Reduced-order H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering via linear matrix inequalities

Necessary and sufficient conditions are derived for the existence of a solution to the continuous-time and discrete-time reduced-order H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filtering problems. These conditions are expressed in terms of linear matrix inequalities (LMIs) and a coupling nonconvex matrix rank constraint. Convex LMI problems are obtained for the full-order and the zeroth-order filtering. An explicit parametrization of all reduced-order filters that correspond to a feasible solution is derived in terms of a contractive matrix, and iterative algorithms are proposed to solve the reduced-order filtering problems using alternating projections.     

Robust H/sub /spl infin// filtering of fuzzy dynamic systems

Robust H/sub /spl infin// filtering of complex nonlinear systems which can be represented by a fuzzy dynamic model is presented. Based on a nominal model, a common positive definite matrix P, and a piecewise continuous Lyapunov function respectively, three kinds of new filtering design methods are proposed using quadratic stability theory and linear matrix inequalities (LMIs). It is shown that the filtering system is quadratically stable with disturbance attenuation if there exists a positive definite matrix solution to a LMI or a set of LMIs. An example is also given to demonstrate the performance of the proposed filtering design methods.     

Explicit formulas for two state Kalman, H/sub 2/ and H/sub /spl infin// target tracking filters

The continuous time, two state, target tracking problem is considered from the Kalman, H/sub 2/, and H/sub /spl infin// filter viewpoint. While previous treatments were numerical in nature, analytic transient responses and infinite horizon solutions with analytic performance expressions are presented here. Tracking indices, involving the maneuver and measurement uncertainties, are shown to have a role for both the steady state and transient responses. In addition, the H/sub /spl infin// tracker has a sensor index involving the performance bound and measurement uncertainty, which, along with the tracking index, plays a significant role in the H/sub /spl infin// tracker expressions. Analytical expressions for the probability of target escape, the probability that the target position will be outside the radar beamwidth (BW), are developed not only to compare the performance of various trackers, but also as a design tool to meet tracking specifications. Examples illustrate the performance of the target trackers as a function of the error gain upper bound.     

Robust neuro-H/sub /spl infin// controller design for aircraft auto-landing

A robust neuro-control scheme is presented for aircraft auto-landing under severe wind conditions and partial loss of control surfaces. In the scheme, a dynamic radial basis function network (RBFN) called minimal resource allocating network (MRAN), that incorporates a growing and pruning strategy, is utilize to aid an H/sub /spl infin// controller using a feedback-error-learning mechanism. The neural network uses only online learning and is not trained "a priori". Specifically, the performance of this neuro-controller for aircraft auto-landing in a microburst along with a partial loss of control effectiveness is analyzed and compared with other control schemes. Simulation studies show that the performance obtained by the neuro-H/sub /spl infin// control scheme is better than the other control schemes under failure and extreme wind conditions.     

Problem of precision missile guidance: LQR and H/sup /spl infin// control frameworks

Addressed here is the precision missile guidance problem where the successful intercept criterion has been defined in terms of both minimizing the miss distance and controlling the missile body attitude with respect to the target at the terminal point. We show that the H/sup /spl infin// control theory, when suitably modified, provides an effective framework for the precision missile guidance problem. The existence of feedback controllers (guidance laws) is investigated for the case of finite horizon and non-zero initial conditions. Both state feedback and output feedback implementations are explored.     

Nonlinear robust observer design for strapdown INS in-flight alignment

A nonlinear observer is proposed for a strapdown inertial navigation system (SDINS) in-flight alignment problem using an H/sub /spl infin// filter Riccati equation and a freedom parameter. The proposed observer improves the filtering stability, convergence, and performance. The characteristics of the observer are analyzed using a Lyapunov function. Simulation results demonstrate a significant reduction in alignment errors by employing the proposed nonlinear observer. The observer is developed in general such that it can be applied to estimating nonlinear systems other than the SDINS in-flight alignment.     

航空发动机控制系统性能恢复设计:H_∞/PR

对于航空发动机这样一类状态及输出矩阵存在摄动的系统,提出了一种直接根据性能指标作为恢复的目标的性能恢复理论设计方法。首先进行具有稳定及性能鲁棒性的状态反馈的H∞控制设计,然后通过设计一个状态观测器使得上述状态反馈控制的特性得以恢复。     

Interval Kalman filtering

The classical Kalman filtering technique is extended to interval linear systems with the same statistical assumptions on noise, for which the classical technique is no longer applicable. Necessary interval analysis, particularly the notion of interval expectation, is reviewed and introduced. The interval Kalman filter (IKF) is then derived, which has the same structure as the classical algorithm, using no additional analysis or computation from such as H/sup /spl infin//-mathematics. A suboptimal IKF is suggested next, for the purpose of real-time implementation. Finally, computer simulations are shown to compare the new interval Kalman filtering algorithm with the classical Kalman filtering scheme and some other existing robust Kalman filtering methods.     

