A model of parameter adaptive law with time varying function for robot control

In this article, a model of adaptive control law for controlling robot manipulators using the Lyapunov based theory of guaranteed the stability of uncertain a system is derived. The novelty of obtained result is that the adaptive control algorithm is developed using a parameter estimation rule depending on manipulator kinematic, dynamic parameters and tracking error. This study is supported by a computer simulation and tracking performance has been improved.     

Finite time control of a class of nonlinear switched systems in spite of unknown parameters and input saturation

This article is devoted to the problem of robust stabilization of uncertain nonlinear switched systems with canonical structure. It is assumed that the constant parameters of the subsystems are unknown and cannot be adopted in the controller design. In addition, the dynamics of the subsystems are perturbed via modeling errors and external disturbances. The effects of unknown actuator saturation are compensated via proper adaptive control signals. The derived controller is based on the terminal sliding mode theory and does not need any prior knowledge about the bounds of the lumped uncertain terms. It is proved that once the system states reach the prescribed sliding manifold in a finite time interval, the whole system becomes insensitive to both the lumped uncertainties and the switching dynamics of the system. The common assumption of having known quadratic Lyapunov functions for the subsystems is relaxed and the derived adaptive approach does not force any limitation on the switching signal of the system. Subsequently, non-conservative conditions are provided to guarantee the global finite time bounded stability of the equilibrium state for the overall uncertain nonlinear switched system under arbitrary switching signals. A numerical computer simulation demonstrates the robust performance of the proposed controller.     

Dynamic Responses Analysis of Bridges With Uncertain Parameters Under Moving Loads北大核心CSCD

针对具有不确定参数桥梁在移动荷载作用下的动力响应分析,首次建立了移动荷载作用下桥梁响应分析的多项式维数分解法.将结构的不确定参数视为独立的随机变量,构造了结构动力响应关于不确定参数的随机函数;进而采用一组变量数目逐次增加的成员函数实现结构动力响应的维数分解,并利用Fourier多项式展开推导成员函数的近似显式表达.通过降维积分方法降低概率空间内的积分维度,高效地实现了展开系数的计算.在数值算例中,进行了具有不确定参数桥梁在移动荷载作用下的响应估计,并与Monte-Carlo模拟进行对比,验证了该文方法的精确性和效率.     

Partial difference equation based model reference control of a multiagent network of underactuated aquatic vehicles with strongly nonlinear dynamics

In a recent work, the authors presented an extension of robust model reference adaptive control (MRAC) laws for spatially varying partial differential equations (PDEs) proposed by them earlier for the decentralized adaptive control of heterogeneous multiagent networks with agent parameter uncertainty using the partial difference equations (PdEs) on graphs framework. The examples provided demonstrated the capabilities of this approach under the assumption that individual vehicles executing coordinated maneuvers were fully actuated and characterized by linear dynamics. However, detailed models for autonomous vehicles–whether terrestrial, aerial, or aquatic–are often underactuated and strongly nonlinear. Using this approach, but assuming the plant parameters to be known, this work presents the model reference (MR) control laws without adaptation for the coordination of underactuated aquatic vehicles modeled individually in terms of strongly nonlinear dynamic equations arising from ideal planar hydrodynamics. The case of unknown plant parameters for this class of underactuated agents with complex dynamics is an open problem. The paper is based on an invited talk on adaptive control presented at the 2008 World Congress of Nonlinear Analysts.     

Bond graph model-based system mode identification and mode-dependent fault thresholds for hybrid systems

Hybrid system models exploit the modelling abstraction that fast state transitions take place instantaneously so that they encompass discrete events and the continuous time behaviour for the while of a system mode. If a system is in a certain mode, e.g. two rigid bodies stick together, then residuals of analytical redundancy relations (ARRs) within certain small bounds indicate that the system is healthy. An unobserved mode change, however, invalidates the current model for the dynamic behaviour. As a result, ARR residuals may exceed current thresholds indicating faults in system components that have not happened. The paper shows that ARR residuals derived from a bond graph cannot only serve as fault indicators but may also be used for bond graph model-based system mode identification. ARR residuals are numerically computed in an off-line simulation by coupling a bond graph of the faulty system to a non-faulty system bond graph through residual sinks. In real-time simulation, the faulty system model is to be replaced by measurements from the real system. As parameter values are uncertain, it is important to determine adaptive ARR thresholds that, given uncertain parameters, allow to decide whether the dynamic behaviour in a current system mode is the one of the healthy system so that false alarms or overlooking of true faults can be avoided. The paper shows how incremental bond graphs can be used to determine adaptive mode-dependent ARR thresholds for switched linear time-invariant systems with uncertain parameters in order to support robust fault detection. Bond graph-based hybrid system mode identification as well as the determination of adaptive fault thresholds is illustrated by application to a power electronic system easy to survey. Some simulation results have been analytically validated.     

