM AUTHOR]

This article investigates the tracking control problem of adaptive fault‐tolerant control (AFTC) for a class of strict‐feedback nonlinear systems with actuator/sensor faults and unmatched disturbances. The sensor/actuator faults include bias, drift, loss of accuracy, and loss of effectiveness. Our main control objective is to investigate an adaptive fault‐tolerant control algorithm with the help of tuning functions, adaptive control technology, fuzzy logic systems (FLSs) and so on. For unknown nonlinear functions and fault items, FLSs and adaptive control technology are utilized to approximate them. Furthermore, over‐parameterization problem existed in the backstepping‐based controller design is solved by introducing the tuning functions. Theoretical analysis proves that our proposed AFTC scheme can ensure that all the signals in the closed‐loop system are bounded and the tracking error remains within a small range of zero even if a series of faults mentioned above occur. In the end, the simulation results show that the presented AFTC strategy is feasible and effective. [ABSTRACT FROM AUTHOR]

This study presents a near‐optimal learning‐based approach for sliding‐mode control of uncertain nonsquare nonlinear systems subject to output constraints. To achieve a compromise between safety and optimality, a reinforcement learning algorithm is proposed to compute the near‐optimal values of the sliding manifold coefficients. In the reinforcement learning algorithm, only measured input‐output data obtained by experiments or simulations are employed. Furthermore, the presented method does not require partial knowledge of the system dynamics to initialize the reinforcement learning process. By employing the tuned sliding vector, an adaptive fuzzy sliding‐mode control (AFSMC) input, including a fuzzy term and a robust term, is generated. The fuzzy term is used to approximate an unknown nonlinear function and the robust term is designed for mismatch compensation. To guarantee that the output constraints are not violated, the adaptation laws for obtaining the fuzzy singletons and the bounds of the approximation errors are designed based on the barrier Lyapunov functions (BLF) theorem. The closed loop asymptotic stability is theoretically analyzed in the article, while the effectiveness of the method is assessed in simulation. [ABSTRACT FROM AUTHOR]

In this article, we are concerned with the input‐to‐state practical stability (ISpS) of nonautonomous nonlinear infinite‐dimensional systems. Sufficient conditions of ISpS are provided based on Lyapunov functions and a nonlinear inequality. We characterize ISpS in terms of uniform practical asymptotic gain property. We show that for a class of admissible inputs the existence of an ISpS‐Lyapunov function implies the ISpS of a system in Banach spaces. These results are used to study the input‐to‐state practical stability of a certain class of nonautonomous semilinear evolution equations. Furthermore, we provide a small‐gain theorem for nonautonomous nonlinear interconnected systems. An example is used to illustrate the application of the developed method. [ABSTRACT FROM AUTHOR]

The highly accurate state estimation of nonlinear systems is needed in many different application fields. In many existing nonlinear filters, the uncompensated nonlinear approximation error and widely used numerical sampling methods both seriously affect the estimation accuracy and numerical stability. In this paper, based on the variational Bayesian framework, a novel iterative nonlinear filter consisting of forward modeling and inverse estimation is proposed. In the forward modeling stage, a linear Gaussian regression process with distributed variational parameters (VPs) is designed to fit the whole nonlinear measurement likelihood. The distributed VPs consider both first and second moments information, so as to compensate for approximation error from the whole likelihood perspective, instead of only the nonlinear function approximation, which can further improve the accuracy of Bayesian posterior update. In the linear Gaussian regression process, the original nonlinear measurement function (NMF) is just viewed as a prior and no longer directly participates in the modeling of the measurement likelihood. Hence, in the inverse estimation stage, when maximizing the evidence lower bound to update the posteriors of the state and VPs, we can obtain closed‐form solutions without numerical sampling methods to approximate the integral of NMF required in many existing methods, which can guarantee numerical stability. Moreover, to avoid the random setting of hyperparameters and to block the propagation of the accumulated error, we propose two rules, estimation and lower bound consistencies, to conduct the hyperparameters' initialization at the beginning of iteration at each sampling time and also derive an optimization method to update hyperparameters during iteration. Finally, the performance of our proposed method is demonstrated in the nonlinear orbital estimation problems. [ABSTRACT FROM AUTHOR]

