Adaptive control of uncertain nonlinear systems using mixed backstepping and Lyapunov redesign techniques

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.

Two adaptive control schemes for a class of uncertain nonlinear systems preceded by actuator nonlinearity are presented. We consider two possible input nonlinearities, that is, backlash-like hysteresis and symmetric dead-zone, which can be simultaneously dealt with by using the proposed compensation controllers. The knowledge on the signs of the unknown plant parameters and the parameters in the input nonlinearity models is not required. Only the boundedness of the reference signal is assumed. The Nussbaum gain approach is employed to remove the assumption on the control gain sign. The first scheme is based on the backstepping technique. The final step of the recursive design is crucial for the closed-loop stability. In the second scheme, a direct adaptive control law is designed. The controller has a simple structure and only one adaptation parameter is updated. In both controllers, it is shown that asymptotic tracking is ensured. Two numerical examples are provided to show the effectiveness of the theoretical results.

The problem of adaptive robust control for uncertain nonlinear systems with time-varying delay is considered in this paper. The upper bound of the uncertainty is assumed to be nonlinear functions with unknown coefficients. By using adaptive control method, a class of adaptive robust state feedback controller is proposed. Based on Lyapunov-Krasovskii method and Lyapunov stability theory, it is shown that the controller designed can render the uniform asymptotic stability of the system. Finally, a numerical example is given to show the controller is valid.

This article focuses on the asymptotic tracking control problem for uncertain nonlinear systems subject to both multiple disturbances and parametric uncertainties. To address this issue, a parameter adaptation law is synthesized to deal with the parametric uncertainties, and an adaptive-gain disturbance estimator (ADE) is constructed to estimate the mismatched and matched disturbances, and compensate them in feedforward channels, which eliminates the impact of disturbances on tracking performance. Meanwhile, an updated law for estimator gain driven by the estimation errors is utilized in the ADE when facing unknown upper bounds of disturbances, which reduces the conservatism of estimator gain selection and is beneficial to practical implementation. Based on the parameter adaption technique and the presented ADE approach, a composite controller is proposed to ensure an excellent asymptotic output tracking performance. The stability analysis shows the proposed controller can attain asymptotic tracking performance in the presence of both time-variant disturbances and parametric uncertainties. Comparative simulation results of the application to a robot manipulator reveal the validity of the developed approach.

This paper design an output tracking controller for a class of uncertain nonlinear systems to address the input quantization and output tracking funnel control problem. By the traditional adaptive control and backstepping technique, an adaptive quantized funnel control scheme is designed. It is shown that the presented controller can ensure that arbitrary closed-loop signals are globally uniformly bounded, and the output tracking error is bounded, and held in the prescribed funnel performance functions. The presented control scheme is checked through the simulation result.

In this paper, a robust adaptive fuzzy control for a class of nonlinear uncertain systems preceded by an unknown dead-zone and with unknown upper bound of uncertainties is developed. The dead-zones are quite commonly encountered in many systems (e.g., DC servosystem, robot, and machine tools), are usually poorly known, and may severely limit the performance of control. In addition, the system uncertainties (e.g., parameter variations, or external load, unmodeled dynamics) often exist. Therefore, the controllers are required to deal with the robust stability and performance of the systems with unknown dead-zone and in the presence of uncertainties, whose upper bound is generally unknown. In the beginning, an adaptive dead-zone compensation is employed to improve system performance. Then the unknown system functions and the unknown upper bound of system uncertainties are respectively approximated by fuzzy logic systems with unknown weights. The unknown bounds caused by the learning error of the slope of dead-zone and the system functions are also tackled by an extra learning law. The above weights are all on-line learned to provide for the controller design. Moreover, the projection terms in these learning laws are designed such that the boundedness of the learning weight can be assured.

Based on backstepping technique, an adaptive inverse control scheme is proposed for a class of uncertain nonlinear systems preceded by unknown hysteretic nonlinearities which are described by Krasnosel'skii-Pokrovkii (KP) model. The pseudo-inversion is introduced to compensate the hysteresis nonlinearities and the error caused by the hysteresis model and pseudo-inversion is estimated online by the adaptive controller. To avoid the possible chattering caused by the sign function, a smooth adaptive controller is designed. The proposed controller ensures the uniformly ultimate boundedness of the closed-loop system. Simulation results show the effectiveness of the proposed scheme.

