Neural network-based robust adaptive control of nonlinear systems with unmodeled dynamics

A neural network-based robust adaptive control design scheme is developed for a class of nonlinear systems represented by input–output models with an unknown nonlinear function and unmodeled dynamics. By on-line approximating the unknown nonlinear functions and unmodeled dynamics by radial basis function (RBF) networks, the proposed approach does not require the unknown parameters to satisfy the linear dependence condition. It is proved that with the proposed control law, the closed-loop system is stable and the tracking error converges to zero in the presence of unmodeled dynamics and unknown nonlinearity. A simulation example is presented to demonstrate the method.     

Controlled systems that are robust with respect to initial data

The notion of robustness with respect to initial data is introduced. This means that several control actions map a fixed initial state to the same final state, and the same control actions map any other initial states to the same final one. The following theorem is proved: a controlled system is robust with respect to initial data iff it admits the maximal group of state symmetries. Examples of investigation of specific controlled systems on robustness with respect to initial conditions are presented.     

一类带不确定输入动态非线性系统的输出反馈鲁棒镇定

研究一类带不确定输入动态非线性系统的输出反馈鲁棒镇定问题.通过在高增益观测器引入新的设计参数,改进了通常的高增益反馈控制的设计方法.在输入动态满足零相对阶最小相位的假设下,基于非分离设计原则给出了动态输出反馈控制器的设计方法,所设计的控制器实现了对任意可允许不确定输入动态的全局鲁棒镇定.     

Stability of non-linear QFT designs based on robust absolute stability criteria

The paper is mainly devoted to the robust stability problem of non-linear QFT designs. The problem is first formulated for SISO non-linear systems, limited in practice to linear-memoryless sector-bounded non-linear interconnections, and in an I/O stability sense. The work investigates several possible robust adaptations of the Circle Criterion, depending on the type of resulting interconnection of linear and non-linear blocks, appearing in the feedback system. Also, the use of the Popov Criterion is investigated as an alternative less conservative than the Circle Criterion in some cases. The proposed techniques are given in usual QFT language, expressed as frequency conditions or boundaries in the Nichols Chart, allowing an easy integration with other design objectives. In addition, multivariable extensions using a conicity condition and the concept of maximal cone are adopted to give stability boundaries in interconnections of SIMO linear-MISO sector-bounded memoryless blocks. All the robust stability criteria are illustrated using significant examples to emphasize the practical application of the resulting techniques.     

Robust approximation‐based adaptive control of multiple state delayed nonlinear systems with unmodeled dynamics

This paper addresses the problem of tracking control for a class of uncertain nonstrict‐feedback nonlinear systems subject to multiple state time‐varying delays and unmodeled dynamics. To overcome the design difficulty in system dynamical uncertainties, radial basis function neural networks are employed to approximate the black‐box functions. Novel continuous functions that deal with whole states uncertainties are introduced in each step of the adaptive backstepping to make the controller design feasible. The robust problem caused by unmodeled dynamics when constructing a stable controller is solved by employing an auxiliary signal to regulate its boundedness. A novel Lyapunov‐Krasovskii functional is developed to compensate for the delayed nonlinearity without requiring the priori knowledge of its upper bound functions. On the basis of the proposed robust adaptive neural controller, all the closed‐loop signals are semiglobal uniformly ultimately bounded with good tracking performance.     

Nonlinear adaptive robust control design for static synchronous compensator based on improved dynamic surface method

In view of single machine to infinite bus system with static synchronous compensator, which is affected by internal and external disturbances, a nonlinear adaptive robust controller is constructed based on the improved dynamic surface control method(IDSC). Compared with the conventional DSC, the sliding mode control is introduced to the dynamic surface design procedure, and the parameter update laws are designed using the uncertainty equivalence criterions. The IDSC method not only reduces the complexity of the controller but also greatly improves the system robustness, speed and accuracy. The derived controller cannot only attenuate the influences of external disturbances against system output, but also has strong robustness to system parameters variance because the damping coefficient is considered in the internal parameter uncertainty. Simulation result reveals that the designed controller can effectively improve the dynamic performances of the power system.     

A note on the robustness of high-gain-observer-based controllers to unmodeled actuator and sensor dynamics

It is shown that a nonlinear output feedback stabilizing controller, which combines a globally bounded state feedback controller with a high-gain observer, is robust with respect to unmodeled fast actuator and sensor dynamics. The actuator and sensor dynamics need to be sufficiently fast relative to the dynamics of the nominal closed-loop system under state feedback, but they need not be faster than the observer dynamics.     

