Robust H/sub /spl infin// control of singular impulsive systems with uncertain perturbations

This paper discusses the problem of robust H/sub /spl infin// control for singular impulsive uncertain systems. Some new fundamental properties of singular systems with impulse effect are derived. Based on the Riccati inequality approach, sufficient conditions for robust H/sub /spl infin// criteria of the corresponding singular impulsive closed-loop systems are established. A simple approach to the design of a robust impulsive controller is then presented. Finally, a design example and simulation results are given to demonstrate the effectiveness of the proposed approach.     

Robust H/sub /spl infin// controller design with recurrent neural network for linear synchronous motor drive

In this paper, a robust controller design with H/sub /spl infin// performance using a recurrent neural network (RNN) is proposed for the position tracking control of a permanent-magnet linear synchronous motor. The proposed robust H/sub /spl infin// controller, which comprises a RNN and a compensating control, is developed to reduce the influence of parameter variations and external disturbance on system performance. The RNN is adopted to estimate the dynamics of the lumped plant uncertainty, and the compensating controller is used to eliminate the effect of the higher order terms in Taylor series expansion of the minimum approximation error. The tracking performance is ensured in face of parameter variations, external disturbance and RNN estimation error once a prespecified H/sub /spl infin// performance requirement is achieved. The synthesis of the RNN training rules and compensating control are based on the solution of a nonlinear H/sub /spl infin// control problem corresponding to the desired H/sub /spl infin// performance requirement, which is solved via a choice of quadratic storage function. The proposed control method is able to track both the periodic step and sinusoidal commands with improved performance in face of large parameter perturbations and external disturbance.     

Low-order H/sub /spl infin// controller design for an active suspension system via LMIs

An application of a new controller order reduction technique with stability and performance preservation based on linear matrix inequality optimization to an active suspension system is presented. In this technique, the rank of the residue matrix of a proper rational approximation of a high-order H/sub /spl infin// controller subject to the H/sub /spl infin//-norm of a frequency-weighted error between the approximated controller and the high-order H/sub /spl infin// controller is minimized. However, because solving this matrix rank minimization problem is very difficult, the rank objective function is replaced with a nuclear-norm that can be reduced to a semidefinite program so that it can be solved efficiently. Application to the active suspension system of the Automatic Laboratory of Grenoble provides a fourth-order controller. The experimental results show that the control specifications are met to a large extent.     

Improved bounded-real-lemma representation and H/sub /spl infin// control of systems with polytopic uncertainties

This brief concerns the problem of the bounded-real-lemma (BRL) representation and H/sub /spl infin// control of linear systems with real convex polytopic uncertainties. In order to use a parameter-dependent Lyapunov function for a system with polytopic uncertainties, the derivative term for the state, which is in the derivative of the Lyapunov function, is reserved; and free weighting matrices are used to express the relationship between the terms of the system equation. This yields a new linear-matrix-inequality approach to BRL representation. In addition, this method is extended to the design of a state-feedback controller that solves the H/sub /spl infin// control problem. Numerical examples demonstrate that the proposed method is effective and is an improvement over previous ones.     

Design of Luenberger state observers using fixed-structure H/sub /spl infin// optimization and its application to fault detection in lane-keeping control of automated vehicles

Lane-keeping control forms an integral part of fully automated intelligent vehicle highway systems (IVHS) and its reliable operation is critical to the operation of an automated highway. We present the design of a fault detection filter for the lane-keeping control systems onboard vehicles used by California-PATH, USA in its automated highways program. We use a Luenberger structure for the fault detection filters and tune the observer gains based on an H/sub /spl infin//-based cost. Such a choice of cost was motivated by the need to explicitly incorporate frequency-domain-based performance objectives. The linear matrix inequality (LMI)-based formulation of an H/sub /spl infin// optimization problem of Luenberger state observers does not allow for the augmentation with dynamic performance weightings in the optimization objective, since it makes the problem a nonconvex optimization problem. We present an algorithm to locally solve the problem of the design of Luenberger state observers using H/sub /spl infin// optimization by transforming the problem into an H/sub /spl infin// static output feedback controller problem. Experimental results demonstrate the efficacy of the tuning methodology by comparing the fault detection performance of filters that use H/sub /spl infin// Luenberger observers versus those that use Kalman filters. Implementation issues of the observers are also discussed.     

Mixed-objective optimization of a track-following controller using linear matrix inequalities

This work describes a design method for track-following controllers in data storage drives using mixed-objective optimization. Stability and performance requirements on the track following controller are established using norm conditions, which are converted to linear matrix inequalities (LMIs). The minimization of the position error in the root-mean-square sense is shown to be an H/sub 2/ norm minimization problem, whereas the vibration rejection requirements are expressed as H/sub 2/ or H/sub /spl infin// norm constraints. The robust stability requirement is enforced by an H/sub /spl infin// norm constraint. The mixed-norm problem is converted into a constrained minimization problem in LMIs, which is solved by convex optimization algorithms. The controller is designed directly in the discrete time domain to avoid typical degradation caused by continuous-time to discrete-time conversion. The proposed controller is implemented and tested on production hard disk drives. Experiments show that the proposed controller reduces the position error by 7%-11% while maintaining comparable stability margins and vibration rejection capability compared with the conventional controllers.     

