Control Gain Sign Research Articles

Adaptive Control With Global Exponential Stability for Parameter-Varying Nonlinear Systems Under Unknown Control Gains.

It is nontrivial to achieve exponential stability even for time-invariant nonlinear systems with matched uncertainties and persistent excitation (PE) condition. In this article, without the need for PE condition, we address the problem of global exponential stabilization of strict-feedback systems with mismatched uncertainties and unknown yet time-varying control gains. The resultant control, embedded with time-varying feedback gains, is capable of ensuring global exponential stability of parametric-strict-feedback systems in the absence of persistence of excitation. By using the enhanced Nussbaum function, the previous results are extended to more general nonlinear systems where the sign and magnitude of the time-varying control gain are unknown. In particular, the argument of the Nussbaum function is guaranteed to be always positive with the aid of nonlinear damping design, which is critical to perform a straightforward technical analysis of the boundedness of the Nussbaum function. Finally, the global exponential stability of parameter-varying strict-feedback systems, the boundedness of the control input and the update rate, and the asymptotic constancy of the parameter estimate are established. Numerical simulations are carried out to verify the effectiveness and benefits of the proposed methods.

Observer-based self-organizing adaptive fuzzy neural network control for non-linear, non-affine systems with unknown sign of control gain and dead zone: A case study of pneumatic actuators

In this paper, an observer-based self-organizing adaptive fuzzy neural network (OSOAFNN) control for non-linear, non-affine systems with the unknown sign of control gain and dead zone is presented. First, a reverse dead-zone compensator scheme to cope with the impact of dead-zone phenomenon existing in control input is investigated. Then, an observed-based control approach to address immeasurable states of the system is proposed, utilizing this approach all states of the system are not needed to be available. A self-organizing fuzzy neural network (SOFNN) technique is presented to approximate the non-linear and unknown function of the observer error dynamics. The proposed fuzzy neural network (FNN) model benefits from two main advantages: (1) the number of rules is automatically generated or pruned and (2) the parameters of antecedent and consequent part of SOFNN are updated through the hybrid tuning, simultaneously. Furthermore, the control law contains a Nussbaum function which deals with the unknown sign of control gain. As the system states are immeasurable, the strictly positive real (SPR) Lyapunov function to guarantee the closed-loop system stability, and tracking error convergence to zero is employed, as well as the boundedness of control parameters are assured through a projection law merged with adaptive law. Finally, the controller is practically implemented on a non-linear, non-affine pneumatic system with unknown dead zone which exploits just a sensor for output measuring. Experimental results show that the proposed controller has satisfactory performance in tracking different trajectories, and tracking error for desired signal case I and case II is limited to [−1.5, 1.5] and [−1,1]mm, respectively.

Fuzzy adaptive control of fractional order chaotic systems with unknown control gain sign using a fractional order Nussbaum gain

In this paper we propose an improved fuzzy adaptive control strategy, for a class of nonlinear chaotic fractional order &#x0028 SISO &#x0029 systems with unknown control gain sign. The online control algorithm uses fuzzy logic sets for the identification of the fractional order chaotic system, whereas the lack of a priori knowledge on the control directions is solved by introducing a fractional order Nussbaum gain. Based on Lyapunov stability theorem, stability analysis is performed for the proposed control method for an acceptable synchronization error level. In this work, the Grunwald-Letnikov method is used for numerical approximation of the fractional order systems. A simulation example is given to illustrate the effectiveness of the proposed control scheme.

Adaptive fuzzy control method for a linear switched reluctance motor

A new direct adaptive fuzzy speed control method for a linear switched reluctance motor with unknown control gain sign is presented. The proposed control system consists of two parts: a fuzzy system and an adaptive law. Fuzzy system approximates an unknown ideal control law with unknown adjustable parameters. After determination of the control law, an appropriate adaptation law is designed to update the adjustable parameters to achieve control objectives. The adaptation law is designed using the error between the unknown ideal control law and fuzzy control law. Unlike previous works, in this study, the unknown control gain sign is taken as an unknown constant parameter and is determined online by an appropriate adaptation law. Proposed control method along with a fuzzy sliding mode speed control and a proportional integral speed control strategies are experimentally studied and the performance index is used to evaluate each strategy. The robustness of the proposed method to the parameters and external load force change has been verified via simulation and experiments. The results indicate that the proposed control method has an acceptable performance.

