Frequency‐based nonlinear controller design for regulating systems subjected to time‐domain constraints

Presented is a nonlinear controller design methodology for a class of linear regulating systems subjected to quantitative time‐domain constraints. The design objective is to satisfy an output time‐domain tolerance given an actuator saturation constraint despite an external step disturbance. The goal is to increase the allowable magnitude of the external disturbance beyond that achievable via linear control subject to the time‐domain specifications. The controller design process is comprised of two phases. In the first phase, a linear controller is designed that balances the trade‐off between output regulation and required actuation. To realize the linear design, the time‐domain performance specifications are mapped into amplitude and phase constraints which are in turn imposed on the frequency response of the linear open‐loop transfer function. In the second phase, the linear controller is then augmented with an odd nonlinearity. The coefficient for the nonlinear term is designed such that the gain and phase distortions (in the sense of describing functions) meet the frequency‐domain constraints. The describing function calculation is automated by a recursive Volterra Series relationship. The nonlinear controller design methodology is experimentally verified on the idle speed control of a Ford 4.6L V‐8 fuel injected engine. Copyright © 2000 John Wiley & Sons, Ltd.     

Estimation of Multi‐Order Spectra for Nonlinear Closed‐Loop Systems

In this paper, a multi‐order spectra estimation method is proposed for a nonlinear closed‐loop system based on the Volterra series. Owing to the correlation between the noise and the input, the estimation accuracy is poor when the nonlinear spectra of the plant is obtained using the traditional estimation method. In order to overcome this problem, a two‐step scheme is used to estimate the multi‐order spectrum of a nonlinear system operating in closed‐loop. Firstly, the generalized frequency response functions (GFRFs) from the reference signal to the input of the plant are estimated, and they are used to simulate the noise‐free input spectra of the plant. Secondly, the GFRFs of the controlled plant are estimated using the noise‐free input spectra and the output spectra. Because the GFRFs are multidimensional functions, the required amount of calculation for the estimation is very large. To reduce computational complexity, a simplified GFRF model is adopted to estimate the multi‐order nonlinear spectrum of the plant. In this model, the GFRF is transformed to a one‐dimensional function. Two simulation experiments are provided to illustrate the proposed approach.     

Comparison of image reconstruction by using near‐field and far‐field data for an imperfect conductor

Image reconstruction by using near‐field and far‐field data for an imperfectly conducting cylinder is investigated. A conducting cylinder of unknown shape and conductivity scatters the incident wave in free space and the scattered near and far fields are measured. By using measured fields, the imaging problem is reformulated into an optimization problem and solved by the genetic algorithm. Numerical results show that the convergence speed and final reconstructed results by using near‐field data are better than those obtained by using far‐field data. This work provides both comparative and quantitative information. © 2001 John Wiley & Sons, Inc. Int J RF and Microwave CAE 11: 69–73, 2001.     

Fixed‐time state estimation for a class of switched nonlinear time‐varying systems

This paper deals with the state estimation problem of a class of nonlinear time‐varying systems with switched dynamics. Based on the concept of fixed‐time stability, an observer is designed to reconstruct the continuous state of switched nonlinear time‐varying systems with state jumps, satisfying the minimal dwell‐time condition. Using the past input and output values of the studied system, some sufficient conditions are provided to estimate the state before the next switching. Some numerical results illustrate the effectiveness of the proposed scheme.     

Impact of amplitude weights on power focusing for near‐field‐focused planar arrays

Near‐field‐focused (NFF) arrays have gained great interest owing to its ability to focus the electromagnetic power at a point near to the antenna. The power focusing can basically be reflected by the sidelobe level and the area of the ?3‐dB focal spot at the focal plane. For an ordinary NFF array with the given phase tapering, it would be an effective way to realize the changing of focused power by controlling the feeding‐current amplitude of the array element. In this article, the effects of the amplitude weights of array element rings on the power focusing with reference to an original NFF array are investigated to address this issue. The focus is on the power focusing changing introduced by amplitude weights changing of element rings, in which different cases of amplitude weights changing are considered. The results from amplitude weights changing are compared with that from an original amplitude weights combination, and compared among those from different cases of amplitude weights changing.     

