Spl Infin Research Articles

H/sub /spl infin// control of differential linear repetitive processes

Repetitive processes are a distinct class of two-dimensional systems (i.e., information propagation in two independent directions) of both systems theoretic and applications interest. They cannot be controlled by direct extension of existing techniques from either standard (termed 1D here) or two-dimensional (2D) systems theory. Here, we give new results on the relatively open problem of the design of physically based control laws using an H/sub /spl infin// setting. These results are for the sub-class of so-called differential linear repetitive processes, which arise in application areas such as iterative learning control.

H/sub /spl infin// control of an irrigation canal pool with a mixed control politics

This paper presents a method to design efficient automatic controllers for an irrigation canal pool, that realize a compromise between the water resource management and the performance in terms of rejecting unmeasured perturbations. This mixed controller design is casted into the H/sub /spl infin// optimization framework, and experimentally tested on a real canal located in Portugal. The experimental results show the effectiveness of the method. We also interpret classical control politics for an irrigation canal (local upstream and distant downstream control) using automatic control tools, and show that our method enables to combine both classical politics, keeping the distant downstream control water management while recovering the local upstream control real-time performance with respect to the user.

Semiblind Channel Estimation for Pulse-Based Ultra-Wideband Wireless Communication Systems

This paper proposes an H/sub /spl infin// based semiblind channel estimation algorithm for pulse-based ultra-wideband (UWB) wireless communication systems. In the proposed scheme, sparsely inserted periodic pilot symbols are exploited to adapt to not only the time-varying channel fading and noise processes but to their changing statistics and potential external disturbances, such as interference. While the existing optimal filtering-based channel estimation schemes, which are optimized mostly for traditional narrowband or wideband systems, require a priori knowledge of the channel and noise statistics, the proposed scheme does not. By further making full use of the channel characteristics unique in UWB systems, the proposed method is thus especially useful for robust operation in the highly frequency-selective UWB indoor channels for which the channel statistics are environment-dependent, and the noise processes do not necessarily satisfy the white Gaussian distribution in the presence of potential narrowband and multiuser interferences. Performance gain of the proposed scheme over the least square method, an existing technique that could also be applied to UWB channels with unknown statistics, and the Wiener filter-based algorithm is also provided.

Exact algorithms for single frame selection on multiaxis Satellites

New multi-axis satellites allow camera imaging parameters to be set during each time slot based on competing demand for images, specified as rectangular requested viewing zones over the camera's reachable field of view. The single frame selection (SFS) problem is to find the camera frame parameters that maximize reward during each time window. We formalize the SFS problem based on a new reward metric that takes into account area coverage and image resolution. For a set of n client requests and a satellite with m discrete resolution levels, we give an algorithm that solves the SFS problem in time O(n/sup 2/m). For satellites with continuously variable resolution (m=/spl infin/), we give an algorithm that runs in time O(n/sup 3/). We have implemented all algorithms and verify performance using random inputs. Note to Practitioners-This paper is motivated by recent innovations in earth imaging by commercial satellites. In contrast to previous methods that required waits of up to 21 days for desired earth- satellite alignment, new satellites have onboard pan-tilt-zoom cameras that can be remotely directed to provide near real-time response to requests for images of specific areas on the earth's surface. We consider the problem of resolving competing requests for images: Given client demand as a set of rectangles on the earth surface, compute camera settings that optimize the tradeoff between pan, tilt, and zoom parameters to maximize camera revenue during each time slot. We define a new quality metric and algorithms for solving the problem for the cases of discrete and continuous zoom values. These results are a step toward multiple frame selection which will be addressed in future research. The metric and algorithms presented in this paper may also be applied to collaborative teleoperation of ground-based robot cameras for inspection and videoconferencing and for scheduling astronomic telescopes.

Modeling by numerical reduction of modes for multivariable control of an optical-fiber draw process