This paper studies the problem of the adaptive control of nonlinear impulsively coupled complex networks. Firstly, a class of adaptive controllers are designed for the nonlinear impulsive differential equations, where the nonlinear function can be decomposed into matching condition and mismatching condition. Secondly, combining with Lasalle invariant set theorem, Schur complement theorem and some inequality techniques, we consider the synchronization of impulsively coupled complex networks via the general adaptive control. Moreover, this paper proposes the pinning adaptive synchronization results for impulsive dynamical complex networks. Finally, the proposed results are verified by some examples in which simulations are available for comparison. [ABSTRACT FROM AUTHOR]

This article studies the adaptive finite‐time tracking control problem for a class of output‐constrained nonlinear interconnected systems with unknown actuator faults and parametric uncertainties. By integrating the lower bounds of unknown virtual control coefficients into the Lyapunov functions design, an adaptive control strategy is proposed on the basis of adaptive estimations and some smooth functions, which make the controller effectively compensate the effects of unknown virtual control coefficients, unknown interconnected terms, and other uncertain nonlinear functions. Besides, the controller can also compensate the effect of actuator faults by fusing a two‐step design method into the backstepping design framework. Simultaneously, in view of the output constraint requirements, a barrier Lyapunov function is introduced, and it is a more general one that can reckon with time‐varying asymmetric output constraints. Furthermore, in light of the finite‐time stability criterion, all the signals of system are bounded and the tracking performance can be guaranteed in a finite time. Finally, the effectiveness of the proposed method is validated by some simulation results. [ABSTRACT FROM AUTHOR]

In this article, the practical prescribed time tracking problem based on event‐triggered control is studied for a class of uncertain nonlinear systems subject to asymmetric state constraints. We design a settling time regulator to get a performance function. Using this function, an event‐triggered adaptive control method is put forward for acquiring specified tracking precision in the prescribed time. Then, the asymmetric state constraints are handled by introducing a novel nonlinear state‐dependent function. In combination with backstepping technique, we construct a coordinate transformation to convert the original state‐constrained space into free space. Besides, a dynamic surface control is proposed to eliminate the demanding feasibility conditions on virtual controllers. The communication between controller and actuator is reduced by adopting the appropriate event‐triggered strategy. Moreover, it is indicated that, without altering the control structure, not only the settling time and tracking precision can be selected by the user but also asymmetric state constraints are satisfied. Simulation examples confirm the effectiveness of the presented control scheme. [ABSTRACT FROM AUTHOR]

It is still an open problem to achieve tracking control with state constraints if the initial states are out of the constrained region. This underlying problem becomes more challenging if the system suffers from modeling uncertainties and external disturbances. In this paper, we investigate such problem for a class of uncertain nonaffine self‐restructuring systems subject to state constraints in the absence of any limitation on the initial values of states. In order to steer the original system states into the desired constraint region in finite time, certain auxiliary system is firstly constructed via introducing auxiliary variables. By resorting to some auxiliary nonlinear functions, the original system with state constraints is transformed into an unconstrained one in the sense that the constraint problem of the original system is equivalent to ensuring the stability of the transformed one. By following the backstepping design technique, an adaptive control scheme is developed that enables the states to enter into the constrained region for any initial point within any fixed time and then never violate it. All the closed loop signals are ensured to be semi‐globally uniformly ultimately bounded. Finally, one numerical simulation example is presented to verify the theoretical analysis. [ABSTRACT FROM AUTHOR]

This article investigates the consensus problem for uncertain nonlinear multi‐agent systems (MASs) with asymmetric output constraint. Different from BLF‐based constraint consensus tracking control, a novel approach based on nonlinear state‐dependent function is proposed to solve the asymmetric output constraint, which need not convert output constraint into tracking error bound. First‐order sliding mode differentiator is incorporated into each step of backstepping control design to reduce computation burden. Further, in combination of proposed event‐triggered mechanism based on time‐varying threshold, a distributed fuzzy adaptive event‐triggered finite‐time consensus method is developed. It can ensure that the consensus tracking error tends to a small neighbor in a finite time and the asymmetric output constraint of each subsystem is not violated. Two simulations are given to demonstrate the effectiveness of control method. [ABSTRACT FROM AUTHOR]