Fault estimation observer design for a class of nonlinear multiagent systems in finite‐frequency domain

This paper focuses on the fault estimation observer design problem in the finite‐frequency domain for a class of Lipschitz nonlinear multiagent systems subject to system components or actuator fault. First, the relative output estimation error is defined based on the directed communication topology of multiagent systems, and an observer error system is obtained by connecting adaptive fault estimation observer and the state equation of the original system. Then, sufficient conditions for the existence of the fault estimation observer are obtained by using a generalized Kalman‐Yakubovich‐Popov lemma and properties of the matrix trace, which guarantee that the observer error system satisfies robustness performance in the finite‐frequency domain. Meanwhile, the pole assignment method is used to configure the poles of the observer error system in a certain area. Finally, the simulation results are presented to illustrate the effectiveness of the proposed method.     

A recursive hierarchical parametric estimation algorithm for nonlinear systems described by Wiener‐Hammerstein models

In this paper, a recursive hierarchical parametric estimation (RHPE) algorithm is proposed for stochastic nonlinear systems which can be described by Wiener‐Hammerstein (W‐H) mathematical models. The formulation of parameters estimation problem is based on the prediction error approach and the gradient techniques. The convergence analysis of the developed RHPE algorithm is derived using stochastic gradient‐based theory. Wiener‐Hammerstein hydraulic process is treated to prove the efficiency of the proposed approach.     

Recursive methods for estimating the radial basis function‐based state‐dependent autoregressive model

Identifying a nonlinear radial basis function‐based state‐dependent autoregressive (RBF‐AR) time series model is the basis for solving the corresponding prediction and control problems. This paper studies some recursive parameter estimation algorithms for the RBF‐AR model. Considering the difficulty of the nonlinear optimal problem arising in estimating the RBF‐AR model, an overall forgetting gradient algorithm is deduced based on the negative gradient search. A numerical method with a forgetting factor is provided to solve the problem of determining the optimal convergence factor. In order to improve the parameter estimation accuracy, the multi‐innovation identification theory is applied to develop an overall multi‐innovation forgetting gradient (O‐MIFG) algorithm. The simulation results indicate that the estimation model based on the O‐MIFG algorithm can capture the dynamics of the RBF‐AR model very well.     

A UD factorization‐based nonlinear adaptive set‐membership filter for ellipsoidal estimation

The extended set‐membership filter (ESMF) for nonlinear ellipsoidal estimation suffers from numerical instability, computation complexity as well as the difficulty in filter parameter selection. In this paper, a UD factorization‐based adaptive set‐membership filter is developed and applied to nonlinear joint estimation of both time‐varying states and parameters. As a result of using the proposed UD factorization, combined with a new sequential and selective measurement update strategy, the numerical stability and real‐time applicability of conventional ESMF are substantially improved. Furthermore, an adaptive selection scheme of the filter parameters is derived to reduce the computation complexity and achieve sub‐optimal estimation. Simulation results have shown the efficiency and robustness of the proposed method. Copyright © 2007 John Wiley & Sons, Ltd.     

Feature‐based recursive observer design for homography estimation and its application to image stabilization

This paper presents a new algorithm for online estimation of a sequence of homographies applicable to image sequences obtained from robotic vehicles equipped with vision sensors. The approach taken exploits the underlying Special Linear group structure of the set of homographies along with gyroscope measurements and direct point‐feature correspondences between images to develop temporal filter for the homography estimate. Theoretical analysis and experimental results are provided to demonstrate the robustness of the proposed algorithm. The experimental results show excellent performance and robustness even in the case of very fast camera motions (relative to frame rate) and severe occlusions.     

Parameter estimation for block‐oriented nonlinear systems using the key term separation

This article considers the parameter estimation problems of block‐oriented nonlinear systems. By using the key term separation, the system output is represented as a linear combination of unknown parameters. We give a key term separation auxiliary model gradient‐based iterative (KT‐AM‐GI) identification algorithm and propose a key term separation auxiliary model three‐stage gradient‐based iterative (KT‐AM‐3S‐GI) identification algorithm by using the hierarchical identification principle. Meanwhile, the multiinnovation theory is used to derived the key term separation auxiliary model three‐stage multiinnovation gradient‐based iterative (KT‐AM‐3S‐MIGI) algorithm. The analysis shows that compared with the KT‐AM‐GI algorithm, the KT‐AM‐3S‐GI algorithm can improve the parameter estimation accuracy and reduce the computational burden. In addition, the KT‐AM‐3S‐MIGI can give more accurate parameter estimates than the KT‐AM‐3S‐GI algorithm and can track time‐varying parameters based on the dynamical window data. This work provides a reference for improving the identification performance of multiinput nonlinear output‐error systems or multivariable nonlinear systems. The simulation results confirm the effectiveness of the proposed algorithm.     