Motivated by a need for a method to derive practical and physical-based dynamic models that capture the essential characteristics of an optical-fiber draw process for precision control of diameter uniformity, we extend the Karhunen-Loeve decomposition technique with a Galerkin procedure to derive a reduced-order model (ROM) for a multivariable distributed-parameter system. We validated the ROM derived from a high-fidelity physics-based model by simulating a modern optical-fiber draw process, the numerical solutions for which have been experimentally verified in our earlier studies. Perturbation studies demonstrated that the 24th-order ROM agrees remarkably well with the original nonlinear semi-two-dimensional and quasi-one-dimensional distributed models. We further examine the efficiency of the ROM in the context of a model-based H/sub /spl infin///LQG fiber drawing control system for the regulation of the fiber diameter and tension. The results show that variations in fiber diameter can be reduced significantly by appropriately distributing the number of retained eigenmodes among the physical state variables in the ROM. We also demonstrate that controlling the surrounding air temperature in addition to the draw speed is very effective in regulating both the fiber diameter and tension while simultaneously keeping the draw speed and temperature fluctuations to a minimum. Note to Practitioners-Because of the stringent production requirements (on draw speed, tension, and temperature), diameter uniformity is a challenging distributed control problem in modern fiber production where progressively larger diameter preforms are drawn at higher speeds. The reduced-order model offers an effective way to observe physical variables in a multivariable distributed-parameter system, which may not be physically measured. While developed in the context of fiber diameter control, the modeling techniques presented in this paper are applicable to other material processing systems, such as deposition thickness control in semiconductor wafer manufacturing.

On the influence of sampling and observation times on estimation of the bandwidth parameter of a Gauss-Markov process

The statistical problem of estimating the bandwidth parameter of a Gauss-Markov (GM) process from a realization of fixed and finite duration T at selectable sampling interval /spl Delta/ is addressed in this paper. As the observation time, T, is fixed and finite, the variance of estimated autocorrelation and continuous-time parameter does not vanish as /spl Delta/ approaches 0. This necessitates a second-order Taylor expansion in deriving the parameter estimator bias and variance. The second-order Taylor expansion produces better bias and variance results than a first-order one does. The distribution of the estimator is also discussed. According to the gradient change of the variance, a key result is that three sample size regions, which are termed finite, large, and very large, corresponding to substantial, gradual, and very slight decrease in the variance of the parameter estimator, respectively, are quantified. In terms of analysis BW, the three regions are (-23,-35),(-35,-55), and (-55,-/spl infin/) dB. The characterization of the tradeoff between the variance decrease and sampling rate results in a practical guideline for choosing sampling rate. These results are applied to the prediction problems of a time invariant GM process to show their value.

Nonsynchronized state estimation of discrete time piecewise linear systems

This paper presents two approaches to H/sub /spl infin// state estimation of discrete-time piecewise linear systems based on a common quadratic Lyapunov function and a piecewise quadratic Lyapunov function, respectively. The key issue addressed in this paper is that the system states and their estimates may stay at different regions of the state space. It is shown that the resulting state estimation error systems is globally stable with l/sub 2/ performance, and the state estimator gains can be obtained by solving a set of linear matrix inequalities. Two simulation examples are finally given to illustrate the performance of the proposed approaches.

Output tracking control of a one-link flexible manipulator via causal inversion

Output tracking control is a challenging problem. This paper introduces a new design procedure for output tracking control of nonminimum phase systems. This new controller achieves stable /spl epsi/-tracking of a reference profile given in real time via a causal inversion approach. In this approach, the nonminimum phase system is first stably inverted on-line to obtain both desired (and stable) state and input trajectories. Then an H/sub /spl infin// optimal controller is used to stabilize the closed-loop system. In contrast to stable inversion, the causal inversion approach does not require precalculation. In contrast to nonlinear regulation, the causal inversion approach avoids the numerical intractability of solving nonlinear PDEs. As an example of the application, a causal inversion-based controller is designed for tip trajectory tracking of a one-link flexible manipulator. Simulation results demonstrate its effectiveness in output tracking.

H/sup /spl infin// adaptive filters for eye blink artifact minimization from electroencephalogram

Two adaptive algorithms (time varying and exponentially weighted) based on the H/sup /spl infin// principles are proposed for the minimization of electrooculogram (EOG) artifacts from corrupted electroencephalographic signals. Performance of the proposed algorithms are compared with the least-mean-square (LMS) algorithm. Improvements in the output signal-to-noise ratio along with time plots are used for the comparison. It is found that the H/sup /spl infin//-based algorithms effectively minimize the EOG artifacts and always outperform the LMS algorithm.

Intelligent Robust Control for Uncertain Nonlinear Time-Varying Systems and Its Application to Robotic Systems

This paper addresses the problem of designing adaptive fuzzy-based (or neural network-based) robust controls for a large class of uncertain nonlinear time-varying systems. This class of systems can be perturbed by plant uncertainties, unmodeled perturbations, and external disturbances. Nonlinear H(infinity) control technique incorporated with adaptive control technique and VSC technique is employed to construct the intelligent robust stabilization controller such that an H(infinity) control is achieved. The problem of the robust tracking control design for uncertain robotic systems is employed to demonstrate the effectiveness of the developed robust stabilization control scheme. Therefore, an intelligent robust tracking controller for uncertain robotic systems in the presence of high-degree uncertainties can easily be implemented. Its solution requires only to solve a linear algebraic matrix inequality and a satisfactorily transient and asymptotical tracking performance is guaranteed. A simulation example is made to confirm the performance of the developed control algorithms.