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.

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

A parameter dependent Riccati equation approach is taken to analyze the stability properties of an output feedback adaptive control law design. The adaptive controller is intended to augment a nominal, fixed gain, observer based output feedback control law. Although the formulation is in the setting of model following adaptive control, the realization of the adaptive controll er does not require implementing the reference model. In this regard, the cost of implementing the adaptive controller above that of a fixed gain control law is far less than that of other methods. The error signals are shown to be uniformly ultimately bounded and an expression for the ultimate bound is provided. The control design process and theoretical results are illustrated using a model for wing-rock dynamics. Research in adaptive output feedback control of uncertain nonlinear systems is motivated by the many emerging applications that employ novel actuation devices for active control of flexible structures and fluid flows. These applications include actuators such as piezo-electric films and s ynthetic jets, which are typically nonlinearly coupled to t he plant dynamics they are intended to control. Models for these applications vary from accurate low frequency models to models that crudely approximate the true dynamics even at low frequencies. Examples of applications include active damping of flexible structures, control of aeroservoelasti c aircraft, and active control of flows. Adaptive control can be used to satisfy performance requirements in the presence of large scale parameter uncertainty, and improved safety in the event of actuator failure.

This study proposes the time-/event-triggered adaptive neural control strategies for the asymptotic tracking problem of a class of uncertain nonlinear systems with full-state constraints. First, we design a time-triggered strategy. The effect caused by the residuals of the estimation via radial basis function (RBF) neural networks (NNs), and the reasonable upper bounds on the first derivative of the reference signal and the derivative of each virtual control, can be eliminated by designing appropriate adaptive laws and utilizing the basic properties of RBF NNs. Moreover, the construction of the barrier Lyapunov functions (BLFs) in this work ensures the compliance of the full-state constraints and also holds the asymptotic output tracking performance. Then, based on the time-triggered strategy, we further design a relative threshold event-triggered strategy. The proposed event-triggered adaptive neural controller can solve the main control objective of this work, that is: 1) the full-state constraint requirements of the system are not violated and 2) the output signal asymptotically tracks the reference signal. Compared with the traditional method, the event-triggered strategy can improve the utilization of communication channels and resources and has greater practical significance. Finally, an example of single-link robot under the proposed two strategies illustrates the validity of the constructed controllers.

A novel adaptive control method is designed for the uncertain nonlinear systems with quantized states under the condition that system nonlinearities do not satisfy the Lipschitz condition. In this paper, the global control for an uncertain nonlinear system with quantized states in the case that the system nonlinearities do not satisfy the Lipschitz condition is first achieved. Separation theorem is used to model the uncertainties appropriately and then an adaptive term is designed to help attenuate the effects of system uncertainties. Furthermore, the global boundedness of all signals of the closed-loop system is proved based on the Lyapunov stability theorem. Finally, simulation results are given to demonstrate the effectiveness of the proposed methods.

Simplified adaptive backstepping control for uncertain nonlinear systems with unknown input saturation and its application

Adaptive actuator failure compensation control of uncertain nonlinear systems with guaranteed transient performance

This paper develops a L1 adaptive output-feedback fault-tolerant controller for uncertain nonlinear systems in the presence of unmodeled actuator dynamics and actuator faults. The proposed controller consists of the output predictor, adaptive laws, and the control law. The output predictor is a dynamic system expressed as a linear system with adaptive parameters which mean the matched uncertainties and the unmatched uncertainties. Piecewise-constant adaptive laws are designed to update the adaptive parameters so that the estimation error is driven to zero at each integration time step. The control law with low-pass filters is introduced to compensate for the performance degradation because of system uncertainties, unmodeled actuator dynamics and faults, and to guarantee the uniform boundedness of the input and output signals of the system. Two simulation examples verify the effectiveness of the proposed controller.