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In this article, the tracking control problem is addressed for uncertain nonlinear systems with actuator saturation and unmeasurable unmodeled dynamics. Being different from the existing performance function control results, to constraint the output tracking error within a predefined boundary in finite time, an improved performance function, that is, finite‐time performance function, is introduced. The design difficulties of asymmetric input saturation and unmodeled dynamics are solved simultaneously for the first time by applying a smooth non‐affine function and a measurable dynamic signal. Furthermore, an adaptive fuzzy control scheme is established via command filtering, which not only guarantees the semi‐global boundedness of all the controlled system signals but also makes the output tracking error that can be restrained by the described performance bound within a finite‐time interval. At last, an effective example is supplied to validate the availability of the presented theoretical finding. [ABSTRACT FROM AUTHOR]

In this research, the issue of decentralised adaptive neural finite-time prescribed performance control is discussed for nonstrict-feedback large-scale nonlinear interconnected systems subject to dead zones input and unknown control direction. The obstacle of 'explosion of complex' occurred in conventional backstepping design can be surmounted by adopting the command filter technique and nonlinearities are approximated by introducing an adaptive neural control approach. To handle the obstacles due to unknown directions and unknown interconnections, Nussbaum-type functions and two smooth functions are used and designed. Meanwhile, error compensation signals are introduced to deal with the problem associated with the dynamic surface method. To constraint the output tracking error within a predefined boundary in finite time, an improved performance function, i.e. finite-time performance function is introduced. Different from existing control results, the developed control methodology does not require any information on the boundedness of dead-zone parameters. It is further proved that the constructed controller not only assures the semi-global boundedness of all the controlled system signals, but also makes the output tracking errors reach within a predefined small set. Finally, both numerical and practical examples are supplied to further validate the effectiveness of the presented theoretic result. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fault‐tolerant fixed‐time control problem is considered via command‐filter technique for stochastic nonlinear systems with sensor fault and actuator hysteresis. With the application of command‐filtering technique, a novel command‐filter compensate mechanism is designed, which implies that the improved control scheme not only eliminates "the explosion of complexity" but also realizes the compensate signal is bounded within fixed‐time interval. The unavailability of state variables caused by sensor fault is solved by applying parameter separation and regrouping approach. Meanwhile, an adaptive auxiliary signal is designed to cope with the backlash‐like hysteresis phenomenon, which can avoid singularity, reduce chattering, and facilitate controller design. Combining backstepping technique and Lyapunov stability theorem, an adaptive fault‐tolerant control approach is developed, which can guarantee all closed‐loop signals remain semi‐globally practical fixed‐time stable (SGPFS) in probability. The validity of the proposed strategy is illustrated by simulation examples. [ABSTRACT FROM AUTHOR]

In this article, under the circumstance of dead zones input and unknown control direction, the adaptive practical fixed‐time control strategy is presented for a general class of multi‐input and multi‐output (MIMO) nonlinear systems. The inherent explosion of computational complexity difficulty is eliminated by adopting a command filter technique and the universal approximation properties of radial basis function neural networks (RBFNNs) are applied to model the unknown nonlinear functions. The difficulties of the dynamic surface method and unknown directions can be handled by invoking error compensation mechanism and Nussbaum‐type functions, respectively. The uniqueness of the presented control scheme is that the tracking system can achieve the fixed‐time stability without relying on the boundedness of dead‐zone parameters. The fixed‐time convergence of the output tracking error and the semiglobally fixed‐time stable of closed‐loop system are assured via the developed adaptive fixed‐time command filtered controller. Finally, a practical example is supplied to further validate the availability of the presented theoretic result. [ABSTRACT FROM AUTHOR]

This paper addresses the output tracking problem of adaptive fixed-time fault-tolerant control for a class of nonlinear systems. In particular, we focus on two types of actuator faults: lock-in-place and loss of effectiveness. Specifically, a robust adaptive fault-tolerant controller is designed to compensate for the effect of actuator faults. By applying the classical backstepping design algorithm and fixed-time control theory, an adaptive fixed-time controller is developed, ensuring that the tracking error converges into a small neighbourhood around the origin within a fixed time where the convergence time is independent of initial conditions. Theoretical analysis and simulation outcomes prove that the closed-loop system is fixed-time stable and all signals are bounded by choosing the parameters appropriately. The effectiveness and feasibility of the presented control scheme are verified through the simulation results. [ABSTRACT FROM AUTHOR]