Remarks on strong stabilization and stable H/sup /spl infin// controller design

A state space based design method is given to find strongly stabilizing controllers for multiple-input-multiple-output plants (MIMO). A sufficient condition is derived for the existence of suboptimal stable H/sup /spl infin// controller in terms of linear matrix inequalities (LMIs) and the controller order is twice that of the plant. A new parameterization of strongly stabilizing controllers is determined using linear fractional transformations (LFTs).

On the optical behavior of the electromagnetic field excited by a semi-infinite electric traveling-wave current

A closed-form solution for the spatial distribution of the electromagnetic field excited by an electric traveling-wave current source is presented. Incomplete Hankel and modified Bessel functions are employed to represent progressive and evanescent wave fields, respectively. It is shown that these fields are expressed in terms of spherical and cylindrical waves exhibiting optical character. Using the properties of the incomplete Hankel and modified Bessel functions, the spatial regions where the fields exist in optical sense are determined. It is shown that different shadow boundaries (SBs), featuring complex shapes, identify discontinuity surfaces for the geometrical optics (GO) field. Three surfaces, one being the well-know Keller's cone, are found to describe in the general case the SBs for both the progressive and the evanescent wave fields. It is demonstrated that these surfaces collapse to the Keller's cone surface in the limit of /spl beta//spl rarr//spl infin/.

Output feedback tracking control of MIMO systems using a fuzzy disturbance observer and its application to the speed control of a PM synchronous motor

One of the most important objectives in the design of control systems is to achieve the good tracking performance in the presence of the internal parameter uncertainty and external disturbance. In this paper, a new multiple-input-multiple-output (MIMO) fuzzy disturbance observer (FDO) based on output measurement is developed to achieve the goal. A filtered signal is introduced to resolve the algebraic loop encountered in the conventional FDO. The contribution of the disturbance observation error /spl zeta/ to updating the parameters of the fuzzy system is analyzed in the sense of L/sub 2/ and L/sub /spl infin//. Then, the MIMO FDO is modified and the high gain observer (HGO) is employed to implement the output tracking control system. It is shown in a rigorous manner that the disturbance observation error, the tracking error and the state observation error converge to a compact set of which size can be kept arbitrarily small. Finally, the suggested method is applied to the speed control of a permanent magnet synchronous motor (PMSM) in the presence of the internal parameter uncertainty and external disturbance. The effectiveness and the feasibility of the suggested method are demonstrated by computer simulation.

Reduced-complexity nonlinear H/sup /spl infin// control of discrete-time systems

In this note, we describe a reduced-complexity solution to the nonlinear H/sup /spl infin// control problem. This reduction applies to systems where some of the states are perfectly known, and is an intermediate problem between full state feedback and the standard measurement feedback problem. The reduction of computational complexity is significant and of practical importance. Online implementation is feasible with 2003 computer technology for a range of practical engineering design problems.

A unified approach to controller design for achieving ISS and related properties

A unified approach to the design of controllers achieving various specified input-to-state stability (ISS) like properties is presented. Both full state and measurement feedback cases are considered. Synthesis procedures based on dynamic programming are given using the recently developed results on controller synthesis to achieve uniform l/sup /spl infin// bound. Our results provide a link between the ISS literature and the nonlinear H/sup /spl infin// design literature.

Designing structure-specified mixed H/sub 2//H/sub /spl infin// optimal controllers using an intelligent genetic algorithm IGA

This brief proposes an efficient method for designing accurate structure-specified mixed H/sub 2//H/sub /spl infin// optimal controllers for systems with uncertainties and disturbance using an intelligent genetic algorithm (IGA). The newly-developed IGA with intelligent crossover based on orthogonal experimental design (OED) is efficient for solving intractable engineering problems with lots of design parameters. The IGA-based method without using prior domain knowledge can efficiently solve design problems of multi-input-multi-output (MIMO) optimal control systems, which is very suitable for practical engineering designs. High performance and validity of the proposed method are evaluated by two test problems, a MIMO distillation column model and a MIMO super maneuverable F18/HARV fighter aircraft system. It is shown empirically that the IGA-based method has good tracking performance, robust stability and disturbance attenuation for both controllers, compared with the existing methods.

