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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 addresses the problem of adaptive tracking control for stochastic nonlinear systems with asymmetric full state constraints. Different from the traditional log‐type or tan‐type barrier Lyapunov functions (BLFs), a new asymmetric BLF is proposed in this article. Then, a state feedback controller is constructed with backstepping method so that all signals of the closed‐system are bounded and the asymmetric state constraint is well kept all the time. Without changing the structure of the controller, the design and the analysis for constrained and unconstrained systems are unified. Finally, the effectiveness of proposed control strategy has been demonstrated by simulations of numerical example and the single‐link robot arm model. [ABSTRACT FROM AUTHOR]

In this article, the event‐triggered‐based adaptive finite‐time secure control problem is considered for nonlinear cyber‐physical systems (CPSs) in the presence of unknown sensor and actuator deception attacks. Due to the existence of unknown deception attacks, the system states are unavailable such that the conventional backstepping cannot be applicable. To solve this problem, a novel coordinate transformation is introduced based on the compromised system states. Then the adaptive controller combined with the triggering mechanism is designed by using adding a power integrator technique. Besides, based on the finite‐time stability theorem, an adaptive switching law is proposed to regulate the dynamic controller parameter such that the unknown deception attacks can be effectively compensated. It is shown that the finite‐time stability can be guaranteed for the nonlinear CPSs and Zeno behavior can be avoided. Finally, a simulation example is provided to show the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This article investigates the nonfragile guaranteed cost (GC) control problem of discrete-time impulsive switched Takagi–Sugeno (T–S) fuzzy systems with input quantization and asynchronous switching. The model-dependent dynamic quantizers are applied to obtain the quantized input signal. To deeply study the GC performance analysis and GC control problems in the presence of quantization, asynchronous switching, and impulses, a novel piecewise cost function containing the quantized input instead of normal input is applied in this article. By using the mode-dependent average dwell time approach and introducing a class of Lyapunov-like functions allowing to increase during the asynchronous period, new sufficient conditions are established to guarantee the asymptotical stability with the GC performance index for the impulsive switched T–S fuzzy systems with quantized control input and asynchronous switching. Then, new design conditions about the nonfragile GC controllers and dynamic quantizers of impulsive switched T–S fuzzy systems are obtained in the form of linear matrix inequalities. Finally, a numerical example and a practical example are provided. [ABSTRACT FROM AUTHOR]

This article studies the output regulation problem (ORP) for nonlinear systems based on prescribed performance control (PPC). The items with the partial derivative of the virtual controller are combined together by using backstepping, and then the fuzzy logic systems (FLSs) are used to approximate these combined items, so that the designed virtual controller does not have the partial derivative of the previous virtual controllers. Therefore, this method not only reduces the calculation burden in the backstepping method, but also avoids the disadvantages of dynamic surface control (DSC). Finally, a function $\Theta $ is constructed such that the overall performance (dynamic performance and steady-state performance) of the tracking error (OPTE) is constrained by PP functions. The proposed control algorithm ensures that all the signals are semi-globally uniformly ultimately bounded (SGUUB), and the tracking error achieves the PPC. Simulation examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we extend the adaptive tracking control to more general nonlinear systems with multiple uncertainties, including output constraint, input delay, unknown parameter, and external disturbances for the first time. Without any growth assumptions, the adaptive backstepping technique is combined with the parameter separation technique to solve the parametric nonlinearities while the related results need to apply restrictive assumptions or use an approximation-based scheme to deal with them. To alleviate the serious uncertainties caused by output constraint and input delay, the barrier Lyapunov function (BLF) and the Pade approximation method are employed in a unified framework when the control coefficient is known. Under the case of the unknown control coefficient, the Nussbaum gain technique is further combined to compensate it. Then, under both cases, universal adaptive state-feedback control strategies merged with rigorous stability analysis are proposed, respectively, which guarantees all the signals are uniformly ultimately bounded. In addition, the reference signal tracks the system output into a compact set of the origin and the constraint of output is not violated. Finally, the proposed controllers are applied to an inverted pendulum system, which demonstrates the designed controller is effective. [ABSTRACT FROM AUTHOR]

