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In this paper, an adaptive technology and the interconnection and damping assignment passivity-based control method are combined to solve the stabilization problem for underactuated mechanical systems with uncertainties (including matched and unmatched). These uncertainties include unknown friction coefficients and unknown terms in kinetic energy and potential energy. A novel adaptive interconnection and damping assignment passivity-based control scheme is proposed and an adaptive stabilization controller is designed to make the closed-loop system locally stable. Verification is conducted on the ball and beam system. The locally asymptotic stability is demonstrated using the LaSalle's invariance principle and approximate linearization. The effectiveness of the proposed control law is verified through numerical simulations. [ABSTRACT FROM AUTHOR]

Summary: In this paper, the problem of adaptive stability control for uncertain high‐order fully actuated (HOFA) nonlinear systems with disturbances is solved. The method of almost disturbance decoupling (ADD) is used to cope with unknown disturbances. Meanwhile, the tuning function is applied to design an adaptive update law. According to the full‐actuation feature of HOFA systems and Lyapunov stability theory, a novel adaptive controller is designed. In the end, the effectiveness of the control strategy is validated by a numerical simulation example and the attitude control of a spacecraft. [ABSTRACT FROM AUTHOR]

An adaptive tracking control problem of high-order nonlinear strict-feedback system (SFS) with non-affine nonlinear faults is considered in this paper. Based on high-order fully actuated (HOFA) systems theory, dynamic surface control technique and universal approximation of fuzzy logic systems, a novel adaptive fuzzy fault-tolerant tracking controllers are directly constructed, it does not need to convert the high-order system into first-order one. By using Lyapunov function theory, the proposed controller design approach can guarantee that the closed-loop system is stable; at the same time, the tracking error can converge to a compact neighborhood with respect to zero. The simulation example has been verified the feasibility and effectiveness of the control approach in this paper. [ABSTRACT FROM AUTHOR]

Summary: The problem of adaptive control is investigated for unknown mixed high‐order fully actuated (HOFA) nonlinear systems. To deal with the parametric uncertainties, the tuning function is utilized to design an adaptive update law without parameter overestimation. Based on the full‐actuation feature of HOFA nonlinear systems and Lyapunov stability theory, an adaptive controller is constructed and its stability is analyzed. Finally, the effectiveness of the control strategy is verified by simulation results. [ABSTRACT FROM AUTHOR]

In this paper, the control problem for a class of stochastic nonlinear systems with incomplete measurements is investigated based on Luenberger-like nonlinear state observer. The systems are described as strict-feedback cyber-physical systems, in which the communication between the control centre and the physical system is subjected to disturbances. The disturbances, such as information packet losing or transmission medium saturation, cause state variables to be unavailable or distorted, which results in incomplete measurements. To solve these problems, two state estimators are designed for different transmission cases, based on which two backstepping control approaches are adopted. The stability conditions of the state estimators and closed-loop system are derived. It is proved that the control methods can guarantee that all the signals of the closed-loop system are uniformly ultimately bounded in mean square. The effectiveness of the proposed methods is confirmed by simulation examples. [ABSTRACT FROM AUTHOR]

Most research on control of nonlinear systems using backstepping concentrates on construction of feedback controllers to achieve stability and/or steady-state tracking performance. Little research considers systematic methods for tuning nonlinear feedback controllers to guarantee the transient performance. This paper investigates how parameters of a backstepping controller can be determined to achieve the predefined settling time and overshoot, which are basic criteria for the transient performance. First, some modifications are made for the backstepping design method by introducing more parameters so that there are more degrees of freedom for parameter tuning. Second, the pole-placement method is used for the linear part of the closed-loop system corresponding to a backstepping controller. Third, an objective function is defined by summing the square of errors between the corresponding coefficients of the desired and real characteristic polynomials. Fourth, constraints are introduced to guarantee the negative semi-definiteness of the time derivative of the Lyapunov function. Fifth, the controller parameters can be found by minimizing the objective function. Finally, simulation and experimental results show that, compared with the existing method, the proposed method is more effective and efficient for fine tuning backstepping controllers. [ABSTRACT FROM AUTHOR]

This paper presents a linear-based gain-determining method for nonlinear adaptive backstepping controllers. Usually, the gains for nonlinear controllers are tuned by the trial and error method. This method becomes more difficult as the number of gains increases. A user-friendly method is proposed in this work to deal with the problem. Firstly, a linear auxiliary system is formed by separating the linear parts from the nonlinear system. Then, linear state-space techniques are used to determine the gains for state-feedback by the linear auxiliary system. After that, by converting the state-feedback gains to backstepping gains, the gains of the nonlinear backstepping controller can be determined. The proficiency of the gain-determining method is proved by simulations with two linear techniques. • Linear techniques can be used for the gain determination for nonlinear control systems. • The ascending gain solution performs better than other solutions in general. • The resulted performance of the nonlinear systems is similar to that of the desired linear systems. [ABSTRACT FROM AUTHOR]