This article studies the predefined‐time observation problem of generalized strict‐feedback second‐order systems commonly encountered in practice. A nonaffine control input, a matched perturbation, and nonlinear functions satisfying the Hölder growth condition are considered. A class of adaptive predefined‐time observers (PTOs) is designed to reconstruct unknown states and lumped perturbations based on a barrier function and specific time‐varying functions. Distinct from existing observers for strict‐feedback systems, the PTO accomplishes a complete reconstruction in a predefined time with trivial peaking observation errors. Furthermore, the upper bound of the settling time of the PTO is tightly and explicitly predefined by only one design parameter, and is irrelevant to the initial conditions. Hence, tuning procedures for the physically realizable temporal demands become less conservative and more straightforward. Moreover, the adaptive coefficients of the PTO are self‐adjusted along with the magnitude of perturbation, efficiently improving the transient performance under wide‐range perturbations. Finally, numerical simulations on a robot manipulator system demonstrate the effectiveness of the PTO. [ABSTRACT FROM AUTHOR]

Deep learning is gradually mainstreaming into data‐driven methods, relying on the advantages of extracting complicated nonlinear features. However, the black‐box property makes its decision rules non‐transparent, resulting in difficulty in attribution tasks, which aim to backtrack the contribution of network inputs to the outputs. Fault isolation and localization are techniques for diagnosing the root cause of system failures, which have a consistent objective with attribution for a deep learning‐based fault observer or classifier. Unfortunately, most fault isolation methods are based on shallow learning methods. Also, many attribution algorithms are linear without considering the influence of nonlinear activation functions. The related concerns motivate us to propose a new approach, namely layer‐wise contribution‐filtered propagation (LCP), for deep learning‐based fault isolation. In LCP, reasonable contributions are defined based on the influence of each layer input on maximizing the absolute output activation. A symbolic function is designed to identify neurons with negative contributions, which are then filtered and forbidden to backpropagate to the previous layer. By guiding correct attribution, LCP is available for any nonlinear activation functions and their combinations. It also provides a solution for fault isolation with stacked sample inputs, in which one single variable has several attributions associated with different times. Finally, two chemical simulations verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, a command filtering‐based adaptive event‐triggered neural network control scheme is proposed for a class of uncertain switched nonlinear systems with unknown control coefficient and input saturation. First, radial basis function neural networks are used as function approximators to estimate unknown nonlinear functions. Then, an event‐triggering mechanism based on the tracking error is introduced to avoid the over‐consumption of communication resources. Furthermore, command filters are employed to solve the problem of complexity explosion that exists in conventional backstepping control design, and the error compensation signals are designed to reduce the errors caused by the filters. Considering that the unknown control gain and input saturation exist in many practical applications, a Nussbaum‐type function is thus introduced into the controller design to address these challenging issues. Finally, stability of the closed‐loop system is strictly proven under a standard Lyapunov stability analysis framework. The effectiveness of the proposed control scheme is illustrated by a simulation example. [ABSTRACT FROM AUTHOR]

This article establishes a mechanical‐electrical‐hydraulic vertical torsional coupling vibration mathematical model, and investigates its vibration suppression control strategy with time varying full state constraints for the rolling mill vertical torsional coupling vibration system. Firstly, the mechanical‐electrical‐hydraulic vertical torsional coupling vibration nonlinear model is developed using dynamic theory, which takes into account nonlinear damping, nonlinear rolling force and the coupling relationship between the vertical vibration system and the torsional vibration system. Then, nonlinear constraint transformation functions and coordinate transformations are implemented to remove the feasibility condition in handling the full state constraints problem, and neural networks are used to approximate unknown nonlinear functions. Furthermore, the vibration suppression control algorithm of the mechanical‐electrical‐hydraulic vertical torsional coupling system is designed with the specific sequence backstepping method and dynamic surface control technique, which can resolve the problem of nesting in the controller design process. Finally, the effective of the proposed method on vibration suppression is verified by the simulation. [ABSTRACT FROM AUTHOR]