Adaptive Failure Compensation for Uncertain Systems with Unknown Utility Decrement of Actuators

AbstractUtility decrement caused by actuator aging and unknown failures of actuators is inevitable in practice. However, there is still no result available to compensate for instantaneous failures of actuators with unknown utility decrement. This paper aims at addressing this problem by considering a class of strict‐feedback nonlinear systems. The controller obtained by our proposed control scheme can be divided into two parts. The first one aims to handle the effects of unknown utility decrement, while the second one makes efforts to compensate for the uncertainties caused by unknown failures. Compared with the existing results, the proposed controller is able to compensate not only the uncertainties caused by unknown instantaneous failures but also the time‐varying utility decrement effect of actuators. Moreover, it does not require the prior knowledge about the sign of the constant control gain. In addition, the pre‐estimation functions of time‐varying gain based on the priori knowledge of utility decrements are fully used to improve the performance of the closed‐loop systems. It is shown that the proposed controller can guarantee the boundedness of all closed‐loop signals.

Neuro observer‐based control of pure feedback MIMO systems with unknown control direction

This study focuses on the problem of neural network (NN)-based tracking control for a class of uncertain multiple-input multiple-output non-linear systems in pure feedback form. An observer based on K-filters, is introduced to estimate immeasurable states. In this method, a priori knowledge of the control gain sign is relaxed by using Nussbaum-type technique. NNs are employed to approximate the unknown non-linear functions and an adaptive neural output feedback controller is constructed via backstepping technique. The Lyapunov theorem is applied to prove that the overall closed-loop adaptive control scheme is semi-globally uniformly ultimately bounded. Finally, simulation results are provided to illustrate the design procedure.

Neuro-adaptive backstepping control of SISO non-affine systems with unknown gain sign

This paper presents two neuro-adaptive controllers for a class of uncertain single-input, single-output (SISO) nonlinear non-affine systems with unknown gain sign. The first approach is state feedback controller, so that a neuro-adaptive state-feedback controller is constructed based on the backstepping technique. The second approach is an observer-based controller and K-filters are designed to estimate the system states. The proposed method relaxes a priori knowledge of control gain sign and therefore by utilizing the Nussbaum-type functions this problem is addressed. In these methods, neural networks are employed to approximate the unknown nonlinear functions. The proposed adaptive control schemes guarantee that all the closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB). Finally, the theoretical results are numerically verified through simulation examples. Simulation results show the effectiveness of the proposed methods.

Adaptive prescribed performance control of output feedback systems including input unmodeled dynamics

In this paper, an adaptive prescribed performance tracking control scheme is investigated for a class of output feedback nonlinear systems with input unmodeled dynamics based on dynamic surface control method. A transformation with respect to tracking error is introduced to implement prescribed performance tracking control. A novel description based on Lyapunov function for unmodeled dynamics is presented to deal with state unmodeled dynamics. The negative impact of nonlinear input unmodeled dynamics is offset by using a normalization signal. With the aid of Nussbaum function, the unknown control gain sign is effectively handled in the controller design. By the theoretical analysis, not only the signals in the closed-loop system are proved to be semi-globally uniformly ultimately bounded, but also the transient tracking performance can be guaranteed. Two simulation examples are provided to show the effectiveness of the proposed approach.

A fuzzy adaptive control approach for nonlinear systems with unknown control gain sign

In this paper, a new direct adaptive controller for nonlinear SISO systems with unknown control gain sign is investigated. The controller design is based on the approximation capability of fuzzy systems. A Nussbaum function is incorporated in the adaptation laws to deal with the unknown control direction (i.e. with the unknown control gain sign). The stability of the closed-loop system is proven using a Lyapunov approach. Finally, simulation results are given to verify the feasibility and effectiveness of the proposed controller.

