Adaptive fault-tolerant control with prescribed performance for switched nonlinear pure-feedback systems

In this paper, the problem of adaptive fuzzy fault-tolerant control is investigated for a class of switched uncertain pure-feedback nonlinear systems under arbitrary switching. The considered actuator failures are modeled as both lock-in-place and loss of effectiveness. By utilizing mean value theorem, the considered pure-feedback systems are transformed into a class of switched nonlinear strict-feedback systems. Under the framework of backstepping design technique and common Lyapunov function (CLF), an adaptive fuzzy fault-tolerant control (FTC) method with predefined performance bounds is developed. It is proved that under the proposed controller, all the signals of the close-loop systems are bounded and the state tracking error for each step remains within the prescribed performance bound (PPB) regardless of actuator faults and the system switchings. In addition, the tracking errors and magnitudes of control inputs can be reduced by adjusting the PPB parameters of errors in the first and last steps. The simulation results are provided to show the effectiveness of the proposed control scheme.     

Global finite-time stabilization for switched stochastic nonlinear systems via output feedback

This paper is concerned with the problem of global finite-time stabilization via output feedback for a class of switched stochastic nonlinear systems whose powers are dependent of the switching signal. The drift and diffusion terms satisfy the lower-triangular homogeneous growth condition. Based on adding a power integrator technique and the homogeneous domination idea, output-feedback controllers of all subsystems are constructed to achieve finite-time stability in probability of the closed-loop system. Distinct from the existing results on switched stochastic nonlinear systems, the delicate change of coordinates are introduced for dominating nonlinearities. Moreover, by incorporating a multiplicative design parameter into the coordinate transformations, the obtained control method can be extended to switched stochastic nonlinear systems with nonlinearities satisfying the upper-triangular homogeneous growth condition. The validity of the proposed control methods is demonstrated through two examples.     

Adaptive fuzzy tracking control for switched uncertain strict-feedback nonlinear systems

This paper concerns an adaptive fuzzy tracking control problem for a class of switched uncertain nonlinear systems in strict-feedback form via the modified backstepping technique. The unknown nonlinear functions are approximated by the generalized fuzzy hyperbolic model (GFHM). It is shown that if the designed parameters in the controller and adaptive laws are appropriately selected, then all closed-loop signals are bounded and the stability of the system can be kept under average dwell time methods. In the end, simulation studies are presented to illustrate the effectiveness of the proposed method.     

Asynchronous input-output finite-time filtering for switched LPV systems

The input-output finite-time filtering problem is addressed for a class of switched linear parameter-varying systems in this paper. Firstly, by constructing a parameter-dependent Lyapunov function and resorting to the average dwell time approach, sufficient conditions ensuring finite-time boundedness and input-output finite-time stability are established for the augmented filtering error system. Then, a parameter-dependent asynchronous filter is designed such that the augmented filtering error system are both finite-time bounded and input-output finite-time stable. Finally, the active magnetic bearing model is introduced and verifies the main algorithms in this paper.     

Adaptive finite-time control for stochastic nonlinear systems subject to unknown covariance noise

This paper is devoted to the adaptive finite-time control for a class of stochastic nonlinear systems driven by the noise of covariance. The traditional growth conditions assumed on the drift and diffusion terms are removed through a technical lemma, and the negative effect generated by unknown covariance noise is compensated by combining adaptive control technique with backstepping recursive design. Then, without imposing any growth assumptions, a smooth adaptive state-feedback controller is skillfully designed and analyzed with the help of the adding a power integrator method and stochastic backstepping technique. Distinctive from the global stability in probability or asymptotic stability in probability obtained in related work, the proposed design algorithm can guarantee the solution of the closed-loop system to be finite-time stable in probability. Finally, a stochastic simple pendulum system is skillfully constructed to demonstrate the effectiveness of the proposed control scheme.     

Finite-time stabilization of a class of upper-triangular switched nonlinear systems

This paper investigates the finite-time stabilization for a class of upper-triangular switched nonlinear systems, where nonlinearities are allowed to be lower-order growing. Due to the special structure of the considered system, the presented methods for lower-triangular switched nonlinear systems in the literature can not be directly utilized. To solve the problem, a state feedback control law with a new structure is designed to guarantee the global finite-time stability of the closed-loop system under arbitrary switching signals by using the recursive design approach and the nested saturation method. A simulation example is provided to show the effectiveness of the proposed method.     