This article addresses the tracking control problem of uncertain fractional-order nonlinear systems in the presence of input quantization and external disturbance. An adaptive backstepping scheme is proposed by combining with radial basis function (RBF) neural networks (NNs), fractional-order disturbance observer (FODO), and backstepping method. The RBF NNs are used to approximate the unknown nonlinearities of fractional-order systems. The FODO is designed to compensate for disturbance and uncertain parameters. The hysteresis quantizer is used to avoid chattering that possibly appears in actual application. The stability of the proposed controller is proved by fractional-order Lyapunov method. In addition, all the signals in the closed-loop system are bounded. The effectiveness of the proposed method is confirmed by the simulation results. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive fixed-time output feedback formation control problem is investigated for nonlinear multi-agent systems with a nonstrict-feedback structure. In the controller design procedure, the neural network state observer is designed to estimate the unmeasurable state variables. Dynamic surface control (DSC) technique is applied to avoid the repeated differentiation for the virtual control signals. The dynamic surface compensation signals can realise the practical fixed-time bounded. Utilising the classified discussion method, the difficulty of controller design caused by the existence of observer error term is addressed. The technique of transformation of the index set is employed to cope with the related variables of the neighbour states, which simplifies the controller design. Under the presented control mechanism, all closed-loop signals remain bound for a fixed period of time, the formation control performance target between all followers and leader can be achieved. And the formation errors and state observers errors are both bounded such that can converge to a little domain around zero. Simulation results are provided to test the availability of the presented strategy. [ABSTRACT FROM AUTHOR]

In this article, the finite-time adaptive fuzzy output-feedback control strategy is presented for a class of multi-input and multi-output (MIMO) nonlinear systems with multiple actuator constraints and unmeasured states. Fuzzy logic systems and a fuzzy adaptive state observer are adopted to estimate the nonlinear uncertainties and the unmeasured states, respectively. The inherent 'explosion of complexity' problem is eliminated by adopting command filter technology and the corresponding error compensation mechanism is exploited to alleviate the influence of the errors generated by command filters. It is further proved that all the signals can be fast finite-time bounded in the closed-loop systems based on the Lyapunov stability theory. Besides, the observer and tracking errors can reach a small region around the origin in fast finite time. Finally, the practicability of the presented theoretic result can be demonstrated through the numerical and practical examples. [ABSTRACT FROM AUTHOR]

In this article, the problem of adaptive fixed‐time tracking control is addressed for non‐triangular structural stochastic switching nonlinear systems. Fuzzy logic systems are used to compensate for unknown nonlinearities, and in the meantime, to avoid the algebraic loop problem, which exists in traditional backstepping controller design processes for non‐triangular structural nonlinear systems. The unknown control gain problem is addressed by the construction of proper Lyapunov function candidates. By employing Lyapunov stability theorem, all the closed‐loop signals can be ensured to be semi‐globally practical fixed‐time stable, the output signal can track the desired signal, and the tracking error can converge to a small zone around the origin. The effectiveness of the developed control approach is verified through simulation results. [ABSTRACT FROM AUTHOR]

In this article, the problem of decentralized fuzzy adaptive control is addressed for a class of stochastic interconnected nonlinear large-scale systems including saturation and unknown disturbance. Fuzzy logic systems (FLSs) are used to estimate packaged nonlinear uncertainties. The command filter technique is presented to eliminate the "explosion of complexity" obstacle associated with the backstepping procedures and the corresponding error compensation mechanism is constructed to alleviate the effect of the errors generated by command filters. The influence of input saturation is compensated by introducing an auxiliary system. Meanwhile, an improved adaptive fuzzy decentralized controller is developed and it is able to minimize calculation time since there is no need for repeated differentiation for the virtual control laws. The presented control scheme not only assures the semi-global boundedness of all the signals in the closed-loop system, but also makes the output tracking errors reach a small neighborhood around the origin. Finally, both numerical and practical examples are provided to illustrate the efficiency and effectiveness of our theoretic result. • A novel adaptive fuzzy decentralized controller is proposed for a class of stochastic interconnected nonlinear large-scale systems. • An auxiliary system is constructed to resolve the difficulty caused by input saturation. • The difficulty due to the interconnection of subsystems is eliminated by introducing two smooth functions. • The proposed adaptive fuzzy command filtered control scheme can solve the explosion of complexity problem inherent in the conventional backstepping control design. [ABSTRACT FROM AUTHOR]