Maximum likelihood‐based gradient estimation for multivariable nonlinear systems using the multiinnovation identification theory

This article considers the identification problems of multivariable input nonlinear systems with unmeasured disturbances. For the identification difficulty caused by the crossproducts between the parameters of the linear block and the nonlinear block, the key term separation technique is adopted to separate the parameters of the nonlinear block from the parameters of the linear block. By combining the model decomposition technique and the hierarchical identification principle, a key term separation‐based maximum likelihood recursive extended stochastic gradient algorithm with reduced computational complexity is presented to estimate all the parameters directly. By introducing the multiinnovation identification theory, a key term separation‐based maximum likelihood multiinnovation extended stochastic gradient algorithm is proposed to improve the parameter estimation accuracy. The simulation results illustrate the effectiveness of the proposed methods.     

Non‐Parametric Identification Method of Volterra Kernels for Nonlinear Systems Excited by Multitone Signal

To solve the problem of Volterra frequency‐domain kernels (VFKs) of nonlinear systems, which can be difficult to identify, we propose a novel non‐parametric identification method based on multitone excitation. First, we have studied the output properties of VFKs of nonlinear systems excited by the multitone signal, and derived a formula for identifying VFKs. Second, to improve the efficiency of the non‐parametric identification method, we suggest an increase in the number of tones for multitone excitation to simultaneously identify multi‐point VFKs with one excitation. We also propose an algorithm for searching the frequency base of multitone excitation. Finally, we use the interpolation method to separate every order output of VFK and extract its output frequency components, then use the derived formula to calculate the VFKs. The theoretical analysis and simulation results indicate that the non‐parametric method has a high precision and convenience of operation, improving the conventional methods, which have the defects of being unable to precisely identify VFKs and identification results are limited to three‐order VFK.     

Design of optimal interval observers using set‐theoretic methods for robust state estimation

This article aims to design an optimal interval observer for discrete linear time‐invariant systems. Particularly, the proposed design method first transforms the interval observer into a zonotopic set‐valued observer by establishing an explicit mathematical relationship between the interval observer and the zonoptopic set‐valued observer. Then, based on the established mathematical relationship, a locally optimal observer gain is designed for the interval observer via the equivalent zonotopic set‐valued observer structure and the Frobenious norm‐based size of zonotopes. Third, considering that the dynamics of the optimal interval observer becomes a discrete linear time‐varying system due to the designed time‐varying optimal gain, an optimization problem to obtain a coordinate transformation matrix and the locally optimal observer gain for the interval observer is formulated and handled. Finally, a theoretic comparison on the conservatism of the interval observer and the zonotopic set‐valued observer is made. At the end of this article, a microbial growth bioprocess is used to illustrate the effectiveness of the proposed method.     

A simplified adaptive sparse digital pre‐distorter for joint mitigation of frequency‐dependent transmitter impairments

The interplay between the unavoidable various nonlinearities of the direct conversion transmitter, such as local oscillator leakage, power amplifier (PA) nonlinearities, and in‐phase and quadrature (I/Q) branch imbalance, and so forth will degrade the communication system performance seriously. To overcome these nonlinear interactive effects, an accurate adaptive sparse behavioral model is proposed for the joint compensation of the transmitter impairments in this article. First, a three‐input nonlinear joint compensation model, which is composed of the nonlinear frequency‐dependent cross terms between the I and Q branches as well as the magnitudes of the input signal, is developed. Second, to prune the redundant terms and reduce the computational complexity of the full three‐input model, an efficient robust quasi‐newton–based adaptive greedy algorithm is developed. To verify the performance of the proposed method, the different imperfect transmitters based on single‐device GaN Class‐F PA and GaN Doherty PA are used for experimental verification and analysis. Experiment results show that the proposed method can efficiently construct a sparse joint compensation model with improved modeling and distortion mitigation capability than the reported I/Q imbalance model, where nonlinear distortion and I/Q imbalance characteristics in the transmitter can be almost completely removed.     

New pixel driving circuit using self‐discharging compensation method for high‐resolution OLED micro displays on a silicon backplane

A new 4T2C pixel circuit formed on a silicon substrate is proposed to realize a high‐resolution 7.8‐μm pixel pitch AMOLED microdisplay. In order to achieve high luminance uniformity, the pixel circuit compensates its Vth variation of the MOSFET for the driving transistor internally by using self‐discharging method. Also presented are 0.5‐in Quad‐VGA and 1.25‐in wide Quad‐XGA microdisplays with the proposed pixel circuit.     

