Spl Infin Research Articles

Reply to "Comment to 'T-S Fuzzy-Model-Based Robust H/spl infin/ Design for Networked Control Systems With Uncertainties'"

Reply to "Comment to 'T-S Fuzzy-Model-Based Robust H_{/spl infin/} Design for Networked Control Systems With Uncertainties'"

Investigations on the polarimetric behavior of a target near the soil

The polarimetric behavior of the diffracted field from an object located close to the ground is investigated for a varying incidence angle. Here, the field is described by the geometrical theory of diffraction in accordance to its asymptotic formulas (k/spl rarr//spl infin/). As a result, a ray system composed of 13 different rays was implemented for the monostatic case by applying the principle of Fermat. The different spatial and creeping waves give a physical insight in the mechanisms involved in the entire scattering process. By varying the angle from perpendicular to grazing incidence 0/spl deg/-90/spl deg/, geometrical surface shadow boundaries are present for the backscattered field. At such boundaries, the spatial waves are replaced by their corresponding creeping waves, leading to a strong attenuation. The diffracted field for look angles related to the transition zones has a characteristic polarimetric behavior, which can be represented on the Poincare sphere. The typical locations on the sphere can be exploited to get information about the geometrical parameters of the target and its height above the ground.

H/sub 2//H/sub /spl infin// filter design for systems with polytope-bounded uncertainty

This correspondence presents a strategy for robust H/sub 2//H/sub /spl infin// filtering design, with regional pole placement, applied to discrete- or continuous-time linear time-invariant (LTI) systems with polytope-bounded uncertainty. To overcome the conservatism of linear matrix inequality (LMI)-based formulations, the proposed design approach is based on a multiobjective optimization algorithm applied directly in the space of the filter parameters. The H/sub 2/ and H/sub /spl infin// norms, computed in all polytope vertices and in possible "worst case" interior points, are taken as the optimization objectives. A combination of branch-and-bound algorithm and LMI guaranteed cost formulations is applied to compute the coordinates of the worst case norms and to validate the filter design to the whole polytope. Examples are presented to illustrate the effectiveness of the proposed strategy.

Achievable rates of transmitted-reference ultra-wideband radio with PPM

In this letter, we study the achievable rates of practical ultra-wideband (UWB) systems using pulse position modulation (PPM) and transmitted-reference (TR) transceivers. TR obviates the need for complex channel estimation, which is particularly challenging in the context of UWB communications. Based on an upper bound we derive for the error probability with random coding, we establish that for signal-to-noise ratio values of practical interest, PPM-UWB with TR can achieve rates on the order of C(/spl infin/)=P/N/sub 0/ (nats/s), where C(/spl infin/) denotes the capacity of an additive white Gaussian noise channel in the UWB regime for average received power P and noise power spectrum density N/sub 0/.

Response to comments on "H/sub /spl infin// fuzzy control design for nonlinear singularly perturbed systems with pole placement constraints: an LMI Approach"

This note responds to the comments published by Ni Zhao and Fu-Chun Sun in IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS-PART B, vol. 34, no. 6, p. 2422, Dec. 2004. Note that Theorems 3.1 and 3.2 are correct. The errors in the proofs have been fixed.

<tex>$H_infty$</tex>Observer Design for Lipschitz Nonlinear Systems

The problem of observer design for Lipschitz nonlinear systems is considered. A new dynamic framework which is a generalization of previously used Lipschitz observers is introduced and the generalized sufficient condition that ensures asymptotic convergence of the state estimates is presented. The equivalence between this condition and an H/sub /spl infin// optimal control problem which satisfies the standard regularity assumptions in H/sub /spl infin// optimization theory is shown and a parameterization of all possible observers is also presented. A design procedure which is less restrictive than the existing design approaches is proposed, and a simulation example is given to illustrate the observer design.