Pattern-based NN control for uncertain pure-feedback nonlinear systems

Implementing human-like learning and control for nonlinear dynamical systems operating in different control situations is an important and challenging issue. This paper presents a pattern-based neural network (NN) control strategy for nonlinear pure-feedback systems via deterministic learning (DL). Firstly, an appropriately designed adaptive neural dynamic surface controller is proposed to achieve the finite time tracking control. By analyzing the recurrent property of NN input signals, a partial persistent excitation (PE) condition for radial basis function (RBF) network is established, the implicit desired control dynamics under different control situations are accurately identified via DL in the case that the dimension of NN input is reduced. And a set of pattern-based experienced actual and virtual controllers is constructed using the learned knowledge. Secondly, to classify different control situations, when the system is operating in different control situations but controlled by current normal experienced controller, the dynamics of each subsystem are accurately identified via DL, n sets of dynamical estimators are constructed using the learned knowledge. Thirdly, in the recognition phase, n sets of residuals are achieved by comparing each set of estimators with the monitored system, sudden change in the control situation is rapidly recognized based on the principle of the earliest occurrence of the minimum residual. Finally, in the control phase, according to the recognition result, the correct experienced actual and virtual controllers will be selected to control the plant, guaranteed stability and superior control performance are achieved without any further re-adaptation online. Simulation studies are given to verify the proposed scheme can not only acquire and memorize knowledge like humans, but also reuse the learned knowledge to achieve rapid recognition and control of current control situation.     

Adaptive neural design frame for uncertain stochastic nonlinear non-lower triangular pure-feedback systems with input constraint

This paper dedicates to dealing with the adaptive neural design problem for uncertain stochastic nonlinear systems with non-lower triangular pure-feedback form and input constraint. On the basis of the mean-value theorem, the pure-feedback structure is first transformed into the desired affine structure, and then the well-known backstepping technology is applied to construct the actual input signal of the controller. Although the considered system has a fairly complex structure, a new adaptive neural tracking controller design frame is established via the flexible application of radial basis function (RBF) neural networks’ (NNs’) structural characteristics. The proposed design frame guarantees the control objective of this paper can be achieved. Finally, a simulation example is given to further illustrate the availability of the proposed control scheme.     

Adaptive control for uncertain nonlinear time-delay systems in a lower-triangular form

In the presence of uncertain time-varying control coefficients, structuring parameter uncertainty and unknown state time delay, this paper proposes a continuous feedback control scheme for highly nonlinear systems without extra nonlinear growth restriction. An expansion of the backstepping method is presented based on dynamic gains and tuning functions. By Lyapunov–Krasovskii functionals, a delay-free controller is designed to regulate the original system states to zero with the other states being globally bounded.     

Adaptive stabilization control for high-order nonlinear time-delay systems with its application

This paper investigates the state-feedback stabilization problem in the smooth case for a class of high-order nonlinear systems with time delays. By generalizing a novel radial basis function neural network (RBF NN) approximation approach to high-order nonlinear systems, we successfully remove the power order restriction and the growth conditions on system nonlinearities. It should be pointed out that the knowledge of NN nodes and weights does not need to be known a priori and operate on-line, and the adaptive parameter is only one. Furthermore, without imposing any growth assumptions on system nonlinearities, we construct a smooth adaptive state-feedback controller which guarantees the closed-loop system to be semi-globally uniformly ultimately bounded (SGUUB). Finally, we apply the proposed scheme to a single-link robot system and a numerical example to demonstrate the effectiveness of the controller.     

Fuzzy observer-based sampled-data control for a class of pure-feedback nonlinear systems

This paper aims at the sampled-data control problem for a class of pure-feedback nonlinear systems. A fuzzy state observer is constructed to evaluate the unavailable states. In this process, fuzzy logic systems are applied to approximate the uncertain nonlinear functions. Based on the new designed state observer, a sampled-data control scheme for the pure-feedback nonlinear systems is proposed. The designed sampled-data controller ensures the boundedness of the nonlinear systems. Finally, two numerical examples are used to demonstrate that the proposed method is efficient.     

