Adaptive Output‐Feedback Control of Nonlinear Systems with Multiple Uncertainties

This paper deals with an adaptive robust tracking control using a multilayer neural network (NN) for a class of nonlinear dynamic systems with unknown time varying state delays. Typical adaptive NN backstepping controllers for uncertain nonlinear systems with time-delay give rise to computation complexity caused by the the repeated derivatives of virtual controllers and nonlinear functions. Moreover, the combined techniques usually result in only uniformly ultimately bounded (UUB) stability caused by the inherent NN approximation error. This paper presents a control scheme that uses an integral sliding mode control as a feedback term and an adaptive neural controller as a feedforward term based on the desired compensation adaptive law (DCAL) technique. First, we develop a new DCAL formulation which avoids the explosion of complexity caused by the general NN backstepping scheme to compensate for nonlinear system uncertainties, bounded system disturbances, and unknown state time delays. Then, using a Lyapunov-Krasovskii (LK) functional, it is shown that the proposed controller renders the class of uncertain nonlinear time-delay systems asymptotically stable.

In this paper, an adaptive dynamic event-triggered output-feedback control scheme is proposed for a class of uncertain nonlinear systems. Specifically, a parameter estimator and a Nussbaum function are incorporated into the dynamic event-triggered control scheme to compensate for serious uncertainties, including the completely unknown parameter allowed in system nonlinearities and the unknown control coefficients (both signs and magnitudes are unknown). Importantly, an additional internal dynamic variable is introduced into the event-triggering mechanism, enabling the control scheme to save network resources more efficiently compared with the static ones in the related works. In addition, by skillfully designing the dynamics of this variable, the influence of the execution error can be fully counteracted. It is shown that, with the proposed control scheme, the system states can asymptotically converge to zero, instead of to a residual set, while excluding the Zeno phenomenon. To validate the effectiveness and superiority of the proposed scheme, two simulation examples are provided.

This paper deals with the problem of fault‐tolerant control (FTC) for a class of nonlinear uncertain systems against actuator faults using adaptive logic‐based switching control method. The uncertainties under consideration are assumed to be dominated by a bounding system which is linear in growth in the unmeasurable states but can be a continuous function of the system output, with unknown growth rates. Several types of common actuator faults, e.g., bias, loss‐of‐effectiveness, stuck and hard‐over faults are integrated by a unified fault model. By utilizing a novel adaptive logic‐based switching control scheme, the actuator faults can be detected and automatically accommodated by switching from the stuck actuator to the healthy or even partly losing‐effectiveness one with bias, in the presence of large parametric uncertainty. In particular, two switching logics for updating the gain in the output feedback controllers are designed to ensure the global stability of the nominal (fault‐free) system and the boundedness of all closed‐loop signals of the faulty system, respectively. Two simulation examples of an aircraft wing model and a single‐link flexible‐joint robot are given to show the effectiveness of the proposed FTC controller. Copyright © 2010 John Wiley & Sons, Ltd.

In this paper, a high-gain nonlinear observer based fault detection and diagnosis (FDD) approach is proposed for a general class of nonlinear uncertain systems with measured output probability density functions (PDFs). The objective of the presented FDD algorithm is to use the measured output probability density functions (PDFs) and the input of the system to construct a exponential observer-based residual generator such that the fault can be detected and diagnosed. The main result is given in a constructive manner by developing a novel nonlinear observer, without resort to any linearization. By a coordinates transformation, the design of the proposed observer does not necessitate the resolution of kind of linear matrix inequalities (LMIs) and its expression is explicitly given. The exponential convergence of the errors in the presence of parameters uncertainties is proved to guarantee the fastness of the proposed fault diagnosis scheme. Furthermore, the bound of the estimation errors in the presence the faults is minimized by appropriately choosing the parameters of the presented observer. Finally a simulation example is given to illustrate the efficiency of the proposed fault detection and diagnosis method.

ABSTRACTQuick and timely fault detection is of great importance in control systems reliability. Undetected faulty sensors could result in irreparable damages. Although fault detection and isolation (FDI) methods in control systems have received much attention in the last decade, these techniques have not been applied for some classes of nonlinear systems yet. This paper deals with the issues of sensor fault detection and isolation for a class of Lipschitz uncertain nonlinear system. By introducing a coordinate transformation matrix for states and output, the original system is first divided into two subsystems. The first subsystem is affected by uncertainty and disturbance. The second subsystem just has sensor faults. The nonlinear term is separated to linear and pure nonlinear parts. For fault detection, two sliding mode observers (SMO) are designed for the two subsystems. The stability condition is obtained based on the Lyapunov approach. The necessary matrices and parameters are obtained by solving the linear matrix inequality (LMI) problem. Furthermore, two sliding mode observers are designed for fault isolation. Finally, the effectiveness of the proposed approach is illustrated by simulation examples.