Modeling of memristor-based chaotic systems using nonlinear Wiener adaptive filters based on backslash operator

Memristor-based chaotic systems have complex dynamical behaviors, which are characterized as nonlinear and hysteresis characteristics. Modeling and identification of their nonlinear model is an important premise for analyzing the dynamical behavior of the memristor-based chaotic systems. This paper presents a novel nonlinear Wiener adaptive filtering identification approach to the memristor-based chaotic systems. The linear part of Wiener model consists of the linear transversal adaptive filters, the nonlinear part consists of nonlinear adaptive filters based on the backslash operator for the hysteresis characteristics of the memristor. The weight update algorithms for the linear and nonlinear adaptive filters are derived. Final computer simulation results show the effectiveness as well as fast convergence characteristics. Comparing with the adaptive nonlinear polynomial filters, the proposed nonlinear adaptive filters have less identification error.     

A Chebyshev interval method for nonlinear dynamic systems under uncertainty

This paper proposes a new interval analysis method for the dynamic response of nonlinear systems with uncertain-but-bounded parameters using Chebyshev polynomial series. Interval model can be used to describe nonlinear dynamic systems under uncertainty with low-order Taylor series expansions. However, the Taylor series-based interval method can only suit problems with small uncertain levels. To account for larger uncertain levels, this study introduces Chebyshev series expansions into interval model to develop a new uncertain method for dynamic nonlinear systems. In contrast to the Taylor series, the Chebyshev series can offer a higher numerical accuracy in the approximation of solutions. The Chebyshev inclusion function is developed to control the overestimation in interval computations, based on the truncated Chevbyshev series expansion. The Mehler integral is used to calculate the coefficients of Chebyshev polynomials. With the proposed Chebyshev approximation, the set of ordinary differential equations (ODEs) with interval parameters can be transformed to a new set of ODEs with deterministic parameters, to which many numerical solvers for ODEs can be directly applied. Two numerical examples are applied to demonstrate the effectiveness of the proposed method, in particular its ability to effectively control the overestimation as a non-intrusive method.     

Optimal input system identification for nonlinear dynamic systems

The estimation accuracy for nonlinear dynamic system identification is known to be maximized by the use of optimal inputs. Few examples of the design of optimal inputs for nonlinear dynamic systems are given in the literature, however. The performance criterion is selected such that the sensitivity of the measured state variables to the unknown parameters is maximized. The application of Pontryagin's maximum principle yields a nonlinear two-point boundary-value problem. In this paper, the boundary-value problem for a simple nonlinear example is solved using two different methods, the method of quasilinearization and the Newton-Raphson method. The estimation accuracy is discussed in terms of the Cramer-Rao lower bound.     

不确定非线性系统的鲁棒自适应控制器

在ｂａｃｋｓｔｅｐｐｉｎｇ程序中，把非线性自适应控制和鲁棒控制连接起来，为参数化的严格反馈系统在不确定性存在的情况下，建立了一种鲁棒自适应控制方案．非线性自适应控制被用来处理系统的线性参数化部分，而鲁棒控制通过引进非线性阻尼项被用来处理不确定性部分．与现有的方案不同，作者给出了非线性阻尼项的无限种选择，而不是仅仅一种选择．通过使用一种合适的选择，能够设计一个鲁棒自适应控制器．它不仅能够保证对不确定性的鲁棒性，而且能够使输出误差任意小，以及用较小的控制努力取得较好的性能．     

Adaptive type-2 fuzzy backstepping control of uncertain fractional-order nonlinear systems with unknown dead-zone

A new problem of adaptive type-2 fuzzy fractional control with pseudo-state observer for commensurate fractional order dynamic systems with dead-zone input nonlinearity is considered in presence of unmatched disturbances and model uncertainties; the control scheme is constructed by using the backstepping and adaptive technique. To avoid the complexity of backstepping design process, the dynamic surface control is used. Also, Interval type-2 Fuzzy logic systems (IT2FLS) are used to approximate the unknown nonlinear functions. By using the fractional adaptive backstepping, fractional control laws are constructed; this method is applied to a class of uncertain fractional-order nonlinear systems. In order to better control performance in reducing tracking error, the PSO algorithm is utilized for tuning the controller parameters. Stability of the system is proven by the Mittag–Leffler method. It is shown that the proposed controller guarantees the boundedness property for the system and also the tracking error can converge to a small neighborhood of the origin. The efficiency of the proposed method is illustrated with simulation examples.     