A comparison of multirate robust track-following control synthesis techniques for dual-stage and multisensing servo systems in hard disk drives

This paper presents the system modeling, design, and analysis of multirate robust track-following controllers for a dual-stage servo system with a microelectromechanical systems (MEMS) microactuator (MA) and an instrumented suspension. A generalized model is constructed which includes a nominal plant, disturbances, uncertainties, and multirate sensing and control. Two major categories of controller design methodologies are considered. The first includes synthesis methodologies that are based on single-input single-output (SISO) design techniques, and includes the sensitivity decoupling (SD) and the PQ methods. In this case, a high sampling-rate inner loop damping control is first implemented using the auxiliary sensor signals. Subsequently, a low-rate outer loop controller is designed for the damped plant using either the SD or PQ design methods. The second category of design methodologies includes those based on multirate, multi-input multi-output (MIMO) design techniques, including mixed H/sub 2//H/sub /spl infin//, mixed H/sub 2///spl mu/, and robust H/sub 2/ synthesis. In this case, a set of controllers, which is periodically time-varying due to multirateness, is designed by explicitly considering plant uncertainty and hence robust stability. Comparisons are made between all the design techniques in terms of nominal H/sub 2/ performance, robust stability, and robust performance between these controllers, when the feedback controller is closed around the full order, perturbed plant. The advantages and disadvantages of each of these methods are discussed, as well as guidelines for their practical implementation.

Robust H/sub /spl infin// filtering for stochastic time-delay systems with missing measurements

In this paper, the robust Hinfin filtering problem is studied for stochastic uncertain discrete time-delay systems with missing measurements. The missing measurements are described by a binary switching sequence satisfying a conditional probability distribution. We aim to design filters such that, for all possible missing observations and all admissible parameter uncertainties, the filtering error system is exponentially mean-square stable, and the prescribed Hinfin performance constraint is met. In terms of certain linear matrix inequalities (LMIs), sufficient conditions for the solvability of the addressed problem are obtained. When these LMIs are feasible, an explicit expression of a desired robust Hinfin filter is also given. An optimization problem is subsequently formulated by optimizing the Hinfin filtering performances. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach

Robust Nonlinear Control Associating Robust Feedback Linearization and<tex>$ H_infty$</tex>Control

In this note, a nonlinear controller for a nonlinear system subject to model uncertainties is proposed. Such a controller associates a robust feedback with a linear H/sub /spl infin// controller. The feedback linearization exactly transforms the nonlinear system into a linear system equal to the linear approximation of the original nonlinear system around a nominal operating point. The robustness of the resulting overall nonlinear controller is proved by theoretical arguments and illustrated through an application example, the control of a magnetic bearing system.

Fuzzy H/sub /spl infin// output feedback control design for singularly perturbed systems with pole placement constraints: an LMI approach

This paper examines the problem of designing an H/sub /spl infin// output feedback controller with pole placement constraints for singular perturbed Takagi-Sugeno (TS) fuzzy models. We propose a fuzzy H/sub /spl infin// output feedback controller that not only guarantees the /spl Lscr//sub 2/-gain of the mapping from the exogenous input noise to the regulated output to be less than some prescribed value, but also ensures closed-loop poles of each subsystem are in a prespecified linear matrix inequality (LMI) region. In order to alleviate the numerical stiffness caused by the singular perturbation /spl epsiv/, the design technique is formulated in terms of a family of /spl epsiv/-independent linear matrix inequalities. The proposed approach can be applied both standard and nonstandard singularly perturbed nonlinear systems. A numerical example is provided to illustrate the design developed in this paper.

Manufacturing Systems: LMI Approach

This note deals with the control of production systems that produce many part types with limited capacity. First, a simple model is used to show that the inventory control problem can be solved using modern control theory. A state feedback controller that forces the cumulative production of the system to track precisely the cumulative demand is proposed. The tracking problem is formulated as an H/sub /spl infin// control problem and the synthesis of the gains of the state feedback controller that guarantees the H/sub /spl infin// tracking performance of the equivalent dynamics is done by solving a given set of linear matrix inequalities (LMIs). A numerical example is provided to show the effectiveness of the developed results. The simple model is then extended to include real facts like inspection and processing times.