This work addresses the nonfragile $H_{\infty }$ controller design problem for a class of discrete-time uncertain nonlinear systems. The norm-bounded uncertainty is contained in the nonlinear plant, which is described by the well-known Takagi–Sugeno (T–S) fuzzy model. The controller gain perturbation is also considered. When the input signal is transmitted from the controller to the system through the digital communication channels, it will be quantized by a static quantizer. The main attention is to design the nonfragile $H_{\infty }$ state-feedback controller for the closed-loop quantized uncertain T–S fuzzy system. By introducing some auxiliary scalars and the fuzzy basis-dependent Lyapunov function approach, sufficient conditions are established in the form of linear matrix inequalities (LMIs). The construction for the nonfragile $H_{\infty }$ controller can be completed by solving these LMIs. In the end, the applicability and effectiveness of the proposed method have been 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 article, the global adaptive fault-tolerant control is considered for a class of uncertain nonlinear systems with sensors, actuator faults, and disturbance. Different from the previous results, there are no a priori bounds of the sensor sensitivity, actuation effectiveness, and disturbance. A switching-type adaptive controller is designed where the controller parameter is tuned online by the proposed switching mechanism. It has also been proven that global stability can be achieved under the designed controller. Finally, a simulation example is provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This article focus on the finite‐time control for a class of stochastic continuous nonlinear systems suffered from unknown control coefficients and unmeasured stochastic inverse dynamics. Based on the modified homogeneous domination and adding a power integrator approach, the finite‐time controller is constructed to assure the global finite‐time stability in probability of stochastic continuous nonlinear systems, in which the negative effects generated by unknown control coefficients are dominated by a control gain. In addition, the use of finite‐time stochastic input‐to‐state stability enables us to produce the theoretical analysis of the finite‐time stability of the closed‐loop system. Finally, a simulation example is supplied to show the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This article considers the cooperative output regulation problem of nonlinear output feedback systems under the communication network modeled by the proximity graph, which is time varying and state dependent. Under the relaxed assumption that the proximity graph is initially connected, based on an improved potential function, we first propose a distributed connectivity-preserving output feedback control law with a linear internal model and distributed observer, which is robust to uncertain parameter and external disturbances in heterogeneous subsystems with strong nonlinearity. Successively, an adaptive design with parameter update law is derived to further tolerate an uncertain parameter in the exosystem, which generates the leader’s trajectory and external disturbances. [ABSTRACT FROM AUTHOR]

The adaptive finite‐time event‐triggered quantized control for the nonlinear systems considering uncertain parameters and external disturbances is investigated in this article. First, for the parametric nonlinear systems with external disturbances, an adaptive finite‐time event‐triggered control scheme with input quantization is proposed. The designed controller can ensure the semiglobal finite‐time stability of the closed‐loop system. Then, to deal with the global finite‐time control problem for the parametric nonlinear systems, a novel adaptive quantized event‐triggered control scheme is constructed. Finally, two simulation examples are utilized to illustrate the effectiveness of the adaptive event‐triggered control schemes. [ABSTRACT FROM AUTHOR]

This article addresses the H∞ filtering problem for a class of discrete-time nonlinear switched systems. Every subsystem of the considered nonlinear-switched systems is represented by the Takagi–Sugeno fuzzy systems with local nonlinear models. Signal quantization and filter parameter perturbation are considered simultaneously in the H∞ filter design. Both the measurement output signal and the performance output signal are quantized by two static quantizers, respectively, before they are transmitted. Based on the average dwell time approach, sufficient conditions for desired H∞ filters are established in the form of linear matrix inequalities. Under the obtained conditions, the filtering error system is exponentially stable and can achieve a weighted H∞ performance index. Finally, a numerical example and a practical example are provided to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Summary: In this article, a novel output‐feedback control scheme is proposed for nonlinear systems involving unknown input saturation, control gain, and unmeasurable disturbances under the condition of an output constraint. First, a proper barrier Lyapunov function and an opportune backstepping are used to alleviate the control burdens caused by output constraint. Then, a novel auxiliary system is introduced with appropriate coordinate transformation, which can create extra freedoms to attenuate the effects brought by input saturation. As a remarkable feature, a composite observer with the estimate of unknown control gain is constructed on the basis of disturbance observer‐based control and state observer control. It can deal with the unmeasurable disturbances and states simultaneously. According to the proposed scheme, it is proven that all the signals in the closed‐loop system are uniformly ultimately bounded, and the tracking error is bounded by the design parameters and saturated input error without the violation of the output constraint. Finally, the effectiveness of the proposed control is verified by two simulation examples. [ABSTRACT FROM AUTHOR]