Observer-based fuzzy adaptive stabilization of uncertain switched stochastic nonlinear systems with input quantization

This paper proposes an observer-based fuzzy adaptive output feedback control scheme for a class of uncertain single-input and single-output (SISO) nonlinear stochastic systems with quantized input signals and arbitrary switchings. The SISO system under consideration contains completely unknown nonlinear functions, unmeasured system states and quantized input signals quantized by a hysteretic quantizer. By adopting a new nonlinear disposal of the quantized input, the relationship between the control input and the quantized input is established. The hysteretic quantizer that we take can effectively avoid the chattering phenomena. Furthermore, the introduction of a linear observer makes the estimation of the states possible. Based on the universal approximation ability of the fuzzy logic systems (FLSs) and backstepping recursive design with the common stochastic Lyapunov function approach, a quantized output feedback control scheme is constructed, where the dynamic surface control (DSC) is explored to alleviate the computation burden. The proposed control scheme cannot only guarantee the boundedness of signals but also make the output of the system converge to a small neighborhood of the origin. The simulation results are exhibited to demonstrate the validity of the control scheme.     

Adaptive finite-time practical consensus protocols for second-order multiagent systems with nonsymmetric input dead zone and uncertain dynamics

This paper investigates adaptive finite-time practical consensus protocols for a class of second-order multiagent systems with a positive odd power, nonsymmetric input dead zone and uncertain dynamics under a directed communication topology. In this study, three major steps are employed to address the existence of the positive odd power, nonsymmetric input dead zone and uncertain dynamics. Overall, based on the technique of adding one power integrator, useful preliminary results are obtained by configuring a suitable fraction power. Furthermore, to circumvent input dead-zone nonlinearity, an adaptive fuzzy logic (FL) method is used to estimate the width of the dead zone. Finally, the difficulty in designing finite-time practical consensus protocols for the multiagent systems with uncertain dynamics is handled by using radial basis function neural networks (RBFNNs) to approximate the related unknown nonlinear functions. Then, given some reasonable assumptions, it is shown that finite-time practical consensus of the second-order multiagent systems is obtained by using the proposed distributed control protocols and adaptive laws. In addition, the proper approach for selecting parameters is provided such that the neighborhood position error and parameter estimate errors for each agent converge to predesigned small regions of the origin in a finite time. The effectiveness of the developed algorithm is finally validated through a numerical simulation.     

Global finite time stabilization of pure-feedback systems with input dead-zone nonlinearity

This paper is concerned with finite-time stabilization of a class of pure-feedback systems with dead-zone input. A systematic design procedure is established to derive the finite-time controller. Firstly, to circumvent the difficulties arising from the nonaffine properties, through a change of coordinates and incorporating mean value theorem, a system transformation technique is introduced to convert the original nonaffine system into an affine one. Then, based on the strengthened finite-time Lyapunov stability theorem as well as utilizing the bounds of dead-zone parameters, the finite-time stabilizer is explicitly constructed via backstepping design approach. It is proven that the designed controller can ensure all the states of the closed-loop system converge to zero in a finite time and maintain at zero afterwards. The proposed design framework is also extended to finite-time stabilization of uncertain pure-feedback systems and finite-time tracking control of pure-feedback systems. The effectiveness of the theoretical results are finally demonstrated by a numerical example and a realistic example.     

Adaptive neural network decentralized stabilization for nonlinear large scale interconnected systems with expanding construction

A backstepping-based adaptive neural network decentralized stabilization approach is presented for the expanding construction of a class of nonlinear large scale interconnected systems in this paper. The expanding construction of large scale interconnected systems is to add some new subsystems into the original system during the operation of the original system. For stabilization of the expanding system, it is more realistic to keep the decentralized control laws of the original subsystems unchanged. And the decentralized control laws of the new subsystems must be designed to stabilize both itself and the resultant large scale system. In this paper, neural networks are used to approximate the unknown nonlinear functions in the new subsystems and the unknown nonlinear interconnection functions. The decentralized control laws and the parameter adaptive laws of the new subsystems are designed by using backstepping technique for the expanding construction of the large-scale interconnected system. Based on Lyapunov stability theory, the uniform and ultimate boundedness of all signals in the closed-loop system is proved. Two illustrative examples show the feasibility of the presented approach.     