A small gain approach to global stabilization of nonlinear feedforward systems with input unmodeled dynamics

In this paper, we study the global robust stabilization problem of strict feedforward systems subject to input unmodeled dynamics. We present a recursive design method for a nested saturation controller which globally stabilizes the closed-loop system in the presence of input unmodeled dynamics. One of the difficulties of the problem is that the Jacobian linearization of our system at the origin may not be stabilizable. We overcome this difficulty by employing a special version of the small gain theorem to address the local stability, and, respectively, the asymptotic small gain theorem to establish the global convergence property, of the closed-loop system. An example is given to show that a redesign of the controller is required to guarantee the global robust asymptotic stability in the presence of the input unmodeled dynamics.     

Global sensitivity analysis of bogie dynamics with respect to suspension components

The effects of bogie primary and secondary suspension stiffness and damping components on the dynamics behavior of a high speed train are scrutinized based on the multiplicative dimensional reduction method (M-DRM). A one-car railway vehicle model is chosen for the analysis at two levels of the bogie suspension system: symmetric and asymmetric configurations. Several operational scenarios including straight and circular curved tracks are considered, and measurement data are used as the track irregularities in different directions. Ride comfort, safety, and wear objective functions are specified to evaluate the vehicle’s dynamics performance on the prescribed operational scenarios. In order to have an appropriate cut center for the sensitivity analysis, the genetic algorithm optimization routine is employed to optimize the primary and secondary suspension components in terms of wear and comfort, respectively. The global sensitivity indices are introduced and the Gaussian quadrature integrals are employed to evaluate the simplified sensitivity indices correlated to the objective functions. In each scenario, the most influential suspension components on bogie dynamics are recognized and a thorough analysis of the results is given. The outcomes of the current research provide informative data that can be beneficial in design and optimization of passive and active suspension components for high speed train bogies.     

Experimental investigation on adaptive robust controller designs applied to a free-floating space manipulator

This paper aims to formulate and investigate the application of various nonlinear H_∞ control methods to a free-floating space manipulator subject to parametric uncertainties and external disturbances. From a tutorial perspective, a model-based approach and adaptive procedures based on linear parametrization, neural networks and fuzzy systems are covered by this work. A comparative study is conducted based on experimental implementations performed with an actual underactuated fixed-base planar manipulator which is, following the DEM concept, dynamically equivalent to a free-floating space manipulator.     

Why multi-load topology designs based on orthogonal microstructures are in general non-optimal

It is well established that for a compliance constraint, the optimal topology of perforated plates under plane stress tends to that for least-weight trusses (Michell structures) as the volume fraction (i.e. the ratio material volume/available volume) approaches zero. It is shown in this note that for two loading conditions the optimal bar orientations for Michell structures are in general non-orthogonal and hence the assumption of orthogonal microstructures in multi-load plate topology optimization must lead to erroneous results.     

采用区域编码的椭圆对直线裁剪算法

裁剪算法的核心问题是速度问题,而求裁剪窗口和裁剪对象的交点是影响裁剪速度的主要因素。特别是椭圆对线段的裁剪,由于椭圆的方程是二次的,求椭圆与线段的交点 需要求解一元二次方程,涉及开方运算,非常浪费机器时间。为提高裁剪速度,设计出5位的区域编码,利用此技术能够迅速而准确地判断出椭圆和线段的位置关系。对于完全可见 或显然完全不可见的线段立即做出保留或弃掉的决定,避免求交运算;对于能够明确断定与椭圆相交的线段,采用中点分割算法求椭圆和线段的近似交点,避免求解一元二次方程 和开方运算;对于其他情形的线段通过求解一元二次方程来完成裁剪。基于前述思想设计出的椭圆对线段裁剪算法与现有的同类算法相比,算法实现简单,裁剪速度具有较大提高 。     

CLF based designs with robustness to dynamic input uncertainties

The problem of robust stabilization of nonlinear systems in the presence of input uncertainties is of great importance in practical implementation. Stabilizing control laws may not be robust to this type of uncertainty, especially if cancellation of nonlinearities is used in the design. By exploiting a connection between robustness and optimality, “domination redesign” of the control Lyapunov function (CLF) based Sontag's formula has been shown to possess robustness to static and dynamic input uncertainties. In this paper we provide a sufficient condition for the domination redesign to apply. This condition relies on properties of local homogeneous approximations of the system and of the CLF. We show that an inverse optimal control law may not exist when these conditions are violated and illustrate how these conditions may guide the choice of a CLF which is suitable for domination redesign.     