This correspondence addresses the problem of designing robust tracking control for a class of uncertain nonlinear MIMO second-order systems. An adaptive neural-network-based output feedback tracking controller is constructed such that all the states and signals involved are uniformly bounded and the tracking error is uniformly ultimately bounded. Only the output measurement is required for feedback. The implementation of the neural network basis functions depends only on the desired reference trajectory. Therefore, the intelligent adaptive output feedback controller developed here possesses the properties of computational simplicity and easy implementation. A simulation example of controlling mass-spring-damper mechanical systems is made to confirm the effectiveness and performance of the developed control scheme.

This study reports adaptive quantized control for a class of uncertain strict‐feedback nonlinear systems with unknown control directions. Combining backstepping technique and Lyapunov stability theory, a systematic analysis method is designed. Based on the disintegration of the hysteresis quantizer, a Nussbaum‐based scheme can be developed to get over the obstacle of the quantized input signal and unknown control directions. Moreover, the number of adaptive laws is small, thereby reducing the computational burden. Then we testify the boundedness of all signals in the closed‐loop system. Besides, the tracking error can converge to an arbitrarily small domain of origin. Finally, a simulation example is provided to verify the feasibility of the control scheme.

This paper is concerned with the problem of output feedback adaptive tracking control for a class of uncertain nonlinear time-delay systems (NTDS) with both uncertain output function and unknown control directions. By introducing a linear state transformation, the original system is transformed into a new system for which output feedback control design becomes feasible. Without the precise information on output function, an input-driven high-gain state observer is presented to estimate the unavailable states of the new system. Moreover, some radial basis function neural networks (RBFNNs) are employed to approximate the lumped unknown nonlinear functions during the procedure of control design. Then, by combining the Lyapunov–Krasovskii functional method, the Nussbaum gain function approach and the backstepping technique, a novel adaptive output feedback control scheme including only one parameter to be updated is developed for such systems. As a result, all signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) while the tracking error can remain in a small neighbourhood of zero. Finally, two simulation examples are given to validate the effectiveness and applicability of the proposed design method.

This paper investigates the problem of adaptive practical tracking control by output feedback for a class of uncertain nonlinear systems without zero dynamics. The uncertain nonlinear perturbed terms of the considered systems are assumed to satisfy a generalised condition which is more relaxed than the triangular-type condition. Furthermore, in contrast to the previous work in the literature, the upper bound of the nonlinearities is a polynomial function of the output, with an unknown growth rate, multiplied by some relaxed conditions of unmeasured states. Due to the presence of unknown parametric uncertainty, a dynamic output compensator with dynamically updated gains is explicitly constructed based on non-separation principle. In particular, we show that for any positive number γ, all the states of the closed-loop systems are globally bounded and the tracking error belongs to the interval [−γ, γ] after some positive finite time. A numerical example illustrates the efficiency of the method.

In the article, the issues of asymptotic adaptive tracking control for the uncertain nonlinear systems in the presence of actuator faults and unknown control directions are investigated. By using the properties of the Nussbaum function and backstepping technique, the problems resulting from the unknown signs of the nonlinear control functions are circumvented successfully. Moreover, a new adaptive asymptotic tracking control method is presented with the fault-tolerant control framework, which is capable of realising zero-tracking performance. The stability of the controlled system is ensured through fractional Lyapunov stability analysis. Finally, the validity of the raised scheme is verified by a simulation example.

Cascade control for a class of uncertain nonlinear systems: a backstepping approach

The design of fault tolerant control (FTC) for a class of uncertain nonlinear systems is studied in this paper. The considered system cannot be feedback linearized, and the nonlinear system functions are all unknown. Besides, some unknown actuator faults and external disturbances enter into the system during operation. A novel fault tolerant controller is proposed by incorporating adaptive fuzzy approximation, backstepping design and robust control into FTC technique. The fuzzy systems which are used to be approximators are nonlinearly parameterized because the fuzzy membership functions are uncertain to designer. Both approximation errors and external disturbances are attenuated by additional control. The designed controller guarantees the closed loop system stable and the output tracking to the reference signal. A simulation example is given to show the effectiveness of the proposed control approach.

Global finite-time adaptive stabilization for nonlinear systems with multiple unknown control directions

SummaryIn this work, a new robust nonlinear feedback control method with dynamic active compensation is proposed; the active control method has been applied to an integral series of finite‐time single‐input single‐output nonlinear system with uncertainty. In further tracking the closed‐loop stability and nonlinear uncertainty, an extended state observer has been employed to solve the immeasurability and nonlinear uncertainty within a nonlinear system. A singular perturbation theory has been used to solve for the finite‐time stability of the closed‐loop system; furthermore, numerical simulations showed that the robust nonlinear feedback controller tracked the uncertainty in a nonlinear Duffing‐type oscillator and has proven the effectiveness of the approximate finite‐time control strategy proposed. By using an approximate finite‐time control approach with active compensation, the uncertainty in a nonlinear system could be accurately estimated and controlled. Copyright © 2017 John Wiley & Sons, Ltd.

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