Summary: In this article, the global finite‐time adaptive control problem is considered for high‐order nonlinear systems in the presence of unknown control coefficients, actuator fault, and external disturbance. Different from the previous results, a tune parameter is introduced to directly compensate the unknown control coefficients rather than the traditional Nussbaum‐gain function. Without requiring a priori knowledge of the uncertainties, a switching‐type adaptive controller is proposed by adding a power integrator method. Based on the modified switching mechanism, the controller parameter can be tuned online such that global finite‐time stability can be achieved. Finally, a simulation example combined with comparison is provided to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this brief, the globally fixed-time control problem is investigated for a general class of uncertain nonlinear systems. The novelties of this brief are two folds. One novelty lies in the propose of a novel variable-gain second-order sliding mode (SOSM) controller. It overcomes the principal shortcomings of first-order sliding mode control and makes it possible to achieve fixed-time stability. The conventional SOSM algorithms can only achieve finite-time stability whose settling time will grow unboundedly when the initial conditions tend to infinity. Another novelty is the extension of constant upper bounds to time-varying upper functions. This enables us to propose a global result, while only local results can be obtained in most of the existing literatures. It is indicated that the proposed novel variable-gain SOSM controller can achieve the establishment of SOSMs in a fixed-time independent of initial conditions. In addition, Lyapunov analysis is given to show that the closed-loop system is globally fixed-time stable. An application to variable-length pendulum is given. [ABSTRACT FROM AUTHOR]

Summary: In this article, the adaptive tracking control problem is considered for a class of uncertain nonlinear systems with input delay and saturation. To compensate for the effect of the input delay and saturation, a compensation system is designed. Radial basis function neural networks are directly utilized to approximate the unknown nonlinear functions. With the aid of the backstepping method, novel adaptive neural network tracking controllers are developed, which can guarantee all the signals in the closed‐loop system are semiglobally uniformly ultimately bounded, and the system output can track the desired signal with a small tracking error. In the end, a simulation example is given to illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Summary: This paper addresses the problem of finite‐time stabilization for a class of low‐order stochastic upper‐triangular nonlinear systems corrupted by unknown control coefficients. Unlike the relevant schemes, the control strategy draws into a dominate gain to cope with the deteriorative effects of both uncertain nonlinearities and unknown control coefficients without using traditional adaptive compensation method. Then, a state feedback controller is constructed by the adding a power integrator method and modified homogeneous domination approach, to ensure the finite‐time stability of the closed‐loop system. Finally, the effectiveness of proposed control strategy has been demonstrated by a simulation example. [ABSTRACT FROM AUTHOR]

This paper is concerned with the practically finite-time (PFT) control problem for a class of more general nonlinear systems subject to mismatching time-varying disturbances. Without any extra assumptions on system nonlinearities, a composite controller is developed by introducing a disturbance observer and finite-time control technique. Based on the designed controller and Lyapunov stability theory, the PFT stability of the closed-loop system is strictly verified and proven to be a better convergence performance. Furthermore, as a byproduct of the proposed design method, the disturbance observer-based PFT control for high-order nonlinear systems is also shown to be possible. To the best of the authors’ knowledge, it is the first PFT control result for high-order nonlinear systems with external disturbances. Finally, an application example of a single-link robot system with disturbances and a numerical example are presented to demonstrate the effectiveness of the proposed scheme, respectively. [ABSTRACT FROM AUTHOR]

In this paper, the problem of adaptive practical tracking is investigated by output feedback for a class of uncertain nonlinear systems subject to nonsymmetric dead-zone input nonlinearity with parameters of dead-zone being unknown. Instead of constructing the inverse of dead-zone nonlinearity, an adaptive robust control scheme is developed by designing an output compensator including two dynamic gains based respectively on identification and non-identification mechanism. With the aid of dynamic high-gain scaling approach and Backstepping method, stability analysis of the closed-loop system is proceeded using non-separation principle, which shows that the proposed controller guarantees that all closed-loop signal is bounded while the output of system tracks a broad class of bounded reference trajectories by arbitrarily small error prescribed previously. Finally, two examples are given to illustrate our controller effective. • An adaptive robust control scheme is developed by designing an output compensator including two dynamic gains based respectively on identification and non-identification mechanism instead of constructing the inverse of dead-zone nonlinearity. • Stability analysis of the closed-loop system is proceeded using non-separation principle, which shows that the proposed controller guarantees that all closed-loop signal is bounded while the output of system tracks a broad class of bounded reference trajectories by arbitrarily small error prescribed previously. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates a composite neural dynamic surface control (DSC) method for a class of pure‐feedback nonlinear systems in the case of unknown control gain signs and full‐state constraints. Neural networks are utilized to approximate the compound unknown functions, and the approximation errors of neural networks are applied in the design of updated adaptation laws. Comparing the proposed composite approximation method with the conventional ones, a faster and better approximation performance result can be obtained. Combining the composite neural networks approximation with the DSC technique, an improved composite neural adaptive control approach is designed for the considered nonlinear system. Then, together with the Lyapunov stability theory, all the variables of the closed‐loop system are semiglobal uniformly ultimately bounded. The infringements of full state constraints can be avoided in the case of unknown control gain signs as well as unknown disturbances. Finally, two simulation examples show the effectiveness and feasibility of the proposed results. [ABSTRACT FROM AUTHOR]