For the stability analysis issue of a T‐S fuzzy system, improved piecewise membership functions dependent approach is proposed to reduce conservatism. Based on a least‐square method, the nonlinear membership functions are approximated by a series of decoupled polynomial functions. Then the piecewise vertices are chosen by a newly proposed derivative‐integral nonuniform division approach. For the robust tracking control task, a series of convex robust stable conditions are obtained. Finally, a mass‐spring‐damper (MSD) simulation example is adopted to illustrate the effectiveness of the designed method. [ABSTRACT FROM AUTHOR]

The issue of event‐triggered‐based decentralized fuzzy control of stochastic interconnected large‐scale nonlinear systems with full‐state constraints is studied in this article. By means of the fixed‐time command filtered dynamic surface control technology with the newly error compensating signals, a newly decentralized event‐triggered control scheme is proposed. Under the proposed scheme, the problem of "curse of dimensionality" that often occurs in the conventional backstepping design process is overcome, and the influence of filtering error on transient performance is effectively reduced. Meanwhile, the asymmetric time‐varying state constraints are dealt with by introducing the nonlinear state‐dependent functions. Compared with the conventional schemes of dealing with state constraints, the limitation that the virtual control functions need to satisfy the feasibility conditions is eliminated. In addition, a novel smooth function is constructed to deal with the obstacles caused by unknown interconnections. Simulation results verify the scheme developed. [ABSTRACT FROM AUTHOR]

This article investigates the distributed optimal output consensus problem of second‐order uncertain nonlinear multiagent systems over weight‐unbalanced directed networks. Under the standard assumption that local cost functions are strongly convex with globally Lipschitz gradients, a novel distributed dynamic state feedback controller is developed such that the outputs of all the agents reach the optimal solution to minimize the global cost function which is the sum of all the local cost functions. The controller design is based on a two‐layer strategy, where a distributed optimal coordinator and a reference‐tracking controller are proposed to address the challenges arising from unbalanced directed networks and uncertain nonlinear functions respectively. A key feature of the proposed controller is that the nonlinear functions containing the uncertainties and disturbances are not required to be globally Lipschitz. Furthermore, by exploiting adaptive control technique, no prior knowledge of the uncertainties or disturbances is required either. Two simulation examples are finally provided to illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this paper, a robust adaptive fault‐tolerant control (FTC) strategy based on hyperbolic tangent function is proposed for a class of mechanical systems with unknown disturbance and unknown nonlinear friction model. The robust adaptive FTC algorithm proposed in this paper can maintain the system performance even after partial failure occurs in the actuator. Different from the traditional fault‐tolerant control algorithms, the proposed algorithm uses the hyperbolic tangent function and a projection algorithm to limit the control input within a known upper bound. In addition, radial basis function neural network is used to approximate the unknown continuous nonlinear function that contains the friction model in the mechanical system. The control target of the system is realized; and the asymptotic stability of the closed‐loop system is proved via the Lyapunov direct method. Finally, the numerical simulation results also demonstrate the effectiveness of the designed controller. [ABSTRACT FROM AUTHOR]

This paper is concerned with utilizing higher‐order derivatives of generalized Lyapunov‐like functions to infer asymptotic stability of the switched nonlinear system without requiring the first derivative of the Lyapunov function for each activated subsystem to be negative definite. In contrast to the existing switched systems literature, we allow generalized Lyapunov‐like functions to increase both during the continuous flows and the discrete jumps. Firstly, a set of sufficient conditions for asymptotic stability of switched nonlinear systems are derived under a state‐dependent switching law. Then, all the above‐mentioned conditions are transformed to a set of bilinearly diagonally dominant sum of squares constraints. Bilinearly diagonally dominant sum of squares programming is proposed as a tool to solve the conditions provided. Finally, two examples are introduced to prove the effectiveness of the above method. [ABSTRACT FROM AUTHOR]

