Adaptive Parameter Update Laws Research Articles

Adaptive synchronization and anti-synchronization of Julia sets generated by the competitive model

In this paper, we study the fractal behaviour of a competitive model that describes the interaction of plankton allelopathy. This paper aims to establish synchronization and anti-synchronization of Julia sets of two competitive systems with some different parameters by using an adaptive control strategy. Firstly, a discrete version of the competitive model is obtained, and then the Julia set of the discrete version is generated by using the escape-time algorithm. Adaptive controllers and parameter update laws for unknown parameters are designed to achieve synchronization and anti-synchronization of Julia sets. Furthermore, we can determine unknown parameters of the competitive system by using this adaptive control technique. Here, the adaptive synchronization and anti-synchronization of Julia sets are accomplished by its trajectories synchronization and anti-synchronization due to the close relation of trajectories of the system with the Julia set of the system. Numerical simulations are carried out to validate several key theoretical results as well as the efficacy and accuracy of the applied methodologies. Moreover, with the help of this analysis, we can study other models of a similar type.

Position and Attitude Tracking Finite-Time Adaptive Control for a VTOL Aircraft using Global Fast Terminal Sliding Mode Control

In this work, the position and attitude tracking finite-time adaptive control problem of a type of vertical take-off and landing (VTOL) aircraft system is studied. Here, the dynamic of the VTOL aircraft is subjected to external disturbances and unknown nonlinearities. Firstly, radial basis function neural networks are introduced to approximate these unknown nonlinearities, and adaptive weight update laws are proposed to replace unknown ideal weights. Secondly, for the errors generated in the approximation process and the external disturbances of the aircraft system, adaptive parameter update laws are presented. After that, based on the designed global fast terminal sliding mode control functions and adaptive update laws, we present the position tracking control laws and the roll angle control law. Then, based on this, the adaptive global fast terminal sliding control laws for the given aircraft system are finally obtained. Meanwhile, the stability of the aircraft control system is proven by using Lyapunov stability theory and designed adaptive control laws. It is not only ensured that the outputs of the aircraft system can track the given trajectories, but also ensured that the tracking errors can converge to approximately zero within a finite time. Finally, the validity of the designed adaptive control laws is verified through three numerical examples. It can be obtained that the finite-time tracking problems of the given aircraft system can be achieved at 18.8766 s and 14.6340 s under the given parameters. The results are consistent with the theoretical analysis. In addition, under the control laws proposed in this work, the aircraft system can achieve tracking after 9.443 s and 9.674 s and the tracking errors are basically close to zero, which is significantly superior to other control methods considered in this work.

A new adaptive iterative learning control of finite-time hybrid function projective synchronization for unknown time-varying chaotic systems

A new adaptive iterative learning control (AILC) scheme is proposed to solve the finite-time hybrid function projective synchronization (HFPS) problem of chaotic systems with unknown periodic time-varying parameters. Fourier series expansion (FSE) is introduced to deal with the problem of uncertain time-varying parameters. The bound of the expanded remaining items is unknown. A typical convergent series is used to deal with the unknown bound in the design process of the controller. The adaptive iterative learning synchronization controller and parameter update laws are designed. Two different chaotic systems are synchronized asymptotically according to different proportional functions on a finite time interval by Lyapunov stability analysis. The simulation example proves the feasibility and effectiveness of the proposed method.

Fractional-Order Financial System and Fixed-Time Synchronization

This study is concerned with the dynamic investigation and fixed-time synchronization of a fractional-order financial system with the Caputo derivative. The rich dynamic behaviors of the fractional-order financial system with variations of fractional orders and parameters are discussed analytically and numerically. Through using phase portraits, bifurcation diagrams, maximum Lyapunov exponent diagrams, 0–1 testing and time series, it is found that chaos exists in the proposed fractional-order financial system. Additionally, a complexity analysis is carried out utilizing approximation entropy SE and C0 complexity to detect whether chaos exists. Furthermore, a synchronization controller and an adaptive parameter update law are designed to synchronize two fractional-order chaotic financial systems and identify the unknown parameters in fixed time simultaneously. The estimate of the setting time of synchronization depends on the parameters of the designed controller and adaptive parameter update law, rather than on the initial conditions. Numerical simulations show the effectiveness of the theoretical results obtained.