This paper focuses on the adaptive containment control problem for nonlinear strict-feedback multi-agent systems with dynamic leaders. An adaptive controller is constructed by backstepping control, first-order filters and compensating signals. The ''explosion of complexity" phenomenon is avoided by introducing first-order filters in traditional backstepping control, and filter errors are handled with compensating signals. All adaptive laws are accumulated to the last step by using tuning functions. The whole control design method is divided into two parts. One is to design adaptive tracking control for dynamic leaders. The other is to design adaptive containment control for followers. Through the proposed control method, the closed-loop system is stable, and all followers can converge to the convex hull built by the leaders. The simulation studies can confirm the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

Summary: This article proposes a novel adaptive prescribed performance control method. Featured with a selected transient performance, the proposed control method can achieve prescribed performance control by a new error transformation method. With the proposed control strategy, the closed‐loop system can follow the prescribed performance with a predefined curve. An adaptive controller is constructed based on the adaptive backstepping technique. By utilizing the Lyapunov stability, asymptotic stability is achieved for the closed‐loop system. Two examples with simulation results are provided to illustrate the proficiency of the proposed control strategy. To make comparisons, the same second‐order transient response is adopted as the performance function for both examples. The selection of gains and parameters are investigated by tests. The expected prescribed performance and the asymptotic stability are achieved in both examples, which verifies the proposed control strategy. Some discussions and comparisons are made accordingly as well. [ABSTRACT FROM AUTHOR]

In this paper, a gain determining method for nonlinear adaptive backstepping technique is proposed by the pole placement method. By introducing a subsystem that can be linearised as a linear system, controller gains can be solved by the pole placement method. Compared with the existing techniques, the proposed method can achieve a transient performance like a linear system with the pole placement method instead of constraining the system in a predefined performance range. Meanwhile, the proposed method does not change the structure of adaptive backstepping controllers, which preserves the advantages of the original backstepping design and avoids increasing the computing effort for the control system. In addition, the applications of the proposed method are demonstrated by three examples, including a 2nd-order nonlinear system, a 3rd-order nonlinear system, and a single-link robot arm. The corresponding simulations are conducted, and the simulation results are illustrated and analysed. Moreover, comparative simulations are conducted to verify the proposed method. [ABSTRACT FROM AUTHOR]

This article studies the adaptive tracking control problem for stochastic nonlinear systems with unknown virtual control coefficients (UVCCs) being functions of system states. Without using the Nussbaum gain technique (NGT), a new method is introduced to deal with UVCCs. The novel adaptive laws are constructed to compensate parameter uncertainties and UVCCs. Using backstepping method, an adaptive controller is designed, which can ensure that the boundedness in probability of all the signals in the closed‐loop system. In the end, a numerical simulation example and a practical example are given to validate the effectiveness and superiority of the proposed controller. [ABSTRACT FROM AUTHOR]