This article discusses adaptive preassigned finite-time stability of nonlinear systems with unknown time-varying powers and full-state constraints. By introducing a concept of practical preassigned finite-time stable, constructing finite-time performance functions and nonlinear transformed functions, and integrating high-power and low-power terms into dynamic surface control design, an adaptive state-feedback controller is designed to eliminate the effects of unknown powers and serious unknown parameters in system dynamics, and decrease the computational burden in previous design methods. It is proved that all the signals of the closed-loop system are bounded, asymmetric time-varying full-state constraints are not transgressed, and systemstates converge to a prescribed arbitrarily small region around zero after a preassigned settling time. Two simulation examples show the effectiveness and advantages of this control scheme. [ABSTRACT FROM AUTHOR]

This article studies the issue of command filter-based adaptive fault-tolerant control for a class of nonlinear systems subject to unknown control directions and disturbance. First, the neural network is employed to deal with the nonlinear functions, and the explosion of the complexity problem is handled by the command filter approach. Second, the bound estimation method and the Nussbaum function are utilized to compensate for the influence of the actuator faults and the unknown directions, respectively. Finally, the tracking error signals are guaranteed to converge into bounded compact sets around the origin, and all closed-loop signals are bounded. The effectiveness of the proposed method is illustrated by three simulations. [ABSTRACT FROM AUTHOR]

In this article, the distributed consensus tracking problem is investigated for a group of heterogeneous nonlinear multiagent systems (MASs). The dynamic of each follower is subject to multiple time-varying state delays and unknown non-identical control coefficients. Most existing results for MASs with unknown non-identical control coefficients are on the condition that only the specific Nussbaum-type function can be used. This constraint is removed by employing the enhanced Nussbaum functions. Some appropriate Lyapunov-Krasovskii functionals are constructed to compensate the delayed nonlinear functions. By applying the finite-time command filters to backstepping technique, a novel distributed adaptive consensus tracking control law is developed, which is independent of multiple state delays. It is proved that each follower's output can track the leader. Finally, the validness of the proposed control algorithm is illustrated by two simulation examples. [ABSTRACT FROM AUTHOR]

In this article, the global stabilization issue is discussed for a class of stochastic continuous time‐delay nonlinear systems suffered from unknown control directions and disturbance. Instead of designing the adaptive law online, a control gain is invoked to adapt for the formidable scene of merely continuous but nonsmooth caused by the low‐order, and to deal with the negative effects of disturbance and multiple unknown nonlinear functions where both input and state time delays are taken into account. Then, by utilizing the homogenous domination approach, a delay‐independent controller is designed with a sign function to compensate for the negative impact generated from disturbance and maintain the global asymptotic stability of the closed‐loop system. Finally, a stochastic simulation is supplied to show the validity of the control scheme. [ABSTRACT FROM AUTHOR]

In this study, a prescribed performance adaptive fault tolerant tracking control scheme is presented for a class of nonlinear large‐scale systems with time delay interconnection, dead zone input, and actuator fault. The radial basis function neural networks are used to approximate unknown nonlinear functions. Different from the barrier Lyapunov functions used to achieve the symmetrical prescribed performance, a new error transformation is introduced in this study to achieve the desired asymmetrical prescribed performance. In addition, Nussbaum function is introduced to solve the difficulties caused by dead zone input and actuator fault. Based on the appropriate Lyapunov–Krasovskii functions, the effect of time delay interconnection could be compensated. By using backstepping procedures, an adaptive fault tolerant tracking control approach is developed for the considered large‐scale systems, and the stability of the closed‐loop systems is analyzed by Lyapunov theory. Meanwhile, the prescribed performance of the tracking error could be guaranteed. Finally, the effectiveness of the proposed control approach is illustrated by two simulation examples. [ABSTRACT FROM AUTHOR]

In this article, a robust model predictive control strategy based on sum‐of‐squares (SOS‐RMPC) is proposed for hypersonic vehicle with state‐dependent input constraints and uncertain parameters. Based on feedback linearization model of hypersonic vehicle, the polytopic linear parameter varying error model with bounded disturbance is established for reference trajectory tracking. The real limits of the actual control inputs are transformed into the constraints of the virtual inputs equivalently with the state‐dependent nonlinear functions. Further, the multivariate linear fitting is used to approximate the state‐dependent input constraints into polynomials. A weighted composite virtual control is formulated as the combination of unconstrained control and auxiliary control. SOS technique is introduced to cast the polynomial constraints into the convex matrix SOS conditions via linear matrix inequality. The virtual control law can be obtained by solving a SOS‐RMPC convex optimization with infinite horizon. The invariant set is designed for the undisturbed error states and the norm‐bounding theory is applied to ensure that the predictive error states with disturbance can remain in the same invariant set. The real control law is obtained by inverse control. The simulation verifies the performance of the designed controller. [ABSTRACT FROM AUTHOR]