Robust output feedback control for dynamic positioning of turret-moored vessels based on bio-inspired state observer and online constructive fuzzy system

This paper investigates the dynamic positioning control of turret-moored vessels with uncertainties, unknown disturbances and velocities. Firstly, a bio-inspired state observer is proposed based on the bio-inspired neural dynamics model to estimate unknown velocities without vessel dynamics model. Meanwhile, an online constructive fuzzy approximator is designed to approximate uncertainties and unknown disturbances. To ensure fuzzy rules adequate and parsimonious, an online constructive scheme is proposed to adjust the fuzzy system structure without any prior knowledge. Based on the designed state observer and fuzzy approximator, a reliability-based robust output-feedback controller is proposed to make the reliability and heading converge to desired values. A reliability-based matrix is applied into the adaptive fuzzy parameter update law to simplify the stability analysis of closed-loop control system. The convergence of reliability can ensure full utilization of mooring system to maintain the vessel within allowable region. Finally, simulations and comparisons show the performance of proposed methods. • The bio-inspired state observer can make the velocity estimation errors converge to zero without the dynamics of vessels. • An online constructive scheme is proposed based on the distances between the current input and existing fuzzy set only. • The online constructive scheme can ensure the fuzzy rules adequate and parsimonious without any prior knowledge. • A reliability-based matrix is designed to build the relationship between the mooring line tension and vessel motion. • The reliability-based matrix is used in the adaptive fuzzy parameter update law to simplify system stability analysis.

Dynamics and synchronization of the complex simplified Lorenz system

In this paper, the complex simplified Lorenz system is proposed. It is the complex extension of the simplified Lorenz system. Dynamics of the proposed system is investigated by theoretical analysis as well as numerical simulation, including bifurcation diagram, Lyapunov exponent spectrum, phase portraits, Poincaré section, and basins of attraction. The results show that the complex simplified Lorenz system has non-trivial circular equilibria and displays abundant and complicated dynamical behaviors. Particularly, the coexistence of infinitely many attractors, i.e., extreme multistability, is discovered in the proposed system. Furthermore, the adaptive complex generalized function projective synchronization between two complex simplified Lorenz systems with unknown parameter is achieved. Based on Lyapunov stability theory, the corresponding adaptive controllers and parameter update law are designed. The numerical simulation results demonstrate the effectiveness and feasibility of the proposed synchronization scheme. It provides a theoretical and experimental basis for the applications of the complex simplified Lorenz system.

System Characterization and Adaptive Tracking Control of Quadrotors under Multiple Operating Conditions

This paper presents an adaptive controller design framework with input compensation for quadrotor systems, which deals with different system operating conditions with a uniform update law for the controller parameters. The motivation of the work is to handle the situation that existing adaptive control schemes are either restricted to the system equilibrium as the hover condition or unable to deal with the diverse system uncertainties which cause system interactor matrix and high-frequency gain matrix to change. An adaptive control scheme equipped with an input compensator is constructed to make the system to have a uniform interactor matrix and a consistent pattern of the gain matrix signs over different operating conditions, which are key prior design conditions for model reference adaptive control applied to quadrotor systems. To deal with the uncertain system high-frequency gain matrix, a gain matrix decomposition technique is employed to parametrize an error system model in terms of the gain parameters and tracking errors, for the design of an adaptive parameter update law with reduced system knowledge. It is ensured that all closed-loop system signals are bounded, and the system output tracks a reference output asymptotically despite the system parameter uncertainties and the uncertain offsets at non-equilibrium operating conditions. The proposed scheme expands the capacity of adaptive control for quadrotors to operate at multiple operating conditions in the presence of system uncertainties. Simulation results of a quadrotor with the proposed adaptive control scheme are presented to show the desired system performance.