This paper focuses on a problem of composite adaptive fuzzy decentralized tracking control for a class of uncertain pure-feedback interconnected large-scale nonlinear systems with unmeasurable states. A fuzzy state observer is designed by using fuzzy logic systems; thus, the unmeasurable states of pure-feedback nonlinear systems are estimated based on the designed fuzzy state observer. A serial–parallel estimation model is designed by using the fuzzy state observer. To avoid the analytic computation, the command filters are employed to produce the command signals and their derivatives. The fuzzy adaptive laws are constructed by using prediction errors and compensating tracking errors. Finally, a controller is constructed by dynamic surface control technique. Through the proposed control method, all the signals in the closed-loop system are bounded, and the output of the system can track the given reference signal. The simulation studies verify the effectiveness of the proposed control method in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the decentralised connectively practical finite-time control problem is studied for a class of p-normal form large-scale systems with expanding construction. First, the decentralised connectively practical finite-time controllers are designed for the p-normal form large-scale systems without expanding construction by combining adding a power integrator technique, the backstepping method, the Lyapunov theory with the neural adaptive technology. The designed controllers can guarantee that all the signals of the closed-loop system are practically finite-time stable and the large-scale system is connectively stable. Then, the expansion of the system is considered. A new subsystem is added to the original system online. It is needed that the decentralised control laws and the adaptive laws of the original system are kept to be unchanged, and only the control laws and the adaptive laws for the newly added subsystem need to be designed. Under the premise, the control laws and the adaptive laws of the new subsystem are designed, which can guarantee that both newly added subsystem and resultant expanded closed-loop large-scale system are connectively practically finite-time stable. The singularity problem arising in the design process for practical finite-time control is solved. Here, the adding a power integrator technique is applied to handle the control design problem for p-normal form systems. And the control laws and the adaptive laws are simplified by neural networks. The two numerical examples including an actual double-inverted pendulum system connected by a spring are presented to show the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This paper provides a new solution for the finite‐time attitude maneuvers of rigid spacecraft. Uncertainties involving unknown inertial parameters, external disturbances and actuator failures are taken into account. With an effort to achieve attitude tracking despite the impact of uncertainties, a non‐singular terminal sliding mode (NTSM) manifold consisting of attitude errors and angular velocity errors is first constructed. After that, a simple but efficient adaptive updating law is derived to estimate the upper bound of the lumped unknown function in the derivative of sliding surface. Combining NTSM technology and pure adaptive control, a chattering‐free fault‐tolerant controller is presented. The premise assumptions on uncertainties in most of the existing achievements are eliminated, which makes the controller less constrained and more practical. The rigorous proof of finite‐time stability is provided and the convergent regions of tracking errors are explicitly expressed. Finally, numerical simulation is conducted to verify the effectiveness of the proposed control scheme and the comparison experiments with relevant literature demonstrate the satisfactory performances. [ABSTRACT FROM AUTHOR]

An adaptive backstepping fault-tolerant control scheme is presented for a class of fractional-order systems in the presence of unknown input dead-zones. The proposed fault-tolerant control scheme ensures all the closed-loop signals are bounded ultimately. Especially, the tracking error can be made as small as possible by choosing appropriate design parameters. Furthermore, this scheme not only works for fractional-order systems with unknown linear terms but also works for these with unknown nonlinear terms. Finally, several practical examples are simulated to verify the effectiveness of the proposed fault-tolerant control scheme. [ABSTRACT FROM AUTHOR]

This work investigates an adaptive finite-time congestion control problem of transmission control protocol/active queue management. By means of the funnel control, neural networks and sliding mode control, a new AQM algorithm is proposed to ensure that the tracking error e 1 t converges to the prescribed boundary in finite time and the transient and steady-state performances of e 1 t can be satisfied. The stability analysis is given to prove that all the signals of the closed-loop system are finite-time bounded. Finally, a comparison example is considered to demonstrate the feasibility and superiority of the presented scheme. [ABSTRACT FROM AUTHOR]

Summary: In this paper, a class of fractional‐order nonlinear systems are considered in the presence of actuator faults. A novel fault tolerant control scheme based on disturbance observer has been presented, where the actuator faults are considered as the system disturbance and can be approximated by the proposed disturbance observer. The developed fault tolerant control guarantees the convergence of the closed‐loop system and the output tracking performance. Finally, a simulation example is presented to verify the effectiveness of the new method. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of event-triggered funnel control for strict-feedback nonlinear systems with unknown parameters. For the first time, an adjustable funnel function is proposed, whose parameters can be adjusted online according to the change of tracking error. Furthermore, based on event-triggered control, an adaptive event-triggered funnel controller is constructed, which guarantees that all the signals in the closed-loop system are bounded. Besides, the output tracking error is further optimized and always falls within an adjustable funnel which has a faster convergence. Meanwhile, the Zeno behavior also is avoided. Simulation results demonstrate the effectiveness of the developed controller. • A funnel is developed, whose parameters are determined by the tracking error. • The tracking error always stays within an adjustable funnel boundary. • The transient performance of tracking error is slightly optimized. [ABSTRACT FROM AUTHOR]

Summary: This paper focuses on the adaptive tracking control problem for strict‐feedback nonlinear systems with zero dynamics via prescribed performance. Based on polynomial fitting, an adjustable performance function is firstly proposed, whose parameters can be adjusted in real time according to the tracking error. Furthermore, an adaptive prescribed performance tracking controller is constructed via the backstepping method, which guarantees that all the states in the closed‐loop system are bounded. Meanwhile, the output tracking error falls within an adjustable performance boundary and asymptotically converges to zero. Simulation comparison demonstrates the advantages of the developed controller as follows: (1) the parameters of the adjustable performance function are adjusted online according to the tracking errors for a faster convergent performance boundary; (2) the steady‐state performance of the system is further optimized simultaneously. [ABSTRACT FROM AUTHOR]