Summary: A new fault‐tolerant approach to input saturation and sensor faults is presented for flexible‐joint robotic stochastic nonlinear systems with finite‐time convergence performance. More precisely, a new command filter is designed and embedded into the backstepping framework, which greatly reduces the amount of calculation. By using the estimation ability of fuzzy logic system and less adjustable parameters, the problems of sensor faults and unknown functions are solved, which facilitates the design of controllers. A smooth function and mean‐value theorem are used to deal with the difficulty associated with system signals. A novel simpler controller is developed to ensure that the trajectory tracking error converges to a sufficiently small neighborhood around the origin within finite time, while there are random noises. Finally, the effectiveness of the presented scheme is verified by simulation results. [ABSTRACT FROM AUTHOR]

This paper solves the finite-time tracking problem of a class of high-order nonlinear systems under event-triggered input. Unlike existing event-triggered frameworks based on signal transmission channels from the sensor to the controller or from the controller to the actuator, these developed trigger mechanisms only compare the difference between the signal to be transmitted and the holding signal. By introducing internal trigger conditions and external trigger conditions, a novel error-to-actuator based event-triggered framework is proposed. It further considers the response of the trigger mechanism to system control performance such that the tracking performance of the system can be guaranteed while reducing the number of signal transmissions. In addition, filter-based techniques (such as the dynamic surface control method), for the first time, are utilised to eliminate some strong constraints that exist in the literature for most high-order nonlinear systems. The effectiveness of the proposed approach is evaluated on simulation examples including comparative studies and a practical example. [ABSTRACT FROM AUTHOR]

An adaptive finite-time approach to the feedback control of stochastic nonlinear systems is presented. The fuzzy logic system (FLS) and a state observer are used to estimate the uncertain function and unmeasured state of the controlled system, respectively. A dynamic surface control (DSC) scheme is employed to deal with the "computational explosion" problem, which is inherent in traditional backstepping methods since the repetitive calculation of the derivatives of virtual control signals is avoided. A new output feedback controller is developed to guarantee that all the signals of the controlled system are bounded within a finite time range and the tracking deviation can converge to an arbitrarily small residual set within finite time. Simulations confirm the analytical and theoretical results of the presented algorithm. • The dynamic surface method solves the problem of "computational explosion". • A fuzzy state observer is constructed to estimate the unmeasured state. • A new output feedback controller is designed. [ABSTRACT FROM AUTHOR]

Summary: This article focuses on the finite‐time adaptive fuzzy control problem based on command filtering for stochastic nonlinear systems subject to input quantization. Fuzzy logic systems are employed to estimate unknown nonlinearities. In the control design, the hysteretic quantized input is decomposed into two bounded nonlinear functions, which solves the chattering problem. Meanwhile, an adaptive fuzzy controller is presented by the combination of command filter technique and backstepping control, which eliminates the computational complexity existing in traditional backstepping design. Under the proposed adaptive mechanism, all the closed‐loop signals remain bounded while the desired system performance can be realized within finite time. The main significance of this work is that (1) the filtering error can be solved on the basis of the designed compensating signals; (2) the requirement of adaptive parameters is decreased to only one, which simplifies the controller design process and may improve the control performance. Two simulation examples are used to validity of the developed scheme. [ABSTRACT FROM AUTHOR]