The topic of adaptive event‐triggered control for multi‐input‐multi‐output nonlinear systems with asymmetric state constraints is considered in this article. First, by introducing unified barrier functions method, the initial system is transformed to a non‐constraints system, which brings that the requirement of feasibility conditions could be eliminated and the constraint functions could be relaxed effectively. Then, an adaptive tracking controller is designed by combining some excellent technology, where command filter is utilized to overcome the explosion of complexity, neural network is introduced to approximate unknown nonlinear function, and event‐triggered mechanism is proposed to save communication resources. The designed control scheme can make the outputs of the system to track the target trajectories within a small bounded error range, all signals in the closed‐loop system are bounded, and all states do not escape the state constraints. Finally, practical and comparative examples are given to verify the effectiveness of the method. [ABSTRACT FROM AUTHOR]

This article investigates the consensus problem of one‐sided Lipschitz nonlinear multi‐agent systems (MASs) with distributed asynchronous impulsive control protocol. Based on the theory of discontinuous Lyapunov stability and impulsive differential equation, some new sufficient criteria about asynchronous impulsive control are derived to guarantee the consensus of one‐sided Lipschitz nonlinear MASs. Different from the existing methods of synchronous impulsive control, the asynchronous impulsive control does not need all agents are controlled simultaneously at one impulsive instant. Compared with the traditional Lipschitz condition, the one‐sided Lipschitz nonlinear function considered in this article can obtain a wider nonlinear range. Finally, some numerical simulation examples are given to verify the correctness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

This article proposes an approach for the estimation of states, actuator, and sensor faults in nonlinear systems represented by a polytopic linear parameter varying (LPV) system with inexact scheduling parameters. In the traditional LPV approaches, the scheduling variables are considered to be perfectly known. However, in practical applications, their measurement may contain precision and calibration errors or noise that can affect the performance of the diagnostic systems. Therefore, this work proposes the design of a proportional multiple‐integral sliding mode observer for fault diagnosis (FD) that copes with LPV systems with inexact scheduling parameters. Due to the introduction of some nonlinear functions, the proposed observer is a nonlinear parameter varying system for which stability and robustness performance are formulated using the Lyapunov technique and a H∞ performance criterion. It is shown that the design conditions boil down to a set of linear matrix inequalities whose solution allows computing the observer gain matrix along with the tunable parameters of the nonlinear functions. Results obtained using the simulator of an octocopter‐type unmanned aerial vehicle are used to demonstrate the applicability and performance of the proposed FD scheme. [ABSTRACT FROM AUTHOR]

This article investigates the fixed‐time consensus tracking control problem for multiagent systems composed of uncertain l‐link robotic manipulators with position and velocity constraints. Fuzzy logic systems are employed to model the uncertain dynamic of the robotic manipulators. In order to cope with the asymmetric yet time‐varying constraints, a nonlinear transformation function is introduced. With the help of the nonlinear transformation function, the original constrained manipulator systems are converted into the equivalent systems without constraint. As long as the boundedness of the state variables in the transformed systems is ensured, the constraint conditions of the original systems are not violated. Then, a fixed‐time adaptive fuzzy control scheme is developed. Under the proposed control method, the consensus tracking error can converge into a small neighborhood of origin in fixed‐time, and all the signals in the closed‐loop systems are bounded. Meanwhile, the motion constraints are not violated all the time. Specially, in view of the property of nonlinear transformation function, it is not necessary to change the control structure when the systems are subjected to no state constraint. Finally, a simulation is presented to illustrate the feasibility and effectiveness of implementing the proposed control algorithms. [ABSTRACT FROM AUTHOR]