LMI approach to the mixed H2/H∞filtering design for discrete-time uncertain systems

The problem of full-order robust filtering design for discrete-time uncertain linear systems is addressed. The uncertain parameters are assumed to belong to convex bounded domains (polytope type uncertainty). The main purpose is to design a stable linear filter such that the filtering error output signal remains bounded. For that, the parameterization of all linear filters assuring quadratic stability with an H_∞ attenuation constraint to the filtering error system is provided in terms of linear matrix inequalities (LMIs). Then, through the definition of an auxiliary cost, an upper bound to the filtering error variance is minimized, providing a mixed H₂/H _∞ guaranteed cost filtering design. Standard optimization procedures with global convergence assured can be used to solve the problem, as illustrated by an example     

Discrete-time min-max tracking

The problem of optimal state estimation of linear discrete-time systems with measured outputs that are corrupted by additive white noise is addressed. Such estimation is often encountered in problems of target tracking where the target dynamics is driven by finite energy signals, whereas the measurement noise is approximated by white noise. The relevant cost function for such tracking problems is the expected value of the standard H/sub /spl infin// performance index, with respect to the measurement noise statistics. The estimator, serving as a tracking filter, tries to minimize the mean-square estimation error, and the exogenous disturbance, which may represent the target maneuvers, tries to maximize this error while being penalized for its energy. The solution, which is obtained by completing the cost function to squares, is shown to satisfy also the matrix version of the maximum principle. The solution is derived in terms of two coupled Riccati difference equations from which the filter gains are derived. In the case where an infinite penalty is imposed on the energy of the exogenous disturbance, the celebrated discrete-time Kalman filter is recovered. A local iterations scheme which is based on linear matrix inequalities is proposed to solve these equations. An illustrative example is given where the velocity of a maneuvering target has to be estimated utilizing noisy measurements of the target position.     

Modified Costas signal

A modification to the Costas signal is suggested. It involves an increase of the frequency separation /spl Delta/f beyond the inverse of the subpulse duration t/sub b/ combined with adding linear FM (LFM) with bandwidth B, in each subpulse. Specific relationships between /spl Delta/f and B will prevent autocorrelation grating lobes, that would normally appear when t/sub b//spl Delta/f>1.     

PCM/FM aeronautical telemetry in frequency selective multipath interference

The performance of PCM/FM using a delay-line detector in multipath interference is analyzed. In aeronautical telemetry applications, the multipath interference causes a in the signal spectrum which is web modeled by a channel composed of a line-of-sight signal and a strong specular reflection with magnitude /spl Gamma/ and excess delay less than a bit time. Analysis shows that the bit error probability is strongly dependent on the location of the within the spectrum. The bit error probability averaged over the location is also analyzed. For the case of no predetection filtering, the average bit error probability is dependent on the depth of the but not on the width. The loss in performance (relative to the AWGN environment) is bounded by (1-/spl Gamma/)/sup -2/ which is the depth of the . For the case of predetection filtering, the average bit error probability is dependent on both the width and depth of the . The performance loss is bounded by (1-/spl Gamma/)/sup -2/spl Gamma// which is less than that for the case of no predetection filtering.     

一类连续线性切换系统的H∞滤波

研究一类连续线性切换系统的H∞滤波问题.首先,利用共同Lyapunov函数方法,给出了切换系统H∞滤波器的存在条件;其次,利用线性矩阵不等式技术,将H∞滤波器的存在性问题转变成一组线性矩阵不等式(LMIs)的可行性问题,根据LMIs的可行解,给出H∞滤波器的设计方法,由该方法得到的滤波器保证滤波误差动态系统满足给定的H...     

Nullifying ACF grating lobes in stepped-frequency train of LFM pulses

An effective way to increase the bandwidth of a coherent pulse-train is to add a frequency step /spl Delta/f between consecutive pulses. A large /spl Delta/f implies a large total bandwidth, hence improved range resolution. However, when the product of the frequency step times the pulse-duration t/sub p/, is larger than one (t/sub p/ /spl Delta/f > 1), the autocorrelation function (ACF) of the stepped-frequency pulse-train suffers from ambiguous peaks, known as "grating lobes." It is well known that replacing the fixed-frequency pulses with linear FM (LFM) pulses of bandwidth B can reduce those grating lobes. We present a simple analytic expression for the ambiguity function (AF) and ACF of such a signal and derive from it very simple relationships between /spl Delta/f, B, and t/sub p/ that will place s exactly where the grating lobes are located, and thus remove them completely.     