Summary: This paper deals with the problem of mixed passivity and H∞ filter design for a class of Markovian jump delay systems with nonlinear perturbation under event‐triggered scheme and quantization. Firstly, based on an integral inequality, a new sufficient condition for the stochastic stability and performance analysis of the filtering error system is proposed. Secondly, a mode‐dependent condition for the solvability of the filter design problem is given in terms of linear matrix inequalities (LMIs). The filter parameters can be derived using feasible solutions of the presented LMIs. Finally, three numerical examples are given to illustrate the effectiveness and advantages of the proposed filter design method. [ABSTRACT FROM AUTHOR]

Summary: This paper gives a first try to the finite‐time control for nonlinear systems with unknown parametric uncertainty and external disturbances. The serious uncertainties generated by unknown parameters are compensated by skillfully using an adaptive control technique. Exact knowledge of the upper bounds of the disturbances is removed by employing a disturbance observer–based control method. Then, based on the disturbance observer–based control, backstepping technique, finite‐time adaptive control, and Lyapunov stability theory, a composite adaptive state‐feedback controller is strictly designed and analyzed, which guarantees the closed‐loop system to be practically finite‐time stable. Finally, both the practical and numerical examples are presented and compared to demonstrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

Abstract This paper addresses the globally adaptive state-feedback control problem for a more general class of stochastic nonlinear systems with an unknown time-varying delay and perturbations. Without imposing any assumptions on the time-varying delay, an adaptive state-feedback controller is skillfully designed by using adaptive backstepping control technique. Then, based on Lyapunov–Razumikhin lemma and stochastic stability theory, it is proven that the constructed controller can guarantee the closed-loop system to be globally asymptotically stable in probability. Finally, a practical example of stochastic chemical reactor system with time delay and perturbations is presented to demonstrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

Summary: This paper extends the result for cooperative output regulation problem for uncertain nonlinear multiagent systems in output feedback form in the sense that the exosystem generating leader's signal and disturbance is allowed to contain unknown parameter, and all parameters in the whole multiagent system can be arbitrarily large. Since only the information of itself and its neighbors is available, constructing a distributed control law is necessary for the asymptotic tracking of the uncertain leader's signal and the rejection of unknown external disturbances, which is also the main challenge here. A series of simulations are conducted to illustrate the efficiency and advantage of our designs together with the comparison of the design in the existing work. [ABSTRACT FROM AUTHOR]

Summary: Second‐order sliding mode (SOSM) control is used to keep exactly a constraint σ of the second relative degree or to avoid chattering phenomenon. Yet, the traditional SOSM controllers are designed based upon the assumption that the uncertainties or their derivatives are bounded by positive constants. In this paper, a global SOSM controller is designed for a general class of single‐input–single‐output nonlinear systems with uncertainties bounded by positive functions. Moreover, a variable‐gain robust exact differentiator is developed such that the SOSM controllers with finite‐time convergence can also be implemented even when the derivative of the constraint σ is unavailable. Simulation results are given to show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

• finite-time adaptive controller is constructed to address the negative effects of dead-zone in stochastic systems. • A barrier Lyapunov function is designed such that the stochastic nonlinear system whose states are constrained and input is perturbed by dead-zone is semi-global finite-time stable in probability. • Without changing the controller structure, the barrier Lyapunov function is applicable to symmetric or asymmetric full-state constraints. This paper seeks to address the problem of state-feedback tracking control for a class of stochastic systems whose states are constrained and input is perturbed by dead-zone. A tan-type barrier Lyapunov function (BLF) and a finite-time adaptive law are proposed such that all states of the system are constrained in the defined bounded compact sets. Based on stochastic Lyapunov theorem, an adaptive state-feedback tracking controller is designed to ensure that the considered stochastic system is semiglobally finite-time stable in probability (SGFSP) and the tracking error signal is bounded. Different from the existing control strategies for stochastic systems, the form of BLF can be used for asymmetric constraints without changing the controller, so the analysis of symmetric or asymmetric full-state constraints is unified. Finally, illustrative simulations are provided to verify the effectiveness of the proposed control strategy. [ABSTRACT FROM AUTHOR]