基于线性矩阵不等式的参数不确定性关联模糊大系统的分散鲁棒镇定

讨论了参数不确定性关联模糊大系统的分散鲁棒镇定问题,所考虑的参数不确定性满足范数有界条件.基于李雅普诺夫稳定性理论及大系统分散控制理论,采用分散化PDC(parallel distributed compensation)控制器,给出了保证该关联模糊大系统闭环渐近稳定的LMI形式的充分条件,通过MATLAB软件中的LMI工具箱可求解出这些LMI中的控制器参数.仿真例子说明了所提方法的有效性.     

Internal dynamics of flat nonlinear SISO systems with respect to a non-flat output

In this article, the internal dynamics of flat nonlinear SISO systems with respect to a real non-flat output is investigated in the coordinates of the flat output and its derivatives. The main result constitutes that the parameterization of the real output by the flat output and its derivatives up to a certain order forms a differential equation which is diffeomorphic to the aforementioned internal dynamics.     

The shield that never was: Societies with single-peaked preferences are more open to manipulation and control

Much work has been devoted, during the past 20 years, to using complexity to protect elections from manipulation and control. Many “complexity shield” results have been obtained—results showing that the attacker’s task can be made NP-hard. Recently there has been much focus on whether such worst-case hardness protections can be bypassed by frequently correct heuristics or by approximations. This paper takes a very different approach: We argue that when electorates follow the canonical political science model of societal preferences the complexity shield never existed in the first place. In particular, we show that for electorates having single-peaked preferences, many existing NP-hardness results on manipulation and control evaporate.     

Periocular-based biometrics robust to eye rotation based on polar coordinates

Conventional iris recognition requires a high-resolution camera equipped with a zoom lens and a near-infrared illuminator to observe iris patterns. Moreover, with a zoom lens, the viewing angle is small, restricting the user’s head movement. To address these limitations, periocular recognition has recently been studied as biometrics. Because the larger surrounding area of the eye is used instead of iris region, the camera having the high-resolution sensor and zoom lens is not necessary for the periocular recognition. In addition, the image of user’s eye can be captured by using the camera having wide viewing angle, which reduces the constraints to the head movement of user’s head during the image acquisition. Previous periocular recognition methods extract features in Cartesian coordinates sensitive to the rotation (roll) of the eye region caused by in-plane rotation of the head, degrading the matching accuracy. Thus, we propose a novel periocular recognition method that is robust to eye rotation (roll) based on polar coordinates. Experimental results with open database of CASIA-Iris-Distance database (CASIA-IrisV4) show that the proposed method outperformed the others.     

Feedback control of uncertain systems: robustness with respect to neglected actuator and sensor dynamics†

A purely algebraic polynomial approach is used to optimize the discrete-time feedback controller for a multivariable plant subject to stochastic reference and disturbance and coloured output measurement noise. A quadratic cost criterion with dynamic weightings is used that includes sensitivity and complementary sensitivity as well as tracking error and control input. The method involves the solution of only one diophantine equation.     

A multi-point reduced-order modeling approach of transient structural dynamics with application to robust design optimization

Predicting the transient response of structures by high-fidelity simulation models within design optimization and uncertainty quantification often leads to unacceptable computational cost. This paper presents a reduced-order modeling (ROM) framework for approximating the transient response of linear elastic structures over a range of design and random parameters. The full-order response is projected onto a lower-dimensional basis spanned by modes computed from a proper orthogonal decomposition (POD) of full-order model simulation results at multiple calibration points. The basis is further enriched by gradients of the POD modes with respect to the design/random parameters. A truncation strategy is proposed to compensate for the increase in basis vectors due to the proposed enrichment strategies. The accuracy, efficiency and robustness of the proposed framework are studied with a two-dimensional model problem. The numerical results suggest that the proposed ROM approach is well suited for large parameter changes and that the number of basis vectors needs to be increased only linearly with the number of design and random parameters to maintain a particular ROM performance. The application of the proposed ROM approach to robust shape optimization demonstrates significant savings in computational cost over using full-order models. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy’s National Nuclear Security Administration under Contract DE-AC04-94AL85000.     

Image authentication based on robust image hashing with geometric correction

Multimedia Tools and Applications - Image authentication based on robust image hashing has been widely discussed with continuous improvements. However, most of the existing methods misjudge the...