This paper focuses on the problem of event-triggered control for a class of uncertain nonlinear strict-feedback systems with zero dynamics via backstepping technique. In the design procedure, the adaptive controller and the triggering event are designed at the same time to remove the assumption of the input-to-state stability with respect to the measurement errors. Besides, we propose an assumption to deal with the problem of zero dynamics. Three different event-triggered control strategies are designed, which guarantees that all the closed-loop signals are globally bounded. The effectiveness of the proposed methods is illustrated and compared using simulation examples. [ABSTRACT FROM AUTHOR]

This paper extends the well-known control method, prescribed performance control (PPC), to network congestion control problems. An adaptive H ∞ tracking problem for Transmission Control Protocol/Active Queue Management (TCP/AQM) system with external disturbance is studied. Firstly, a modified network model is given. And then, the model is changed to an equivalent error model by using error transformation. Next, to solve the network congestion problem, prescribed performance, backstepping technique, adaptive control and H ∞ control are combined to design a congestion controller. Due to the use of prescribed performance, the controller can guarantee both the transient and steady state performance of the system. Meanwhile, the output of the system can track the desired queue, and unknown link capacity can be estimated. Finally, a simulation result is shown to clarify the feasibility and effectiveness of proposed approach. [ABSTRACT FROM AUTHOR]

Transition rules are the core of urban cellular automata (CA) models. Although the logistic cellular automata (Logistic-CA) is commonly used for rules extraction, it cannot always achieve satisfactory performance because of the spatial heterogeneity and the inherent complexity of urban expansion. This article presents an ensemble-urban cellular automata (Ensemble-CA) model to achieve better transition rules. First, an uncertainty map that assesses the performance of transition rules spatially was achieved. Then, two auxiliary models (i.e. classification and regression tree, CART; and artificial neural network, ANN), both of which have been stabilized with a Bagging algorithm, were prepared for integration using a proposed self-adaptive-nearest neighbors (-NN) combination algorithm. Thereafter, those unconfident sites were replaced with the ensemble output. This model was applied to Guangzhou, China, for an urban growth simulation from 2003 to 2008. Static validation confirmed that this ensemble framework (i.e. without substitution of uncertain sites) can achieve better performance (0.87) in terms of receiver operating characteristic (ROC) statistics (area under the curve, AUC), and outperformed the best single model (ANN, 0.82) and other common strategies (e.g. weighted average, 0.83). After the substitution of unconfident sites, the AUC of Logistic-CA was elevated from 0.78 to 0.81. Subsequently, two urban growth mechanisms (i.e. pixel- and patch-based) were implemented separately based on the integrated transition rules. Experimental results revealed that the accuracy obtained from simulation of the Ensemble-CA increased considerably. The obtained kappa outperformed the single model, with improvements of 1.74% and 2.76% for pixel- and patch-based approaches, respectively. Correspondingly, landscape similarity index (LSI) improvements of these two mechanisms were 4.24% and 1.82%. [ABSTRACT FROM AUTHOR]

This study focuses on the control of a novel active vibration isolator using an adaptive backstepping approach. The developed active isolator is introduced and its dynamic model is presented. It is shown that the unknown nonlinear restoring force and damping parameter pose control challenges. The nonlinear restoring force is approximated as a polynomial with unknown coefficients. Adaptive control is chosen as a suitable approach to tackle the control challenges. An existing lower-order adaptive backstepping controller is modified in order to include the actuator dynamics and avoid the zero convergence of the estimated parameter vector. An extensive experimental study is conducted to test the effectiveness of the modified controller. The performance of the controller is compared with that of the lower-order controller. The results from several testing scenarios are presented and interpreted, and the issues related to parameter estimation and control performance are addressed. [ABSTRACT FROM PUBLISHER]

Abstract: In this paper, the problem of the adaptive neural control is considered for a class of pure-feedback stochastic nonlinear systems. Based on the radial basis function (RBF) neural networks' universal approximation property, an adaptive neural controller is developed via backstepping technique. It is shown that the proposed controller can guarantee that all the signals in the closed-loop system are bounded in the sense of mean quartic value. Compared with the existing results on adaptive control of stochastic pure-feedback nonlinear systems, the main novelty of this note is that a systematic design procedure is presented for a class of pure-feedback stochastic nonlinear systems with a more general form of the diffusion term. Simulation results are presented to demonstrate the effectiveness of the proposed scheme. [Copyright &y& Elsevier]