Robust event-driven tracking control with preassigned performance for uncertain input-quantized nonlinear pure-feedback systems

This paper presents a simplified design methodology for robust event-driven tracking control of uncertain nonlinear pure-feedback systems with input quantization. All nonlinearities and quantization parameters are assumed to be completely unknown. Different from the existing event-driven control approaches for systems with completely unknown nonlinearities, the main contribution of this paper is to design a simple event-based tracking scheme with preassigned performance, without the use of adaptive function approximators and adaptive mirror models. It is shown in the Lyapunov sense that the proposed event-driven low-complexity tracker consisting of nonlinearly transformed error surfaces and a triggering condition can achieve the preselected transient and steady-state performance of control errors in the presence of the input quantization.     

Non-fragile finite-time extended dissipative control for a class of uncertain discrete time switched linear systems

In this paper, the issues of finite-time extended dissipative analysis and non-fragile control are investigated for a class of uncertain discrete time switched linear systems. Based on average dwell-time approach, sufficient conditions for the finite-time boundedness and finite-time extended dissipative performance of the considered systems are proposed by solving some linear matrix inequalities, where using the concept of extended dissipative, we can solve the H_∞, $L_2?L_{\infty },$ Passivity and (Q, S, R)-dissipativity performance in a unified framework. Furthermore, two form of non-fragile state feedback controllers are designed to guarantee that the closed-loop systems satisfy the finite-time extended dissipative performance. Finally, simulation example is given to show the efficiency of the proposed methods.     

Command filter-based finite-time adaptive fuzzy control for nonlinear systems with uncertain disturbance

In this paper, a command filter-based adaptive fuzzy controller is constructed for a class of nonlinear systems with uncertain disturbance. By using the error compensation signals and fuzzy logic system, a command filter-based control strategy is presented to make that the tracking error converge to an any small neighborhood of zero and all closed-loop signals are bounded. In the design procedure, fuzzy logic system is employed to estimate unknown package nonlinear functions, which avoids excessive and burdensome computations. The control scheme not only resolves the explosion of complexity problem but also eliminates the filtering error in finite-time. An example has evaluated the validity of the control method.     

Adaptive finite-time consensus of a class of disturbed multi-agent systems

In this paper, the finite-time exponential consensus problem is addressed for a class of multi-agent systems against some disturbed factors, which include system uncertainties, communication perturbations, and actuator faults. All disturbed factors are supposed to be influenced by internal and external effects of systems. The internal effects are described in terms of dependency on the system states, while the external actions are restricted by constant bounds. To obtain the information of the rate of dependency on the states and constant bounds, an adaptive mechanism is designed to estimate the rate and bounds. Based on these estimates, a distributed adaptive sliding mode controller is constructed to eliminate the effects of those disturbed factors. Then exponential consensus of the closed-loop adaptive multi-agent system is achieved within a finite time based on Lyapunov stability theory. The efficiency of the developed adaptive consensus control strategy is verified by a coupled system with four F-18 aircrafts of decoupled longitudinal model.     

Asynchronous switching for switched nonlinear input delay systems with unstable subsystems

We study the input-to-state stability (ISS) of switched nonlinear input delay systems under asynchronous switching. Our results apply to cases where some subsystems of the switched systems are not necessarily stable under the influence of input delay. By making a compromise among the matched-stable period, the matched-unstable period, and the unmatched period and allowing the increase of the Lyapunov–Krasovskii functional (LKF) on all the switching times, the extended stability criteria for switched delay systems in generally nonlinear setting are derived first. Then, we focus on switched nonlinear input delay systems where the presence of the input delay leads to the instability of some subsystems of it. By explicitly constructing input-to-state stable LKF, the sufficient conditions for ISS of switched nonlinear input delay systems under asynchronous switching are presented. Finally, two examples are given to illustrate the effectiveness of the proposed theory.