This article presents a fuzzy finite-time command filtering output feedback control method for a class of nonlinear systems. A fast convergent output feedback control algorithm based on backstepping finite-time command filtering is developed. Fuzzy logic system is used to estimate uncertain functions in nonlinear systems. A fuzzy state observer is designed to measure the unknown state. The developed finite-time command filtering feedback control method overcomes well the computational complexity problem due to the calculation of the derivatives of virtual control signals. A compensation mechanism is also introduced to compensate for the error caused by the filter. The proposed method ensures not only that all signals in the closed-loop system are finite-time bound, but also that the tracking error converges to a small neighborhood around the origin. The effectiveness of the proposed method is demonstrated in the simulation results. [ABSTRACT FROM AUTHOR]

Summary: An adaptive finite‐time decentralized control algorithm for a class of large‐scale stochastic nonlinear systems is presented. The fuzzy logic system is used to estimate uncertain nonlinearities. One advantage of the developed scheme is that each subsystem only needs to update one adaptive parameter, which alleviates the burden of online estimation. The dynamic surface control method is employed to reduce the "complexity explosion" caused by the repetitive derivation of the intermediate variable function in the backstepping control scheme. A new decentralized controller is designed so that all signals of the controlled system are bounded and the tracking error converges to a small residual set around the origin within a finite time. The simulation results of a numerical example illustrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

This paper addresses the finite-time tracking control problem for a class of nonaffine nonlinear systems with unknown dead zones using an adaptive fuzzy control scheme. The unknown nonlinear functions of the system are approximated by the fuzzy logic systems and a finite-time stability theorem is used to construct the control signal. The novelty of the proposed control method is that the tracking system can reach the stable equilibrium within a finite period of time without the knowledge of the boundaries of the dead zone parameters. The simulation results show that the system is semi-global practical finite-time stable and the tracking deviation converges to a small neighborhood of zero in a finite period of time. [ABSTRACT FROM AUTHOR]

This paper addresses the trajectory tracking control problem of a class of nonstrict-feedback nonlinear systems with the actuator faults. The functional relationship in the affine form between the nonlinear functions with whole state and error variables is established by using the structure consistency of intermediate control signals and the variable-partition technique. The fuzzy control and adaptive backstepping schemes are applied to construct an improved fault-tolerant controller without requiring the specific knowledge of control gains and actuator faults, including both stuck constant value and loss of effectiveness. The proposed fault-tolerant controller ensures that all signals in the closed-loop system are semiglobally practically finite-time stable and the tracking error remains in a small neighborhood of the origin after a finite period of time. The developed control method is verified through two numerical examples. [ABSTRACT FROM AUTHOR]

This paper presents an adaptive neural control approach for nonstrict-feedback nonlinear systems in presence of unmodeled dynamics, unknown control directions and input dead-zone nonlinearity. To handle the difficulty due to uncertain control directions, Nussbaum gain functions are applied. Based on the structural characteristic of radial basis function neural networks, a backstepping-based adaptive neural control algorithm is developed. The main contributions of this paper lie in the fact that a backstepping-based neural control algorithm is developed for nonstrict-feedback nonlinear systems with unmodeled dynamics, unknown control directions and actuator dead-zone, and the total number of adaptive laws is not greater than the order of control system. As a beneficial result, the controller is much easier to be implemented in practice with less computational burden. A simulation example is given to reveal the viability of the presented approach. It is demonstrated by both theoretical analysis and simulation study that the presented control strategy ensures the semiglobally uniform ultimate boundedness of all closed-loop system signals. [ABSTRACT FROM AUTHOR]

This paper is concerned with the trajectory tracking control problem of a class of nonaffine stochastic nonlinear switched systems with the nonlower triangular form under arbitrary switching. Fuzzy systems are employed to tackle the problem from packaged unknown nonlinearities, and the backstepping and robust adaptive control techniques are applied to design the controller by adopting the structural characteristics of fuzzy systems and the common Lyapunov function approach. By using Lyapunov stability theory, the semiglobally uniformly ultimate boundness in the fourth-moment of all closed-loop signals is guaranteed, and the system output is ensured to converge to a small neighborhood of the given trajectory. The main advantages of this paper lie in the fact that both the completely nonaffine form and nonlower triangular structure are taken into account for the controlled systems, and the increasing property of whole state functions is removed by using the structural characteristics of fuzzy systems. The developed control method is verified through a numerical example. [ABSTRACT FROM AUTHOR]