Trajectory-tracking of 6-RSS Stewart-Gough manipulator by feedback-linearization control using a novel inverse dynamic model based on the force distribution algorithm

ABSTRACT

6-RSS Stewart-Gough parallel manipulator contains six crank-rod limbs connecting the base and moving platforms to each other, forming a 6DOF manipulator. In this paper, we introduce a novel decoupled inverse dynamic model for this manipulator based on the Force Distribution Algorithm. The performance of the proposed model was evaluated in tracking a complex trajectory (of multiple segments with simultaneous translational and rotational motions) using feedback-linearization control in the joint space and compared with that of the Lagrangian inverse dynamic model. Results showed that this model leads to a better performance in feedback-linearization control, especially when the reference trajectory is quantized, and with less calculation burden in comparison with the Lagrangian model. The control system employing both models showed robustness against payload uncertainty on the moving platform (150% of the moving platform’s mass). The performance assessment and the robustness approval were performed in simulation using a Simscape model specifically built for this purpose in the Simulink environment.     

A low-order active fault-tolerant state space self-tuner for the unknown sampled-data nonlinear singular system using OKID and modified ARMAX model-based system identification

In this paper, we present two control schemes for the unknown sampled-data nonlinear singular system. One is an observer-based digital redesign tracker with the state-feedback gain and the feed-forward gain based on off-line observer/Kalman filter identification (OKID) method. The presented control scheme is able to make the unknown sampled-data nonlinear singular system to well track the desired reference signal. The other is an active fault tolerance state-space self-tuner using the OKID method and modified autoregressive moving average with exogenous inputs (ARMAX) model-based system identification for unknown sampled-data nonlinear singular system with input faults. First, one can apply the off-line OKID method to determine the appropriate (low-) order of the unknown system order and good initial parameters of the modified ARMAX model to improve the convergent speed of recursive extended-least-squares (RELS) method. Then, based on modified ARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown sampled-data nonlinear singular system with immeasurable system state. Moreover, in order to overcome the interference of input fault, one can use a fault-tolerant control scheme for unknown sampled-data nonlinear singular system by modifying the conventional self-tuner control (STC). The presented method can effectively cope with partially abrupt and/or gradual system input faults. Finally, some illustrative examples including a real circuit system are given to demonstrate the effectiveness of the presented design methodologies.     

基于极大极小方法的一类非线性系统的自适应控制

研究一类具有非线性不确定参数的非线性系统的自适应模型参考跟踪问题.假设系统的非线性项关于不确定参数是凸或凹的.去掉了在先前有关研究中要求参考模型矩阵有小于零的实特征值的条件.既考虑了状态反馈控制方式,也考虑了输出反馈控制方式.在采用输出反馈控制时,假设非线性项满足李普希兹条件,但李普希兹常数未知.基于一种极大极小方法,提出了一种自适应控制器的设计方法.控制器是连续的,能保证闭环系统的所有变量有界,并且渐近精确跟踪参考模型.举例说明了本结论的有用性.     

Adaptive fuzzy sliding mode control scheme for uncertain systems

Most physical systems inherently contain nonlinearities which are commonly unknown to the system designer. Therefore, in modeling and analysis of such dynamic systems, one needs to handle unknown nonlinearities and/or uncertain parameters. This paper proposes a new adaptive tracking fuzzy sliding mode controller for a class of nonlinear systems in the presence of uncertainties and external disturbances. The main contribution of the proposed method is that the structure of the controlled system is partially unknown and does not require the bounds of uncertainty and disturbance of the system to be known; meanwhile, the chattering phenomenon that frequently appears in the conventional variable structure systems is also eliminated without deteriorating the system robustness. The performance of the proposed approach is evaluated for two well-known benchmark problems. The simulation results illustrate the effectiveness of our proposed controller.     

Design of a coordinated adaptive backstepping tracking control for nonlinear uncertain active suspension system

This paper presents a novel adaptive backstepping tracking control for nonlinear uncertain active suspension system, which can achieve the coordinated control over the sprung-mass acceleration and suspension dynamic displacement for nonlinear uncertain active suspension system based on a developing model-reference system. First, according to adaptive backstepping control principle, this model-reference system is designed with purpose of providing the ideal reference trajectories for the sprung-mass displacement and vertical velocity, respectively. Then, the design of a coordinated adaptive backstepping tracking controller is conducted to make the control plant accurately track the prescribed performances of the model-reference system by virtue of the backstepping technique and Lyapunov stability theory, in which a virtual controller with online parameter regulation rules is designed and implemented to guarantee the stability of vehicle body. Finally, a numerical example is provided to verify the effectiveness of our designed adaptive backstepping tracking controller under various operating scenarios.     