Observer-based indirect adaptive fuzzy control for SISO nonlinear systems with unknown gain sign

This paper develops an observer-based indirect adaptive fuzzy control scheme for a class of single-input single-output (SISO) nonlinear systems. The considered systems have unknown nonlinear functions, unknown control gain sign, and unmeasurable state variables. In this study, fuzzy systems are utilized to approximate unknown nonlinear functions, and a fuzzy adaptive state observer is designed to estimate the unmeasured state. A robust controller is used to compensate for the lumped errors, and the Nussbaum gain function is incorporated in the robust controller to estimate the unknown gain sign. Based on the strictly positive real Lyapunov design approach, the parameter adaptive laws are designed by the fuzzy basis functions rather than by its filtering. It is proved that all the signals in the closed-loop systems are bounded and that the tracking error converges asymptotically to zero. A simulation example is used to demonstrate the effectiveness of the proposed scheme.

Observer-based adaptive robust control of nonlinear nonaffine systems with unknown gain sign

In this paper, a direct adaptive robust controller for a class of SISO nonaffine nonlinear systems is presented. The existence of an ideal controller is proved based on the Implicit Function Theorem. Since the Implicit Function Theorem only guarantees the existence of the controller and does not provide a way to construct it, a neural network is employed to approximate the unknown ideal controller. In addition, an observer is designed to estimate the system states because all the states may not be available for measurements. In this method, a priori knowledge about the sign of control gain is not required and, in order to cope with unknown control direction, the Nussbaum-type technique is used. Moreover, only one adaptive parameter is needed to be updated and also a robust term is used in the control signal to reduce the effect of external disturbances and approximation errors. Furthermore, the stability analysis for the closed-loop system is presented based on the Lyapunov stability method. Theoretical results are illustrated through a simulation example. These simulations show the effectiveness of the proposed method.

Adaptive output feedback neural network control of uncertain non-affine systems with unknown control direction

This paper deals with the problem of adaptive output feedback neural network controller design for a SISO non-affine nonlinear system. Since in practice all system states are not available in output measurement, an observer is designed to estimate these states. In comparison with the existing approaches, the current method does not require any information about the sign of control gain. In order to handle the unknown sign of the control direction, the Nussbaum-type function is utilized. In order to approximate the unknown nonlinear function, neural network is firstly exploited, and then to compensate the approximation error and external disturbance a robustifying term is employed. The proposed controller is designed based on strict-positive-real (SPR) Lyapunov stability theory to ensure the asymptotic stability of the closed-loop system. Finally, two simulation studies are presented to demonstrate the effectiveness of the developed scheme.

Asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity and unknown gain signs

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.

Zero-error tracking control of uncertain nonlinear systems in the presence of actuator hysteresis

In this paper, the problem of adaptive tracking control is addressed for a class of nonlinear systems with unknown constant parameters and unknown actuator nonlinearity. The actuator nonlinearity is modelled as the backlash-like hysteresis, which is described by a differential model. The prior knowledge on the control gain sign is not required, and only the assumption on the reference signal is made. By combining the adaptive backstepping technique with the Nussbaum gain approach, an adaptive compensation controller design approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking error can converge to zero asymptotically despite the presence of the actuator hysteresis. Two simulation examples are included to illustrate the effectiveness of the proposed approach.

Adaptive iterative learning control of discrete‐time varying systems with unknown control direction

SUMMARYWithout using Nussbaum gain, a novel method is presented to solve the unknown control direction problem for discrete‐time systems. The underlying idea is to fully exploit the convergence property of parameter estimates in well‐known adaptive algorithms. By incorporating two modifications into the control and the parameter update laws, respectively, we present an adaptive iterative learning control scheme for discrete‐time varying systems without the prior knowledge of the sign of control gain. It is shown that the proposed adaptive iterative learning control can achieve perfect tracking over the finite time interval while all the closed‐loop signals remain bounded. An illustrative example is presented to verify effectiveness of the proposed scheme. Copyright © 2012 John Wiley & Sons, Ltd.