This article is concerned with the issue of adaptive prescribed performance tracking control for a class of pure‐feedback nonlinear systems with full‐state time‐varying constraints. By using the hyperbolic tangent function as nonlinear mapping technique, the obstacle of the full‐state constraints is resolved. A novel adaptive control method is proposed by prescribed performance control with command filtered backstepping design, and the insufficient of the dynamic surface method is conquered by the error compensation mechanism. Radial basis function neural networks are utilized to approximate the unknown nonlinear functions. Based on the Lyapunov stability theory, it is shown that all signals in the closed‐loop system are semiglobal uniformly ultimately bounded and the output tracking error always converges to the prescribed performance bound. Two simulation examples demonstrate the capability of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This article concentrates upon an adaptive practical preassigned finite‐time fault‐tolerant control problem for a class of time‐delay nonlinear systems in nonstrict‐feedback form with full state constraints (FSCs) and actuator fault. The completely unknown nonlinear functions exist in the system are identified by the neural networks (NNs). It is challenged to investigate finite‐time fault‐tolerant control problem for nonlinear systems while encountering the time‐delays, actuator faults and FSCs simultaneously, which increases the difficulty of design. The Lyapunov–Krasovskii functionals and the hyperbolic tangent functions are utilized to eliminate the effect of time‐varying delays. The actuator fault considered in this article contains the loss of effectiveness and the bias fault, simultaneously. By combining a modified barrier Lyapunov function with finite‐time performance function, the finite‐time fault‐tolerant controller is designed. It is demonstrated that the proposed adaptive controller guarantees that the system states converge to a preassigned zone at a finite‐time and all the signals of the closed‐loop system remain semiglobally practical finite‐time stable. Numerical examples are offered to illustrate the feasibility of the theoretical result. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates the issue of fuzzy‐approximation‐based adaptive exact tracking control for a class of uncertain nonlinear systems with mismatched external disturbances. Due to the existence of unstructured nonlinear functions and unexpected disturbances, most of the current reported results on adaptive control of high‐order nonlinear strict‐feedback systems are semi‐globally bounded. In this paper, a novel backstepping‐based adaptive sliding control scheme is proposed, which makes the tracking error converge to zero in spite of the presence of uncertain nonlinearities and disturbances. In particular, under the framework of adaptive control mechanism, the upper bounds of fuzzy approximation errors and external disturbances are properly estimated. Based on the estimation information, an asymptotic adaptive tracking control strategy is constructed, such that the tracking error will be forced to keep sliding along the origin once the bounds are reached. Therefore, the exact tracking control objective is achieved. Simulation example verifies the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Summary: This article focuses on the problem of adaptive finite‐time neural backstepping control for multi‐input and multi‐output nonlinear systems with time‐varying full‐state constraints and uncertainties. A tan‐type nonlinear mapping function is first proposed to convert the strict‐feedback system into a new pure‐feedback one without constraints. Neural networks are utilized to cope with unknown functions. To improve learning performance, a composite adaptive law is designed using tracking error and approximate error. A finite‐time convergent differentiator is adopted to avoid the problem of "explosion of complexity." By theoretical analysis, all the signals of system are proved to be bounded, the outputs can track the desired signals in a finite time, and full‐state constraints are not transgressed. Finally, comparative simulations are offered to confirm the validity of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Summary: This article is concerned with the polynomial filtering problem for a class of nonlinear stochastic systems governed by the Itô differential equation. The system under investigation involves polynomial nonlinearities, unknown‐but‐bounded disturbances, and state‐ and disturbance‐dependent noises ((x,d)‐dependent noises for short). By expanding the polynomial nonlinear functions in Taylor series around the state estimate, a new polynomial filter design method is developed with hope to reduce the conservatism of the existing results. In virtue of stochastic analysis and inequality technique, sufficient conditions in terms of parameter‐dependent linear matrix inequalities (PDLMIs) are derived to guarantee that the estimation error system is input‐to‐state stable in probability. Moreover, the desired polynomial matrix can be obtained by solving the PDLMIs via the sum‐of‐squares approach. The effectiveness and applicability of the proposed method are illustrated by two numerical examples with one concerning the permanent magnet synchronous motor. [ABSTRACT FROM AUTHOR]