Adaptive Model Recovery Scheme for Multivariable System Using Error Correction Learning

In automatic control design, identifying the system parameters based on an effective identification algorithm is often necessary. Given that many realistic plants are a multivariable system, such identification is considered critical. Most of the available multivariable system identification techniques are designed based on prediction error-correction learning, which produces an unsatisfactory estimation accuracy and low convergence speed, especially in the case of strong external interference. In this article, an adaptive identification scheme is proposed to achieve model recovery for a multivariable system based on a novel error correction learning framework. First, three fictitious sub-models are established by means of the hierarchical principle, in which the high computational burden of the identification approach is avoided. Second, the aforementioned identification method is proposed to recover the parameter information of each sub-model. To improve the identification performance, the identification error information contained in the system data is derived and used to establish a criterion function. According to the identification error and initial parameter error data, a novel criterion function structure relying on the regularization and punishment mechanisms is proposed. Based on this criterion function, a new adaptive error correction learning parameter update law is then deduced. A numerical example and a real-world plant are examined to verify the advantage and practicality of the presented adaptive identification scheme.

Adaptive Fuzzy Feedback Controller Design for Finite-Time Mittag-Leffler Synchronization of Fractional-Order Quaternion-Valued Reaction-Diffusion Fuzzy Molecular Modeling of Delayed Neural Networks

This paper addresses an adaptive fuzzy feedback controller design problem for finite-time Mittag-Leffler synchronization (FTMLS) of fractional-order quaternion-valued reaction-diffusion T-S fuzzy molecular modeling of delayed neural networks. A novel approach is proposed to effectively deal with the joint effects from fuzzy rules and reaction-diffusion terms for the class of T-S fuzzy fractional-order reaction-diffusion delayed quaternion-valued neural networks (FORDDQVNNs) under consideration. By employing Lyapunov stability theory, Caputo fractional derivative, several algebraic criteria are established to guarantee the FTMLS of T-S fuzzy FORDDQVNNs via designed fuzzy feedback controller. Moreover, the adaptive controller and parameter update laws are designed via adaptive control methods. Compared with existing results in the literature, we also show that our results are less conservative than existing ones with these illustrative T-S fuzzy FORDDQVNNs. A numerical example is presented to verify the analysis results and illustrate the effectiveness of the proposed FTMLS conditions.

Adaptive hybrid complex projective combination–combination synchronization in non-identical hyperchaotic complex systems

In this paper, we propose an adaptive hybrid complex projective combination–combination synchronization method to synchronize the hyperchaotic (HC) complex Lorenz system and HC complex Lu system. The adaptive control laws and parameter update laws are derived from making the state of HC complex systems asymptotically stable by using Lyapunov stability theory. During these studies, the coupled HC complex systems (master and slave systems) evolve in a distinct direction with a constant intersection phase angle. Numerical simulations are performed to illustrate the validity and effectiveness of the proposed scheme using MATLAB.

Fault detection and estimation for a class of PIDE systems based on boundary observers

SummaryIn this paper, we propose a simultaneous state estimation and fault estimation approach for a class of first‐order hyperbolic partial integral differential equation systems. Specifically, we consider the multiplicative boundary actuator and sensor faults, ie, unknown fault parameters multiplying by the boundary input or boundary state (ie, output). As a consequence, two difficulties arise immediately: (1) simultaneous estimation of both plant state and faults is a nonlinear problem due to the multiplication between fault parameters and plant signals; (2) no prior information is available to determine the type (actuator or sensor) of faults. To overcome these difficulties, this paper develops adaptive fault parameter update laws and embeds the resulting laws into the plant state observer design. First, we propose new approaches to estimate actuator fault and sensor fault, respectively. Next, we develop a novel method to simultaneously estimate actuator and sensor faults. The proposed observer and update laws, designed using only one boundary measurement, ensure both state estimation and fault parameter estimation. By choosing appropriate Lyapunov functions, we prove that the estimates of state and fault parameters converge to an arbitrarily small neighborhood of their true values. Numerical simulations are used to demonstrate the effectiveness of the proposed estimation approaches.