The sector bound approach to quantized feedback control

This paper studies a number of quantized feedback design problems for linear systems. We consider the case where quantizers are static (memoryless). The common aim of these design problems is to stabilize the given system or to achieve certain performance with the coarsest quantization density. Our main discovery is that the classical sector bound approach is nonconservative for studying these design problems. Consequently, we are able to convert many quantized feedback design problems to well-known robust control problems with sector bound uncertainties. In particular, we derive the coarsest quantization densities for stabilization for multiple-input-multiple-output systems in both state feedback and output feedback cases; and we also derive conditions for quantized feedback control for quadratic cost and H/sub /spl infin// performances.

The Empirical Distribution of Rate-Constrained Source Codes

Let X = (X/sub 1/,...) be a stationary ergodic finite-alphabet source, X/sup n/ denote its first n symbols, and Y/sup n/ be the codeword assigned to X/sup n/ by a lossy source code. The empirical kth-order joint distribution Q/spl circ//sup k/[X/sup n/,Y/sup n//spl rceil/(x/sup k/,y/sup k/) is defined as the frequency of appearances of pairs of k-strings (x/sup k/,y/sup k/) along the pair (X/sup n/,Y/sup n/). Our main interest is in the sample behavior of this (random) distribution. Letting I(Q/sup k/) denote the mutual information I(X/sup k/;Y/sup k/) when (X/sup k/,Y/sup k/)/spl sim/Q/sup k/ we show that for any (sequence of) lossy source code(s) of rate /spl les/R lim sup/sub n/spl rarr//spl infin//(1/k)I(Q/spl circ//sup k/[X/sup n/,Y/sup n//spl rfloor/) /spl les/R+(1/k)H (X/sub 1//sup k/)-H~(X) a.s. where H~(X) denotes the entropy rate of X. This is shown to imply, for a large class of sources including all independent and identically distributed (i.i.d.). sources and all sources satisfying the Shannon lower bound with equality, that for any sequence of codes which is good in the sense of asymptotically attaining a point on the rate distortion curve Q/spl circ//sup k/[X/sup n/,Y/sup n//spl rfloor//spl rArr//sup d/P(X/sup k/,Y~/sup k/) a.s. whenever P(/sub X//sup k//sub ,Y//sup k/) is the unique distribution attaining the minimum in the definition of the kth-order rate distortion function. Consequences of these results include a new proof of Kieffer's sample converse to lossy source coding, as well as performance bounds for compression-based denoisers.

Inverse optimal adaptive control for attitude tracking of spacecraft

The attitude tracking control problem of a rigid spacecraft with external disturbances and an uncertain inertia matrix is addressed using the adaptive control method. The adaptive control laws proposed in this paper are optimal with respect to a family of cost functionals. This is achieved by the inverse optimality approach, without solving the associated Hamilton-Jacobi-Isaacs partial differential (HJIPD) equation directly. The design of the optimal adaptive controllers is separated into two stages by means of integrator backstepping, and a control Lyapunov argument is constructed to show that the inverse optimal adaptive controllers achieve H/sub /spl infin// disturbance attenuation with respect to external disturbances and global asymptotic convergence of tracking errors to zero for disturbances with bounded energy. The convergence of adaptive parameters is also analyzed in terms of invariant manifold. Numerical simulations illustrate the performance of the proposed control algorithms.

On the relationship between the GLRT and UMPI tests for the detection of signals with unknown parameters

The generalized likelihood ratio test (GLRT) is widely used in signal processing applications such as image processing, wireless communications, medical imaging, classification, and signal detection. However, the GLRT does not have many known properties, other than that it is invariant, uniformly most powerful invariant (UMPI) for problems that fit the linear model, and asymptotically (N/spl rarr//spl infin/) UMPI in general. Since it is invariant, it belongs to the class of tests for which the UMPI test is optimal. In this paper, we consider a general class of detection problems in which unknown signal parameters imply a problem invariance that can be described analytically by orthogonal subgroups. This invariance is natural for problems with unknown signal parameters and, for example, include those of the matched subspace detectors of Scharf and Friedlander. We derive the GLRT and UMPI detectors for this general signal class for the case of Gaussian noise. An expression is found that relates the two test statistics showing the UMPI statistic to be the sum of two terms, one of which is the GLRT. Using this, we find that the GLRT and UMPI tests are asymptotically equivalent as signal-to-noise ratio (SNR) approaches infinity (or as probability of false alarm approaches zero). These results are illustrated by extending an example given by Nicolls and de Jager to show the analytic relationship between the GLRT and UMPI tests. The results indicate that the performance between the tests becomes close at signal-to-noise ratios (SNRs) associated with operating points of the receiver operating curve that are typically of interest in signal detection applications.