An H/sub /spl infin// optimization and its fast algorithm for time-variant system identification

In some estimation or identification techniques, a forgetting factor /spl rho/ has been used to improve the tracking performance for time-varying systems. However, the value of /spl rho/ has been typically determined empirically, without any evidence of optimality. In our previous work, this open problem is solved using the framework of H/sub /spl infin// optimization. The resultant H/sub /spl infin// filter enables the forgetting factor /spl rho/ to be optimized through a process noise that is determined by the filter Riccati equation. This paper seeks to further explain the previously derived H/sub /spl infin// filter, giving an H/sub /spl infin// interpretation of its tracking capability. Additionally, a fast algorithm of the H/sub /spl infin// filter, called the fast H/sub /spl infin// filter, is presented when the observation matrix has a shifting property. Finally, the effectiveness of the derived fast algorithm is illustrated for time-variant system identification using several computer simulations. Here, the fast H/sub /spl infin// filter is shown to outperform the well known least-mean-square algorithm and the fast Kalman filter in convergence rate.     

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.     

H/sub /spl infin// filtering for fuzzy singularly perturbed systems with pole placement constraints: an LMI approach

This paper addresses the problem of designing an H/sub /spl infin// filter for a class of nonlinear singularly perturbed systems described by a Takagi-Sugeno (TS) fuzzy model. Based on a linear matrix inequality (LMI) approach, we develop a fuzzy H/sub /spl infin// controller that guarantees that i) the L/sub 2/-gain from an exogenous input to a filter error is less than or equal to a prescribed value and ii) the poles of each local filter are within a prespecified region. In order to alleviate the ill-conditioning resulting from the interaction of slow and fast dynamic modes, solutions to the problem are given in terms of linear matrix inequalities, which are independent of the singular perturbation /spl epsiv/, when /spl epsiv/ is sufficiently small. The proposed approach does not involve the separation of states into slow and fast ones, and it can be applied not only to standard but also to nonstandard singularly perturbed nonlinear systems. A numerical example is provided to illustrate the design developed in this paper.     

Genetic algorithm approach to fixed-order mixed H/sub 2//H/sub /spl infin// optimal deconvolution filter designs

The mixed H/sub 2//H/sub /spl infin// optimal deconvolution filter is proposed to achieve the H/sub 2/ optimal reconstruction and a desired robustness against the effect of uncertainties in signal processing from the H/sub /spl infin// norm perspective. However, the conventional mixed H/sub 2//H/sub /spl infin// optimal design filters are very complicated and are not practical for industrial applications. For simplicity of implementation and conservation of operation time, the fixed-order mixed H/sub 2//H/sub /spl infin// optimal deconvolution filter design is interesting for engineers in signal processing from the practical design perspective. In this study, to avoid the trap of local minima, a design method based on the genetic algorithm is introduced to treat the nonlinear optimization design problem of the fixed-order mixed H/sub 2//H/sub /spl infin// deconvolution filter. The convergence property of our design algorithm is also discussed. Finally, an example is presented to illustrate the design procedure and confirm the robustness performance of the proposed method.     

Finite horizon H/sub /spl infin// fixed-lag smoothing for time-varying continuous systems

In this paper, we aim to solve the long-standing H/sub /spl infin// fixed-lag smoothing problem for time-varying continuous systems. By applying a novel innovation analysis approach in an indefinite linear space, a sufficient and necessary condition for the existence of an H/sub /spl infin// fixed-lag smoother is derived. The H/sub /spl infin// smoother is calculated by performing the linear matrix differential equation and the integral equation.     

Robust H/sub /spl infin// filtering for Uncertain2-D continuous systems

This paper considers the problem of robust H/sub /spl infin// filtering for uncertain two-dimensional (2-D) continuous systems described by the Roesser state-space model. The parameter uncertainties are assumed to be norm-bounded in both the state and measurement equations. The purpose is the design of a 2-D continuous filter such that for all admissible uncertainties, the error system is asymptotically stable, and the H/sub /spl infin// norm of the transfer function, from the noise signal to the estimation error, is below a prespecified level. A sufficient condition for the existence of such filters is obtained in terms of a set of linear matrix inequalities (LMIs). When these LMIs are feasible, an explicit expression of a desired H/sub /spl infin// filter is given. Finally, a simulation example is provided to demonstrate the effectiveness of the proposed method.     