Adaptive Sensor Fault Detection for Rail Vehicle Suspension Systems

This paper develops an adaptive sensor fault detection scheme for rail vehicle suspension systems with uncertain parameters and sensor faults. A parameterized model of the input-to-output description of the rail vehicle suspension systems is developed, based on which different parameterized output estimators are constructed to detect different unknown sensor fault patterns. As a representative study, three fault detection estimators are presented using estimation errors between the sensor output and the output estimates. Robust adaptive parameter update laws are used to ensure desired system performance of the output estimators, for the construction of the fault detection scheme. The proposed adaptive detection scheme not only can handle large parameter uncertainties in rail vehicle suspension system models, but also can check whether sensor fault occurs in rail vehicle suspension system models or not, and identify the patterns of the sensor faults. Simulation study verifies the effectiveness of the developed adaptive sensor fault detection scheme.

Reliability-Based Robust Online Constructive Fuzzy Positioning Control of a Turret-Moored Floating Production Storage and Offloading Vessel

In this paper, a mathematical model for a floating production storage and offloading (FPSO) vessel is introduced at first. Considering the unknown system parameters and environmental disturbances, we proposed a reliability-based robust online constructive fuzzy controller. An online constructive scheme is constructed to ensure the fuzzy system’s fuzzy rules adequate and parsimonious without any prior knowledge about the number of fuzzy rules and the structure of fuzzy system. In addition, the reliability-based matrix is applied to design a new adaptive fuzzy parameter update law which can not only approximate the unknown term containing the non-square reliability-based matrix but also make it possible to analyze the closed-loop system’s stability, which is quite difficult to be analyzed because the reliability-based matrix is non-square. Our proposed online constructive fuzzy controller can not only maintain the FPSO vessel at the desired reliability and heading but also ensure all signals in the closed-loop control system are bounded. Simulations and comparisons with a reliability-based structure-fixed fuzzy controller show our proposed reliability-based online constructive fuzzy controller can achieve the positioning control by using the fuzzy approximator with adequate and parsimonious fuzzy rules.

Synchronization-based parameter estimation of fractional-order neural networks

This paper focuses on the parameter estimation problem of fractional-order neural network. By combining the adaptive control and parameter update law, we generalize the synchronization-based identification method that has been reported in several literatures on identifying unknown parameters of integer-order systems. With this method, parameter identification and synchronization can be achieved simultaneously. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.

Adaptive Modified Hybrid Robust Projective Synchronization Between Identical and Nonidentical Fractional-Order Complex Chaotic Systems With Fully Unknown Parameters

In this paper, a robust adaptive sliding mode controller is proposed. Under the existence of external disturbances, modified hybrid projective synchronization (MHPS) between two identical and two nonidentical fractional-order complex chaotic systems is achieved. It is shown that the response system could be synchronized with the drive system up to a nondiagonal scaling matrix. An adaptive controller and parameter update laws are investigated based on the Lyapunov stability theorem. The closed-loop stability conditions are derived based on the fractional-order Lyapunov function and Mittag-Leffler function. Finally, numerical simulations are given to verify the theoretical analysis.

Complex Generalized Synchronization and Parameter Identification of Nonidentical Nonlinear Complex Systems.