Robust /spl Hscr//sub /spl infin// filtering for discrete-time linear systems with uncertain time-varying parameters

This paper deals with the problem of robust /spl Hscr//sub /spl infin// filtering for linear discrete-time state-space models with uncertain time-varying parameters. The parameters enter affinely into the state-space model matrices, and their admissible values and variations are assumed to belong to given intervals. A method is derived for designing a linear stationary asymptotically stable filter with a prescribed /spl Hscr//sub /spl infin// performance, in spite of large parameter uncertainty. The proposed method incorporates information on available bounds on both the admissible values and variation of the uncertain parameters and is based on a Lyapunov function with quadratic dependence on the parameters. The filter design is given in terms of linear matrix inequalities.

<tex>$H_infty$</tex>Control for Discrete-Time Nonlinear Stochastic Systems

In this note, we develop an H/sub /spl infin//-type theory for a large class of discrete-time nonlinear stochastic systems. In particular, we establish a bounded real lemma (BRL) for this case. We introduce the notion of stochastic dissipative systems, analogously to the familiar notion of dissipation associated with deterministic systems, and utilize it in the derivation of the BRL. In particular, this BRL establishes a necessary and sufficient condition, in terms of a certain Hamilton Jacobi inequality (HJI), for a discrete-time nonlinear stochastic system to have l/sub 2/-gain/spl les//spl gamma/. The time-invariant case is also considered as a special case. In this case, the BRL guarantees necessary and sufficient conditions for the system to have l/sub 2/-gain/spl les//spl gamma/, by means of a solution to a certain algebraic HJI. An application of this theory to a special class of systems which is a characteristic of numerous physical systems, yields a more tractable HJI which serves as a sufficient condition for the underlying system to possess l/sub 2/-gain/spl les//spl gamma/. Stability in both the mean square sense and in probability, is also discussed. Systems that possess a special structure (norm-bounded) of uncertainties in their model are considered. Application of the BRL to this class of systems yields a linear state-feedback stabilizing controller which achieves l/sub 2/-gain/spl les//spl gamma/, by means of certain linear matrix inequalities (LMIs).

On the Dead-Time Compensation from<tex>$L^1$</tex>Perspectives

It is known that both H/sup 2/ and H/sup /spl infin// optimization problems for dead-time systems are solved by controllers having the so-called modified Smith predictor (dead-time compensator) structure. This note shows that this is also true for the L/sup 1/ control problem. More precisely, it is demonstrated that the use of the modified Smith predictor enables one to reduce the standard L/sup 1/ problem for systems with a single loop delay to an equivalent delay-free problem. The (sub)optimal solution therefore always contains the modified Smith predictor.

Stability analysis and H/sub /spl infin// controller design of fuzzy large-scale systems based on piecewise Lyapunov functions

This paper presents a novel approach to stability analysis of a fuzzy large-scale system in which the system is composed of a number of Takagi-Sugeno (T-S) fuzzy subsystems with interconnections. The stability analysis is based on Lyapunov functions that are continuous and piecewise quadratic. It is shown that the stability of the fuzzy large-scale systems can be established if a piecewise Lyapunov function can be constructed, and, moreover, the function can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. It is also demonstrated via a numerical example that the stability result based on the piecewise quadratic Lyapunov functions is less conservative than that based on the common quadratic Lyapunov functions. The H infinity controllers can also be designed by solving a set of LMIs based on these powerful piecewise quadratic Lyapunov functions.