Summary: This article proposes an adaptive iterative learning radial basis function (RBF) scheme to solve the trajectory‐tracking problem for perturbed robot manipulators with unknown iteration varying disturbances and unknown dead‐zone input. It is well known that the presence of the dead zone in actuators and mechatronics devices gives rise to extra difficulty due to the presence of singularity in the input channels. Hence, it is interesting to take this problem into account when synthesizing a controller. This synthesis is made here. In addition, the control design is very simple in the sense that we use, only, the proportional gain. Therefore, the considerable amount noise caused by the sensors for velocity measurements of robot manipulators is avoided. Another advantage of this work is that the unknown disturbances are assumed to be time varying and also varying from iteration to iteration. Thus, the RBF neural network is used to approximate these unknown nonlinear functions. Using the Lyapunov theory, the analysis of the stability of the closed‐loop system is guaranteed when the iteration number tends to infinity. Finally, simulation results on the PUMA 560 arm are provided to illustrate the effectiveness of the proposed method. In order to evaluate the performance of our controller, a comparison of our results with other method is also given. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the problem of adaptive fuzzy asymptotic tracking control for multiple input multiple output nonlinear systems in nonstrict‐feedback form. Full state constraints, input quantization, and unknown control direction are simultaneously considered in the systems. By using the fuzzy logic systems, the unknown nonlinear functions are identified. A modified partition of variables is introduced to handle the difficulty caused by nonstrict‐feedback structure. In each step of the backstepping design, the symmetric barrier Lyapunov functions are designed to avoid the breach of the state constraints, and the issues of overparametrization and unknown control direction are settled via introducing two compensation functions and the property of Nussbaum function, respectively. Furthermore, an adaptive fuzzy asymptotic tracking control strategy is raised. Based on Lyapunov stability analysis, the developed control strategy can effectually ensure that all the system variables are bounded, and the tracking errors asymptotically converge to zero. Eventually, simulation results are supplied to verify the feasibility of the proposed scheme. [ABSTRACT FROM AUTHOR]

Summary: This paper studies the problem of adaptive observer‐based radial basis function neural network tracking control for a class of strict‐feedback stochastic nonlinear systems comprising an unknown input saturation, uncertainties, and unknown disturbances. To handle the issue of a non‐smooth saturation input signal, a smooth function is chosen to approximate the saturation function and the state observer is used to estimate unmeasured states. By the so‐called command filter method in the controller design procedure, the implementation complexity is reduced in the proposed backstepping method. Moreover, a radial basis function neural network is deployed to reconstruct the unknown nonlinear functions. In addition, the gains of all radial basis function neural networks are updated through one updating law leading to a minimal learning parameter which is independent of the number of neural nodes and the order of the system. Comparing with the existing results, the proposed approach can stabilize a constrained stochastic system more effectively and with less computational burden. Finally, a practical example shows the performance of the proposed controller design. [ABSTRACT FROM AUTHOR]

Summary: In this work, we develop a robust adaptive fault‐tolerant tracking control scheme for a class of input‐quantized strict‐feedback nonlinear systems in the presence of error/state constraints and actuation faults. The problem is rather complicated yet challenging if nonparametric uncertainties and unknown quantization parameters as well as time‐varying yet completely undetectable actuation faults are involved in the considered systems. Compared with the most existing approaches in the literature, the proposed control exhibits several attractive advantages: (1) upon using a nonlinear decomposition for quantized input and employing the robust technique for actuation fault, not only the exact knowledge of quantization parameters are not required, but also the actuation fault can be easily compensated since neither fault detection and diagnosis/fault detection and identification nor controller reconfiguration is needed; (2) based on the error/state‐dependent unified nonlinear function, the constraints on tracking error and system states are directly handled and the cases with or without constraints can also be addressed in a unified manner without changing the control structure; and (3) the utilization of unified nonlinear function‐based dynamic surface control not only avoids the problem of the explosion of complexity in traditional backstepping design, but also bypasses the demanding feasibility conditions of virtual controllers. Furthermore, by using the Lyapunov analysis, it is ensured that all signals in the closed‐loop systems are uniformly ultimately bounded. The effectiveness of the developed control algorithm is confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]