In this paper, generalized synchronization (GS) is extended from real space to complex space, resulting in a new synchronization scheme, complex generalized synchronization (CGS). Based on Lyapunov stability theory, an adaptive controller and parameter update laws are designed to realize CGS and parameter identification of two nonidentical chaotic (hyperchaotic) complex systems with respect to a given complex map vector. This scheme is applied to synchronize a memristor-based hyperchaotic complex Lü system and a memristor-based chaotic complex Lorenz system, a chaotic complex Chen system and a memristor-based chaotic complex Lorenz system, as well as a memristor-based hyperchaotic complex Lü system and a chaotic complex Lü system with fully unknown parameters. The corresponding numerical simulations illustrate the feasibility and effectiveness of the proposed scheme.

Adaptive Visual Servo Control of Robotic Harvesting Systems

Harvesting efficiency is a critical factor in determining whether robotic harvesting can be economically superior to hand picking. One practical challenge in robotic harvesting is to grasp a moving fruit, where unsuccessful pick cycles may result in lower harvesting efficiency. The fruit motion can be due to exogenous disturbances such as wind gust, canopy unloading, and particularly, fruit detachment forces. In this paper, an adaptive visual servo control law is presented to estimate and subsequently compensate the unknown time-varying fruit motion. The fruit motion in the image plane and along the optical axis is modeled as a second-order spring-mass system. The unknown parameters of fruit motion are identified using an adaptive parameter update law, and a robust feedback term is included in the control law to account for modeling uncertainties. Lyapunov-based stability analysis guarantees uniformly ultimately bounded regulation of the robot to the fruit position. Simulation results are provided to verify the feasibility of the developed controller.

Multivariable adaptive output rejection of unmatched input disturbances

SummaryAdaptive control schemes are developed for uncertain multivariable systems with unmatched input disturbances and are applied to an aircraft flight turbulence compensation problem. Key relative degree conditions from system input and disturbance are derived in terms of system interactor matrices for the design of a nominal state or output feedback control law that ensures desired asymptotic output tracking and disturbance rejection. To deal with an uncertain system high‐frequency gain matrix, a gain matrix decomposition technique is employed to parametrize an error system model in terms of the parameter and tracking errors, for the design of an adaptive parameter update law with reduced system knowledge. Both adaptive state and output feedback control schemes are presented in detail for systems with general interactor matrices, based on an LDS gain decomposition parametrization, and LDU and SDU decomposition‐based designs are also discussed, to develop unified adaptive disturbance rejection techniques for multivariable systems. All closed‐loop system signals are bounded, and the system output tracks a reference output asymptotically despite the system and disturbance parameter uncertainties. Simulation results of an aircraft flight control system with adaptive turbulence compensation are presented to show the desired system disturbance rejection performance. Copyright © 2015 John Wiley & Sons, Ltd.

Adaptive Control and Synchronization of Sprott J System With Estimation Of Fully Unknown Parameters

Abstract This communication develops an adaptive scheme for control and synchronization of Sprott J system with fully unknown parameters. The scheme provides an elegant strategy of designing estimators for identification of the unknown parameters of the underlying dynamical system. Adaptive control and update laws are proposed to globally stabilize the chaotic Sprott J system. A pair of identical Sprott J systems with un- known parameters are globally synchronized with the help of adaptive control and parameter update laws. The results are established using LaSalle invariance principle, which lays down weaker restrictions on the derivatives of the Lyapunov function, and producing more general results. All the results obtained in the paper are global in nature. Numerical simulations are performed to illustrate the validity and effectiveness of the proposed adaptive control and synchronization scheme in the context of the Sprott J system. The parameter identification capability of the scheme is also explored.

Adaptive Synchronization of Fractional Neural Networks with Unknown Parameters and Time Delays

In this paper, the parameters identification and synchronization problem of fractional-order neural networks with time delays are investigated. Based on some analytical techniques and an adaptive control method, a simple adaptive synchronization controller and parameter update laws are designed to synchronize two uncertain complex networks with time delays. Besides, the system parameters in the uncertain network can be identified in the process of synchronization. To demonstrate the validity of the proposed method, several illustrative examples are presented.