一种应用于混合H2/H∞飞行跟踪控制的扩展LMI方法（英文）

Lyapunov变量和系统矩阵之间的耦合导致混合H2/H∞飞行跟踪控制器设计问题非凸。借助于扩展LMI方法,非凸优化问题被转化为凸的线性矩阵不等式(LMI)表达式。通过引入松弛变量,上述的耦合得以消除。而且,一个充要条件被证明成立以求解混合H2/H∞飞行跟踪控制器,该控制器不仅能够稳定被控系统,并且能够保证系统在正常和故障情况下均满足混合H2/H∞性能指标。这种新的扩展LMI表达式提供了额外的自由度去求解非凸优化问题,并减小了控制器设计的保守性。关于ADMIRE模型的仿真结果说明这种扩展LMI方法的优越性。     

Sigma-mean monitoring for the local area augmentation of GPS

The local area augmentation system (LAAS) is a ground-based differential GPS system being developed to support aircraft precision approach and landing navigation with guaranteed integrity. To quantitatively appraise navigation integrity, an aircraft computes vertical and lateral protection levels using the standard deviation of pseudo-range correction errors, /spl sigma//sub pr/spl I.bar/gnd/, broadcast by the LAAS ground facility (LGF). Thus, one significant integrity risk is that the true standard deviation (sigma) of the pseudo-range correction error distribution may grow to exceed the broadcast correction error sigma or that the true mean of the correction error distribution becomes excessive during LAAS operation. This event may occur due to unexpected anomalies of GPS measurements. To insure that the true error distribution is bounded by a zero-mean Gaussian distribution with the broadcast sigma value, real-time sigma and mean monitoring is necessary. Both direct estimation and cumulative sum (CUSUM) methods are useful to detect violations with acceptable residual integrity risk. For sigma monitoring, the estimation method more rapidly detects small violations of /spl sigma//sub pr/spl I.bar/gnd/ but the fast initial response (FIR) CUSUM variant more promptly detects significant violations that would pose a larger threat to user integrity. For the purposes of mean monitoring, the FIR CUSUM variant is superior to the estimation method in detecting any mean violations. The results demonstrate that real-time protection is achievable against all sizes of sigma/mean failures that can threaten navigation integrity.     

利用遗传算法和LMI设计固定结构H2/H∞飞行控制律

 在设计飞翼式无人机(UAV)的横航向飞行控制系统时,为了使无人机具有较好的动态特性和阵风抑制能力,同时又便于工程实现,提出了固定结构的H₂/H_∞控制律设计方法。对于由此遇到的双线性矩阵不等式(BMI)问题,先用线性矩阵不等式(LMI)方法得到控制律参数和H₂/H_∞性能指标的映射关系,再用此映射关系作为适应度函数,用改进的遗传算法求解使H₂/H_∞性能最优的控制律参数。仿真结果表明,使用固定结构的H₂/H_∞控制方法的无人机动态响应迅速平滑,在侧风干扰下的滚转角振荡幅值仅是原经典控制方法的一半。     

一种鲁棒Sigma-point滤波算法及其在相对导航中的应用

研究了一种鲁棒Sigma-point滤波方法在无人机编队相对导航问题上的应用。该方法采用Huber估计方法,将Sigma-point滤波量测更新转化为求解线性回归问题,新的Sigma-point滤波方法是一种混合L1、L2范数最小估计,当量测噪声为受污染的高斯白噪声时,该方法具有一定的鲁棒性。给出了编队无人机相对惯导方程和相对视线矢量测量原理,应用鲁棒Sigma-point滤波方法融合相对惯导信息和相对视线矢量信息,估计出无人机之间的相对姿态、相对速度和相对位置。仿真结果表明,与扩展卡尔曼滤波和常规Sigma-point滤波相比,鲁棒Sigma-point滤波可以获得更高的估计精度。     

某新机综合飞行/推进系统H∞控制器设计

针对国内某新型战机及其装配的新型涡轮风扇发动机,本文研究了该综合飞行/推进系统一体化控制问题.首先建立了飞行子系统、推进子系统数学模型,在此基础上得到了飞行/推进系统综合模型;利用H∞混合灵敏度控制器设计方法,设计了综合系统控制器,对控制器设计中的一些关键问题作了讨论;最后通过仿真,表明所设计的综合控制系统具有较好的性能.     

Theorem for the combination of bistatic radar measurements using least squares

In order to improve position finding performance, least squares method is often used to combine the measurement sets of bistatic radar system. However, which measurement sets can be combined by least squares method and which cannot have received little attention until now. We address this issue based on 2 measurements of bistatic radar system, for example (/spl rho/, /spl theta//sub T/), and present a new theorem, with proof, which shows that the least squares estimator can be obtained by combining any two measurement sets if these measurement pairs are disjoint. We provide an example that satisfies this condition, which shows that the least square combination of measurement sets yield improved performance especially in the vicinity of the transmitter and the receiver.