H/sub /spl infin// filtering for multiple-time-delay measurements

The aim of this paper is to study the H/sub /spl infin// filtering problem for linear continuous-time systems with both current and multiple-time-delay measurements. The key technique applied for deriving the filter is the reorganized innovation analysis approach in Krein space. A necessary and sufficient condition for the existence of an H/sub /spl infin// filter is derived, and the solution to the H/sub /spl infin// filter is given in terms of solutions of Riccati and matrix differential equations. An example is finally presented to show the effectiveness of the proposed approach.

Optimal estimation for continuous-time systems with delayed measurements

This note focuses on the traditional problem of the Kalman filtering for linear continuous-time systems. Although the problem has been studied widely in the past decades, little work has been done for the time-delayed systems and some fundamental problems remain to be solved. This note proposes a new tool, namely, reorganization innovation analysis approach , to investigate the filtering problem for systems with delayed measurements. The Kalman filter is given in terms of the solution of standard Riccati equations. The performance is clearly demonstrated through analytical results and simulation. The solved problem in this note is related with some more complicated problems such as H/sub /spl infin// fixed-lag smoothing, H/sub /spl infin// control with preview and control with input delays.

Design and Real-Time Implementation of Robust FACTS Controller for Damping Inter-Area Oscillation

An application of a normalized H/sub /spl infin// loop-shaping technique for design and simplification of damping controllers in the liner matrix inequalities (LMI) framework is illustrated in this paper. The solution is sought numerically using LMIs with additional pole-placement constraints. This ensures that the time-domain specifications are met besides robust stabilization. The designed control algorithm is implemented using a rapid prototyping controller. The performance of the controller is validated in real time using a detailed model of the power system implemented using Linux PC-based, multi-processor technology. The coupling between the controller and the power system is through a set of DAC and ADC modules in the analogue domain.

Bounds on expansion in LZ'77-like coding

We investigate the maximum increase in number of phrases that results from changing k consecutive symbols in a string x having length n parsed using an LZ'77-like algorithm. We consider a class of compression algorithms that partition a sequence into a collection y of nonoverlapping, variable-length phrases and encode them. Each phrase either is a singleton or matches a substring that starts to its left. We show that changing a single symbol of x in position i can yield an expansion that is of order O(n-i)/sup 2/3/ as (n-i)/spl rarr//spl infin/. Our lower bound requires an alphabet size of O(n-i)/sup 1/3/. We also show that changing k consecutive symbols starting from position i can yield an expansion having a similar but somewhat more involved form. The paper contains both analytically derived upper and lower bounds, and algorithms for numerically computing tighter bounds. While deriving the bounds, we provide a detailed analysis of how expansion can arise when changing consecutive symbols. This problem is motivated by management policies for computer systems, such as the IBM Memory eXpansion Technology (MXT) or the IBM iSeries compressed disks, that use LZ'77-like coding on small compression units, such as 1-4 kbyte, and store the compressed data in memory or on disk tracks. Here, when a change of a portion of the compression unit occurs, for example, an L2 cache line, or a 512-byte disk sector, the data is recompressed and potentially stored in a different location. Knowing the maximum expansion, rather than the average expansion, is an important factor for designing policies for allocation and management of memory or disk space.

Positive real synthesis using matrix inequalities for mechanical networks: application to vehicle suspension

This paper presents a procedure for the synthesis of positive real controllers based on matrix inequalities. Problems with H/sub 2/ and H/sub /spl infin// cost are considered and the resulting bilinear matrix inequality problems are solved using local, iterative algorithms. The procedure is applied to the synthesis of passive suspensions for the optimization of certain performance measures for a quarter-car model. The characterization of the positive real constraint using matrix inequalities and the use of a new mechanical element called the inerter, permits the optimization over the entire class of positive real admittances and the realization of the resulting admittance using passive elements. The optimization results are compared with previous results obtained using optimization over fixed-structure admittances. The proposed method can reproduce the previous results and achieve better results in certain cases. Results of the experimental testing of a mechanical network involving an inerter are presented.