This paper makes the first attempt to address the global output-feedback tracking control problem for nonlinear systems in the presence of time delay, nonsymmetric input saturation, and external disturbances. As one of the distinctive features, the growth assumptions imposed on system time-delay nonlinearities are removed in this output-feedback case. To handle the unmeasurable states and disturbances, the composite state observer and disturbance observer are constructed simultaneously. Based on these two observers, an output-feedback controller is designed by introducing an auxiliary system to eliminate the effect of input saturation and using a Lyapunov–Krasovskii functional to deal with time delay. It is shown that the designed controller can ensure the closed-loop system to be globally uniformly ultimately bounded. Particularly, instead of converging to an arbitrarily small neighborhood of zero as in related results, the tracking error is proven to be bounded by the saturation input error and design parameters that can be explicitly tuned. Finally, a chemical reactor system is presented to demonstrate the effectiveness and usefulness of the proposed scheme. [ABSTRACT FROM PUBLISHER]

Summary: This paper addresses the problem of tracking control for a class of uncertain nonstrict‐feedback nonlinear systems subject to multiple state time‐varying delays and unmodeled dynamics. To overcome the design difficulty in system dynamical uncertainties, radial basis function neural networks are employed to approximate the black‐box functions. Novel continuous functions that deal with whole states uncertainties are introduced in each step of the adaptive backstepping to make the controller design feasible. The robust problem caused by unmodeled dynamics when constructing a stable controller is solved by employing an auxiliary signal to regulate its boundedness. A novel Lyapunov‐Krasovskii functional is developed to compensate for the delayed nonlinearity without requiring the priori knowledge of its upper bound functions. On the basis of the proposed robust adaptive neural controller, all the closed‐loop signals are semiglobal uniformly ultimately bounded with good tracking performance. [ABSTRACT FROM AUTHOR]

This paper investigates the finite-time control problem for a class of stochastic nonlinear systems with stochastic integral input-to-state stablility (SiISS) inverse dynamics. Motivated by finite-time stochastic input-to-state stability and the concept of SiISS using Lyapunov functions, a novel finite-time SiISS using Lyapunov functions is introduced firstly. Then, by adopting this novel finite-time SiISS small-gain arguments, using the backstepping technique and stochastic finite-time stability theory, a systematic design and analysis algorithm is proposed. Given the control laws that guarantee global stability in probability or asymptotic stability in probability, our design algorithm presents a state-feedback controller that can ensure the solution of the closed-loop system to be finite-time stable in probability. Finally, a simulation example is given to demonstrate the effectiveness of the proposed control scheme. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper studies coordinated control of multiple Lagrangian systems with parametric uncertainties subject to external disturbances by proposing a fully distributed continuous control law based on the improved self-tuning adaptive observer inspired by non-identifier-based high-gain adaptive control technique. Under this distributed continuous control law, a group of Lagrangian systems are driven to the convex hull spanned by multiple heterogenous dynamic leaders, which can be any combination of step signals of arbitrary unknown magnitudes, ramp signals of arbitrary unknown slopes, and sinusoidal signals of arbitrary unknown amplitudes, initial phases, and any unknown frequencies. It is also worth to mention that this control law we propose, depending neither on any information of leader systems for uninformed followers, nor on external disturbances, even independent of neighbors' velocity, can achieve asymptotic tracking of multiple leaders without any additional condition instead of ensuring the ultimate boundedness of the containment error as in the literature. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In addressing the adaptive neural backstepping control for multiple-input and multiple-output nonlinear systems in pure-feedback form with time-delay and input quantisation, we construct a high-gain state observer and an output-feedback adaptive control scheme using backstepping method, with neural networks to estimate the uncertain nonlinear functions. Then, we propose an output feedback neural controller that ensures all the state trajectories in the time-delay quantised nonlinear systems are ultimately bounded, with the control signal being quantised by either a hysteretic quantiser or a logarithmic quantiser. An illustrative example is presented to show the applicability of the new control method developed. [ABSTRACT FROM AUTHOR]

This paper proposes a new adaptive controller for a class of uncertain nonlinear systems with a quantized signal. Fuzzy logic systems are utilized to approximate nonlinear terms without imposing prior matching conditions required. A hysteretic type of quantizer is incorporated to reduce chattering. A new adaptive backstepping controller is designed to guarantee that the underlying uncertain nonlinear system is semiglobally uniformly ultimately bounded. Two numerical examples are presented to demonstrate the effectiveness and potential of the proposed techniques. [ABSTRACT FROM PUBLISHER]