Observer‐based fault estimators using iterative learning scheme for nonlinear time‐delay systems with intermittent faults

This paper deals with the intermittent fault estimation problem for a class of nonlinear time‐delay systems with measurement noise. The time delays are assumed to occur in state vector, nonlinear term as well as output vector, thus reflecting the time delays influence in reality more closely. The aim of the problem is to estimate the intermittent fault by using iterative learning scheme, with the property of index, hence attenuating the influence from measurement noise. Different from existing fault estimating schemes, the state error information and fault estimating information in the previous iteration are used in the current iteration to improve the estimating results. The stability and convergence of iterative learning observer and uniform boundedness of dynamic error system are achieved by using Lyapunov function and optimal function design. Simultaneously, an improved sufficient condition for the existence of such an estimator is established in terms of the linear matrix inequality by the Schur complements and Young relations. Furthermore, the results are both suited for the systems with time‐varying delay and the systems with constant delay. Finally, two numerical examples are proposed to illustrate the effectiveness of the proposed method, and a comparability example is presented to demonstrate its superiority. Copyright © 2017 John Wiley & Sons, Ltd.     

Data‐based output feedback control using least squares estimation method for a class of nonlinear systems

This paper develops a data‐based output feedback control method for a class of nonlinear systems, which have unknown mathematical models. The dynamic model of the system is assumed to be smooth, while the corresponding Jacobian matrices are constant matrices in each sampling period. We employ a zero‐order hold and a fast sampling technique to sample and measure the output signal. When these measured data contain white noises, we use the least squares method to estimate the corresponding Jacobian matrices. The feedback gain matrix is calculated and adjusted adaptively in real time according to them. Theoretical analysis on the convergence condition is provided, and simulation results are used to demonstrate the feasibility of this method. Copyright © 2013 John Wiley & Sons, Ltd.     

UCov: a user‐defined coverage criterion for test case intent verification

The goal of regression testing is to ensure that the behaviour of existing code, believed correct by previous testing, is not altered by new program changes. This paper argues that the primary focus of regression testing should be on code associated with (1) earlier bug fixes and (2) particular application scenarios considered to be important by the developer or tester. Existing coverage criteria do not enable such focus, for example, 100% branch coverage does not guarantee that a given bug fix is exercised or a given application scenario is tested. Therefore, there is a need for a new and complementary coverage criterion in which the user can definea test requirement characterizing a given behaviour to be covered as opposed to choosing from a pool of pre‐defined and generic program elements. This paper proposes this new methodology and calls it UCov, a user‐defined coverage criterion wherein a test requirement is an execution pattern of program elements, and possibly predicates, that a test case must satisfy. The proposed criterion is not meant to replace existing criteria, but to complement them as it focuses the testing on important code patterns that could go untested otherwise. UCov supports test case intent verification. For example, following a bug fix, the testing team may augment the regression suite with the test case that revealed the bug. However, this test case might become obsolete due to code modifications not related to the bug. But if a test requirement characterizing the bug was defined by the user, UCov would determine that test case intent verification failed. The UCov methodology was implemented for the Java platform, was successfully applied onto 10 real‐life case studies and was shown to have advantages over JUnit. The implementation comprises the following tools: (1) TRSpec: allows the user to easily specify complex test requirements; (2) TRCheck: checks whether user‐defined test requirements were satisfied, that is, supports test case intent verification; and (3) TRMigrate: migrates user‐defined test requirements to subsequent versions of a given program. Copyright © 2016 John Wiley & Sons, Ltd.     

Fully autonomous micro air vehicle flight and landing on a moving target using visual–inertial estimation and model‐predictive control

The Mohamed Bin Zayed International Robotics Challenge (MBZIRC) held in spring 2017 was a very successful competition well attended by teams from all over the world. One of the challenges (Challenge 1) required an aerial robot to detect, follow, and land on a moving target in a fully autonomous fashion. In this paper, we present the hardware components of the micro air vehicle (MAV) we built with off the self components alongside the designed algorithms that were developed for the purposes of the competition. We tackle the challenge of landing on a moving target by adopting a generic approach, rather than following one that is tailored to the MBZIRC Challenge 1 setup, enabling easy adaptation to a wider range of applications and targets, even indoors, since we do not rely on availability of global positioning system. We evaluate our system in an uncontrolled outdoor environment where our MAV successfully and consistently lands on a target moving at a speed of up to 5.0 m/s.