Wireless information collecting and processing terminals, such as cell phones, sensors and smart wearable devices, are expected to be deployed on a large scale in the future to promote the continuous advancement of the global information revolution. Since most of these terminals connect to each other using long-distance and high-speed networks by multiple routers and eventual access the internet, the application of mobile internet is gradually increasing and data traffic on the mobile internet is growing exponentially, from which arises congestion in wireless networks on multiple routers. This research solves the congestion problem for wireless networks with multiple bottleneck routers. First, the wireless network model is expanded to multi-router networks, which considers the interrelationships between connecting routers. Afterwards, a new Active Queue Management (AQM) method called Congestion Control Based on Adaptive Integral Backstepping (CCAIB) is designed to handle congestion in wireless networks. In CCAIB, an adaptive control method is used to estimate the packet loss ratios of wireless links and a controller is designed based on the estimation results through a backstepping procedure. It can be shown from the simulation results that the performance of CCAIB is better than the H∞ algorithm in queue length stability. Besides, the window size of CCAIB is 100 times that of the H∞ algorithm, and the proportion of packets marked as discarded when using CCAIB is about 0.1% of the H∞ algorithm. Moreover, CCAIB has satisfactory adaptability to network parameters such as wireless link capacity, propagation delay, wireless packet loss ratios, desired queue length and router location. [ABSTRACT FROM AUTHOR]

This paper is concerned with robust stabilization problem for a class of nonaffine pure-feedback systems with unknown time-delay functions and perturbed uncertainties. Novel continuous packaged functions are introduced in advance to remove unknown nonlinear terms deduced from perturbed uncertainties and unknown time-delay functions, which avoids the functions with control law to be approximated by radial basis function (RBF) neural networks. This technique combining implicit function and mean value theorems overcomes the difficulty in controlling the nonaffine pure-feedback systems. Dynamic surface control (DSC) is used to avoid “the explosion of complexity” in the backstepping design. Design difficulties from unknown time-delay functions are overcome using the function separation technique, the Lyapunov–Krasovskii functionals, and the desirable property of hyperbolic tangent functions. RBF neural networks are employed to approximate desired virtual controls and desired practical control. Under the proposed adaptive neural DSC, the number of adaptive parameters required is reduced significantly, and semiglobal uniform ultimate boundedness of all of the signals in the closed-loop system is guaranteed. Simulation studies are given to demonstrate the effectiveness of the proposed design scheme. [ABSTRACT FROM AUTHOR]

In the face of large-scale parametric uncertainties, the single-model (SM)-based sliding mode control (SMC) approach demands high gains for the observer, controller, and adaptation to achieve satisfactory tracking performance. The main practical problem of having high-gain-based design is that it amplifies the input and output disturbance as well as excites hidden unmodeled dynamics, causing poor tracking performance. In this paper, a multiple model/control-based SMC technique is proposed to reduce the level of parametric uncertainty to reduce observer-controller gains. To this end, we split uniformly the compact set of unknown parameters into a finite number of smaller compact subsets. Then, we design a candidate SMC corresponding to each of these smaller subsets. The derivative of the Lyapunov function candidate is used as a resetting criterion to identify a candidate model that approximates closely the plant at each instant of time. The key idea is to allow the parameter estimate of conventional adaptive sliding mode control design to be reset into a model that best estimates the plant among a finite set of candidate models. The proposed method is evaluated on a 2-DOF robot manipulator to demonstrate the effectiveness of the theoretical development. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we address the problem of adaptive neural control for a class of multi-input multi-output (MIMO) nonlinear time-delay systems in block-triangular form. Based on a neural network (NN) online approximation model, a novel adaptive neural controller is obtained by constructing a novel quadratic-type Lyapunov–Krasovskii functional, which not only efficiently avoids the controller singularity, but also relaxes the restriction on unknown virtual control coefficients. The merit of the suggested controller design scheme is that the number of online adapted parameters is independent of the number of nodes of the neural networks, which reduces the number of the online adaptive learning laws considerably. The proposed controller guarantees that all closed-loop signals remain bounded, while the output tracking error dynamics converges to a neighborhood of the origin. A simulation example is given to illustrate the design procedure and performance of the proposed method. [Copyright &y& Elsevier]

Abstract: This paper focuses on adaptive fuzzy tracking control for a class of uncertain single-input /single-output nonlinear strict-feedback systems. Fuzzy logic systems are directly used to approximate unknown and desired control signals and a novel direct adaptive fuzzy tracking controller is constructed via backstepping. The proposed adaptive fuzzy controller guarantees that the output of the closed-loop system converges to a small neighborhood of the reference signal and all the signals in the closed-loop system remain bounded. A main advantage of the proposed controller is that it contains only one adaptive parameter that needs to be updated online. Finally, an example is used to show the effectiveness of the proposed approach. [Copyright &y& Elsevier]

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]