On the design of observer-based fuzzy adaptive controller for nonlinear systems with unknown control gain sign

In this paper, an observer-based fuzzy adaptive controller for nonlinear systems with unknown control gain sign is investigated. Because the system states are not available for measurement, a tracking-error observer is constructed. In this controller, the adaptive fuzzy system is used to approximate the unknown nonlinearities and the Nussbaum function is incorporated to deal with the unknown control direction (i.e. with the unknown control gain sign). The stability of the closed-loop system is proven using the strictly positive real (SPR) condition and Lyapunov theory. Finally, simulation results are given to verify the feasibility and effectiveness of the proposed controller.

Adaptive tracking H-infinity control for switched nonlinear systems with unknown control gain sign

This paper addresses the adaptive tracking control scheme for switched nonlinear systems with unknown control gain sign. The approach relaxes the hypothesis that the upper bound of function control gain is known constant and the bounds of external disturbance and approximation errors of neural networks are known. RBF neural networks (NNs) are used to approximate unknown functions and an H-infinity controller is introduced to enhance robustness. The adaptive updating laws and the admissible switching signals have been derived from switched multiple Lyapunov function method. It’s proved that the resulting closed loop system is asymptotically Lyapunov stable such that the output tracking error performance and H-infinity disturbance attenuation level are well obtained. Finally, a simulation example of Forced Duffing systems is given to illustrate the effectiveness of the proposed control scheme and improve significantly the transient performance.

Fuzzy adaptive control for a class of nonlinear systems with unknown control gain

This paper deals with the direct adaptive control using fuzzy systems of a class of uncertain SISO nonlinear systems with unknown control gain sign. Within this scheme, a fuzzy system is used to generate directly the control input signal without dynamic system estimation, and the Nussbaum-type function is used to deal with the unknown control gain sign. At first, we present a direct adaptive control scheme for nonlinear systems with the known control gain sign where the parameter adaptation law is driven by tracking and identification errors. Then, this control scheme is generalized for the case of unknown control gain sign. The stability analysis of the closed-loop system is performed using a Lyapunov approach and simulation results are provided to verify the effectiveness of the proposed design.

Adaptive NN control for discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints

This paper focuses on the problem of adaptive neural network tracking control for a class of discrete-time pure-feedback systems with unknown control direction under amplitude and rate actuator constraints. Two novel state-feedback and output-feedback dynamic control laws are established where the function tanh ( ⋅ ) is employed to solve the saturation constraint problem. Implicit function theorem and mean value theorem are exploited to deal with non-affine variables that are used as actual control. Radial basis function neural networks are used to approximate the desired input function. Discrete Nussbaum gain is used to estimate the unknown sign of control gain. The uniform boundedness of all closed-loop signals is guaranteed. The tracking error is proved to converge to a small residual set around the origin. A simulation example is provided to illustrate the effectiveness of control schemes proposed in this paper.

Sign Inverting Control logic for time delayed systems, with experiments

A new control strategy is introduced in this paper for Linear Time Invariant (LTI) systems with a single time delay. Earlier research findings on this class of systems reveal the delay intervals for stable operation, exhaustively, exactly and completely. The newly developed Sign Inverting Control (SIC) logic suggests a very practical procedure of reversing the sign of the feedback control gain, in order to argument the stable delay intervals. The sign reversal concept is based on some interesting mathematical features of LTI-Time Delay Systems (LTI-TDS) which were first recognised under a recent paradigm called the Cluster Treatment of Characteristic Roots (CTCR). Example case studies as well as the experimental trials demonstrate the practicality and the advantages of the new logic, Sign Inverting Control law.