The state-feedback decentralized stabilization problem is considered for interconnected nonlinear systems in the presence of unmodeled dynamics. The functional relationship in affine form between the strong interconnected functions and error signals is established, which makes backstepping-based fuzzy control successfully generalized to strong interconnected nonlinear systems. By combining adaptive control with both backstepping design and the approximation property of fuzzy systems, an adaptive decentralized control algorithm is developed. It is demonstrated by both theoretical analysis and simulation study that the proposed control strategy ensures semiglobally uniformly ultimately bounded of all signals within the closed-loop systems. [ABSTRACT FROM PUBLISHER]

This paper is concerned with the observer-based fuzzy output-feedback control for stochastic nonlinear multiple time-delay systems. On the basis of the consistent form of virtual input signals and increasing characteristics of the system upper bound functions, a variable splitting technique is employed to surmount the difficulty occurred in the nonlower-triangular form. In the controller design procedure, a state observer is first designed, and then an adaptive fuzzy output-feedback control method is presented by combining backstepping design together with fuzzy systems’ universal approximation capability. The proposed adaptive controller guarantees the semi-global boundedness of closed-loop system trajectories in terms of fourth-moment. Two simulation examples are displayed to demonstrate the feasibility of the suggested controller. [ABSTRACT FROM PUBLISHER]

Adaptive neural intelligent control is investigated for a class of pure-feedback nonlinear time-delay systems with unmodeled dynamics in nonlower-triangular form, which views the lower-triangular structure as a special structure. A variable partition technique is applied to surmount the difficulty in the nonlinear functions of whole state variables. By utilizing the backstepping recursive design approach and the universal approximation capability of neural networks, an adaptive neural controller is systemically designed. Then, based on the utilization of Lyapunov–Krasovskii functionals, the semiglobally uniform boundedness of all closed-loop signals is guaranteed. Finally, the suggested control method is verified through a numerical example. The main advantage of this paper is that an intelligent control method is developed for pure-feedback nonlinear systems with state time delay, unmodeled dynamics and nonlower triangular form. Further developments will focus on how to deal with the problem of output feedback control of pure-feedback nonlinear time-delay systems with unmodeled dynamics and nonlower-triangular structure. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes an output tracking control via virtual reference model for a class of nonlinear discrete-time systems with time-varying delay and disturbance. First, a Takagi–Sugeno (T–S) fuzzy model represents the discrete-time nonlinear system with time-varying delay. Second, a fuzzy observer design estimates immeasurable state. Third, a virtual desired variable (VDV) based tracking controller design guarantees H ∞ control performance for the overall system. Using Lyapunov’s stability analysis, we obtain sufficient conditions for stability of estimation, control, and robustness. The advantages are as follows: (i) allow unknown time-varying delay; (ii) ensure robust output tracking; (iii) provide relaxed conditions via a three-steps procedure to find observer and controller gain. To verify the theoretical derivation, we carry out numerical simulations on a stirred tank reactor system as an example. Satisfactory results validate the claims. [Copyright &y& Elsevier]

In this work, a novel hybrid control strategy is proposed for robust trajectory tracking control of robotic systems. The main interest of using hybrid design is to reduce the controller gains so as to reduce control efforts from the single model certainty equivalence principle- based adaptive controllers. For this purpose, we allow the parameter estimate of conventional adaptive control design to be switched into a model that best approximates the plant among a finite set of models. First, we uniformly divide the compact set of unknown parameters into a finite number of smaller compact subsets. Then we construct a finite set of candidate controller for each of these smaller compact subsets. The derivative of the Lyapunov function candidate is employed to identify a controller that closely approximates the plant at each instant of time. The idea of introducing hybrid approach in adaptive control framework is to achieve good transient tracking performance with smaller values of controller gains in the presence of large-scale parametric uncertainties. The proposed method is implemented and evaluated on two 3 degree-of-freedom Phantom Premimum™ 1.5 telerobotic systems to demonstrate the effectiveness of the theoretical development. [ABSTRACT FROM AUTHOR]