An LMI approach to the H/sub /spl infin// filter design for uncertain systems with distributed delays

This paper investigates the problem of robust H/sub /spl infin// filter design for linear distributed delay systems with norm-bounded time-varying parameter uncertainties. The distributed delays are assumed to appear in both the state and measurement equations. The problem we address is the design of a filter, such that for all admissible uncertainties, the resulting error system is asymptotically stable and satisfies a prescribed H/sub /spl infin// performance level. A sufficient condition is obtained to guarantee the existence of desired H/sub /spl infin// filters, which can be constructed by solving certain linear matrix inequalities. The effectiveness of the proposed design method is demonstrated by a numerical example.     

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

In this paper, the robust H/sub /spl infin// 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 H/sub /spl infin// 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 H/sub /spl infin// filter is also given. An optimization problem is subsequently formulated by optimizing the H/sub /spl infin// filtering performances. Finally, a numerical example is provided to demonstrate the effectiveness and applicability of the proposed design approach.     

A comparative study of the use of the generalized hold function for HDDs

This work is concerned with the application of H/sub /spl infin// control with the generalized hold function (GHF) to track-following control of hard disk drives (HDDs). In HDDs, the sampling frequency is limited primarily by the fact that a high sampling frequency tends to decrease the available data storage capacity of the devices, since the position error signal (PES) must be stored on the disk. Under such conditions, GHF provides a possible way to enhance servo performance without requiring more PES data. We investigate its possibility, comparing the results with other conventional H/sub /spl infin// control design results, including continuous/discrete-time and single/multirate control. Our results show that this controller has better performance due to the nature of the control input of the GHF.     

Design of reduced-order H/sub /spl infin// filter for Markovian jumping systems with time delay

This brief is concerned with the reduced-order H/sub /spl infin// filtering problem for Markovian jumping linear systems with time delay, where the jumping parameters are modeled by a discrete-time Markov process. Sufficient conditions for the existence of the reduced-order H/sub /spl infin// filter are proposed in terms of linear matrix inequalities (LMI) and a coupling nonconvex matrix rank constraint. In particular, the sufficient conditions for the existence of the zeroth-order (or static) H/sub /spl infin// filter can be expressed in terms of a set of strict LMIs. The explicit parameterization of the desired filter is also given. Finally, a numerical example is given to illustrate the proposed approach.     

Fixed-order robust H/sub /spl infin// filter design for Markovian jump systems with uncertain switching probabilities

This paper discusses the fixed-order robust H/sub /spl infin// filtering problem for a class of Markovian jump linear systems with uncertain switching probabilities. The uncertainties under consideration are assumed to be norm-bounded in the system matrices and to be elementwise bounded in the mode transition rate matrix, respectively. First, a criterion based on linear matrix inequalities is provided for testing the H/sub /spl infin// filtering level of a filter over all the admissible uncertainties. Then, a sufficient condition for the existence of the fixed-order robust H/sub /spl infin// filters is established in terms of the solvability of a set of linear matrix inequalities with equality constraints. To determine the filter, a globally convergent algorithm involving convex optimization is suggested. Finally, a numerical example is used to illustrate that the developed theory is more effective than the existing results.     

Robust filtering for 2-D state-delayed systems with NFT uncertainties

This paper is concerned with the robust filtering problem for two-dimensional (2-D) state-delayed systems with uncertainties represented by nonlinear fraction transformation. The authors first establish the stability H/sub /spl infin// performance and generalized H/sub 2/ performance criteria for the system. Based on the results, the authors propose efficient methods to solve the robust H/sub /spl infin// filtering, generalized H/sub 2/ filtering, and mixed generalized H/sub 2//H/sub /spl infin// filtering problems by using a parameter-dependent Lyapunov function approach. The methods involve solving linear matrix inequalities. Two examples are given to show the effectiveness of the proposed approach.     

Robust and precision motion control system of linear-motor direct drive for high-speed X-Y table positioning mechanism

In this paper, design and implementation of an H/sub /spl infin//-based precision motion control system is presented for a high-speed linear-motor direct-drive X-Y table positioning mechanism in semiconductor wire-bonding applications. The system works with a cascaded robust feedback control, which has an inner loop velocity controller and an outer loop position controller, and an autotuning feedforward compensator. The design aim is to achieve high and consistent tracking performance even in the presence of considerable resonance uncertainties and external disturbances. Toward this aim the velocity controller is designed using H/sub /spl infin// optimization technique, based on reduced-order modeling that considers three significant resonance modes and neglects all other resonance modes having an insignificant amplitude and/or too high frequency. These neglected modes and variations of the three resonance modes from machine to machine (due to manufacturing tolerance) and/or with different operating conditions are taken care of by appropriate additive uncertainty representation in the design phase. The resulting system is validated and implemented with a profile motion of a maximum acceleration of 5.2 g (1g=9.81 m/s/sup 2/) on mass-produced wire bonding machines.