Online affine model identification of nonlinear processes using a new adaptive neuro-fuzzy approach

This paper presents a new online identification algorithm to drive an adaptive affine dynamic model for nonlinear and time-varying processes. The new algorithm is devised on the basis of an adaptive neuro-fuzzy modeling approach. Two adaptive neuro-fuzzy models are sequentially identified on the basis of the most recent input-output process data to realize an online affine-type model. A series of simulation test studies has been conducted to demonstrate the efficient capabilities of the proposed algorithm to automatically identify an online affine-type model for two highly nonlinear and time-varying continuous stirred tank reactor (CSTR) benchmark problems having inherent non-affine dynamic model representations. Adequacy assessments of the identified models have been explored using different evaluation measures, including comparison with an adaptive neuro-fuzzy inference system (ANFIS) as the pioneering and the most popular adaptive neuro-fuzzy system with powerful modeling features.     

Robust synchronization of drive–response chaotic systems via adaptive sliding mode control

A robust adaptive sliding control scheme is developed in this study to achieve synchronization for two identical chaotic systems in the presence of uncertain system parameters, external disturbances and nonlinear control inputs. An adaptation algorithm is given based on the Lyapunov stability theory. Using this adaptation technique to estimate the upper-bounds of parameter variation and external disturbance uncertainties, an adaptive sliding mode controller is then constructed without requiring the bounds of parameter and disturbance uncertainties to be known in advance. It is proven that the proposed adaptive sliding mode controller can maintain the existence of sliding mode in finite time in uncertain chaotic systems. Finally, numerical simulations are presented to show the effectiveness of the proposed control scheme.     

Adaptive Mixture Modeling Metropolis Methods for Bayesian Analysis of Nonlinear State-Space Models

We describe a strategy for Markov chain Monte Carlo analysis of nonlinear, non-Gaussian state-space models involving batch analysis for inference on dynamic, latent state variables and fixed model parameters. The key innovation is a Metropolis–Hastings method for the time series of state variables based on sequential approximation of filtering and smoothing densities using normal mixtures. These mixtures are propagated through the nonlinearities using an accurate, local mixture approximation method, and we use a regenerating procedure to deal with potential degeneracy of mixture components. This provides accurate, direct approximations to sequential filtering and retrospective smoothing distributions, and hence a useful construction of global Metropolis proposal distributions for simulation of posteriors for the set of states. This analysis is embedded within a Gibbs sampler to include uncertain fixed parameters. We give an example motivated by an application in systems biology. Supplemental materials provide an example based on a stochastic volatility model as well as MATLAB code.     

Falling and explosive,dormant, and rising markets via multiple‐regime financial time series models

A multiple‐regime threshold nonlinear financial time series model, with a fat‐tailed error distribution, is discussed and Bayesian estimation and inference are considered. Furthermore, approximate Bayesian posterior model comparison among competing models with different numbers of regimes is considered which is effectively a test for the number of required regimes. An adaptive Markov chain Monte Carlo (MCMC) sampling scheme is designed, while importance sampling is employed to estimate Bayesian residuals for model diagnostic testing. Our modeling framework provides a parsimonious representation of well‐known stylized features of financial time series and facilitates statistical inference in the presence of high or explosive persistence and dynamic conditional volatility. We focus on the three‐regime case where the main feature of the model is to capturing of mean and volatility asymmetries in financial markets, while allowing an explosive volatility regime. A simulation study highlights the properties of our MCMC estimators and the accuracy and favourable performance as a model selection tool, compared with a deviance criterion, of the posterior model probability approximation method. An empirical study of eight international oil and gas markets provides strong support for the three‐regime model over its competitors, in most markets, in terms of model posterior probability and in showing three distinct regime behaviours: falling/explosive, dormant and rising markets. Copyright © 2009 John Wiley & Sons, Ltd.     

Fuzzy confidence interval for pH titration curve

In this paper we present a new method of confidence interval identification for Takagi–Sugeno fuzzy models in the case of the data with regionally changeable variance. The method combines a fuzzy identification methodology with some ideas from applied statistics. The idea is to find, on a finite set of measured data, the confidence interval defined by the lower and upper bounds. The confidence interval which defines the band that contains the measurement values with certain confidence. The method can be used when describing a family of uncertain nonlinear functions or when the systems with uncertain physical parameters are observed. In our example the proposed method is applied to model the pH-titration curve.