Abstract: The problem of model-based stabilization of a nonlinear system based on its approximate discrete-time model is addressed, under the assumption that both the feedforward and the feedback paths are subject to network-induced constraints. These constraints include irregularity of the transfer intervals, time-varying communication delays, and the possibility of packet losses. A communication protocol that copes with these constraints is proposed. A “Stability+performance recovery” result for the nonlinear model-based networked control system (NCS) is formulated and proven.Simulation results presented confirm that the proposed method improves the maximum allowable transfer interval. [Copyright &y& Elsevier]

In this paper, a novel constraint-following control for uncertain robot manipulators that is inspired by analytical dynamics is developed. The motion can be regarded as external constraints of the system. However, it is not easy to obtain explicit equations for dynamic modeling of constrained systems. For a multibody system subject to motion constraints, it is a common practice to introduce Lagrange multipliers, but using these to obtain explicit dynamical equations is a very difficult task. In order to obtain such equations more simply, motion constraints are handled here using the Udwadia-Kalaba equation(UKE). Then, considering real-life robot manipulators are usually uncertain(but bounded), by using continuous controllers compensate for the uncertainties. No linearizations/approximations of the robot manipulators systems are made throughout, and the tracking errors are bounds. A redundant manipulator of the SCARA type as the example to illustrates the methodology. Numerical results are demonstrates the simplicity and ease of implementation of the methodology. [ABSTRACT FROM AUTHOR]

This paper is concerned with the tracking control problem of a class of non-strict-feedback nonlinear systems with unmodeled dynamics and time-delay. In the backstepping procedure, a dynamic signal is designed to handle the unmodeled dynamics and the Lyapunov–Krasovskii functions are applied to compensate for the effect of time delay. Meanwhile, a neural network-based approximator is used to approximate the unknown nonlinear functions in the system. It is proved by the theoretical analysis that the presented controller guarantees the semi-global boundedness of all signals in the closed-loop systems, and the output tracking error eventually converges to a small area around zero. Simulation results are presented to illustrate the validity of the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract This paper focuses on the problem of adaptive funnel control for strict-feedback nonlinear systems with unmodeled dynamics. To present a control scheme with prescribed performance bounds on tracking errors, an improved funnel error transformation is introduced and merged into the controller design. Fuzzy logic systems are employed to handle uncertain nonlinear functions, an adaptive fuzzy funnel controller is constructed via backstepping. It is proven that the presented controller ensures that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded and the tracking error evolves within a pre-specified performance funnel. The developed control method is verified through one numerical example. [ABSTRACT FROM AUTHOR]

In this paper, an adaptive decentralized fuzzy control scheme is presented for a class of multiple-input and multiple-output (MIMO) nonlinear interconnected systems with unmodeled dynamics and dead zones. In the controller design procedure, fuzzy logic systems are used to approximate the unknown nonlinear functions and then an adaptive fuzzy controller is developed by combining adaptive technique with backstepping. The proposed control scheme can guarantee that all signals in the closed-loop system are semi-globally uniformly ultimately bounded in mean square. Simulation results are provided to illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper addresses the tracking control problem of a class of high-order uncertain nonlinear systems under time-varying asymmetric output constraints. Most relevant results in the literature have two main restrictions: R1) some constraints need to be imposed on powers and growth conditions have to be established for the nonlinear functions of the system; R2) nonlinear bounding functions must be derived based on repeated derivations of virtual control variables during the design process. By integrating an improved technique of adding a power integrator with a dynamic surface control (DSC) method, we develop a systematic tracking control scheme that eliminates both of the above restrictions. Moreover, with an improved time-varying nonlinear transformed function introduced for high-order systems, the proposed scheme can be regarded as a unified tool in the sense that it works no matter whether the constraint is symmetric, asymmetric, or even without a constraint. The above results are also extended to systems with uncertain gain functions, and the proposed scheme estimates only one adaptive parameter. The simulation results of two deterministic practical applications show that the proposed control scheme is effective not only for high-order systems, but also for high-order-free systems. [ABSTRACT FROM AUTHOR]