H/sub ∞/ prediction and smoothing for discrete-time systems: a J-spectral factorization approach

Colaneri, Patrizio; Maroni, M.; Shaked, U.

doi:10.1109/cdc.1998.757888

Cited by 15 publications

(8 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Clearly, for such values of γ the filter cannot exist, but there exists a fixed-lag smoother associated with a certain preview horizon length N achieving the desired attenuation level. As shown in [5], the computation of the stabilizing solution Δ of (1.14) and of the corresponding J-spectral factor Ω(z) are crucial steps to obtain efficiently the minimum-lag smoothing filter achieving the desired attenuation level. Notably, the solution Δ can be directly used to initialize an iterative algorithm to work out a minimum-lag central smoother; see [13,2].…”

Section: Contribution Of the Papermentioning

confidence: 99%

“…In fact if (1.7a) is not satisfied we may resort to a Silverman transfomation (see [6]) that, employing a spectral interactor matrix, yields an equivalent problem in which DD > 0. If (1.7d) is not satisfied, we may perform a preliminary feedback transformation, as described in [5], and obtain an equivalent problem, in which (1.7d) is satisfied.…”

Section: Introduction and Problem Statement Consider The Discrete-tim...mentioning

confidence: 99%

See 1 more Smart Citation

Algebraic Riccati Equation and J-Spectral Factorization for Hinfty Smoothing and Deconvolution

Colaneri¹,

Ferrante²

2006

SIAM J. Control Optim.

View full text Add to dashboard Cite

This paper deals with a general steady-state estimation problem in the H∞ setting. The existence of the stabilizing solution of the related algebraic Riccati equation (ARE) and of the solution of the associated J-spectral factorization problem is investigated. The existence of such solutions is well established if the prescribed attenuation level γ is larger than γ f (the infimum of the values of γ for which a causal estimator with attenuation level γ exists). We consider the case when γ ≤ γ f and show that the stabilizing solution of the ARE still exists (except for a finite number of values of γ) as long as a fixed-lag acausal estimator (smoother) does. The stabilizing solution of the ARE may be employed to derive a state-space realization of a minimum-phase J-spectral factor of the J-spectrum associated with the estimation problem. This J-spectral factor may be used, in turn, to compute the minimum-lag smoothing estimator. Some of the aspects of the J-spectral factorization problem and the properties of its solutions are discussed in correspondence to the (finite number of) values of γ for which the stabilizing solution of the ARE does not exist.

show abstract

Section: Contribution Of the Papermentioning

confidence: 99%

Section: Introduction and Problem Statement Consider The Discrete-tim...mentioning

confidence: 99%

Algebraic Riccati Equation and J-Spectral Factorization for Hinfty Smoothing and Deconvolution

Colaneri¹,

Ferrante²

2006

SIAM J. Control Optim.

View full text Add to dashboard Cite

show abstract

“…Clearly, for such values of γ the filter cannot exist, but there exists a fixed-lag smoother associated with a certain preview horizon length N achieving the desired attenuation level. As shown in [6], the computation of the stabilizing solution ∆ of (12) and of the corresponding J-spectral factor Ω(z) are crucial steps to obtain efficiently the minimum-lag smoothing filter achieving the desired attenuation level. Notably, the solution ∆ can be directly used to initialize an iterative algorithm to work out a minimum-lag central smoother, see [13], [2].…”

Section: Contribution Of the Papermentioning

confidence: 99%

Algebraic Riccati equation and J-spectral factorization for H<sub>∞</sub> smoothing and deconvolution

Colaneri

Ferrante

2006

Proceedings of the 45th IEEE Conference on Decision and Control

Self Cite

View full text Add to dashboard Cite

This paper deals with a general steady-state estimation problem in the H∞ setting. The existence of the stabilizing solution of the related algebraic Riccati equation (ARE) and of the solution of the associated J-spectral factorization problem is investigated. The existence of such solutions is well-established if the prescribed attenuation level γ is larger than γ f (the infimum of the values of γ for which a causal estimator with attenuation level γ exists). We consider the case when γ ≤ γ f and show that the stabilizing solution of the ARE still exists (except for a finite number of values of γ) as long as a fixed-lag acausal estimator (smoother) does. The stabilizing solution of the ARE may be employed to derive a state-space realization of a minimum-phase J-spectral factor of the J-spectrum associated with the estimation problem. This J-spectral factor may be used, in turn, to compute the minimum-lag smoothing estimator.

show abstract

“…An H ∞ estimator is such that the energy gain between the input noises (including process and measurement noises) and the estimation error is bounded by a prescribed level [71,28,79] and is applicable to situations where no information on statistics of input noises is available. To obtain more efficient H ∞ estimation algorithms, some attempts have been made in recent years; see, e.g., [27,16,17,81]. However, problems such as H ∞ fixed-lag smoothing, multiple-step ahead prediction and filtering for time delay systems are known to be challenging and deserve further investigations.…”

Section: Introductionmentioning

confidence: 99%

Control and Estimation of Systems with Input/Output Delays

2007

Lecture Notes in Control and Information Sciences

View full text Add to dashboard Cite

PrefaceTime delay systems exist in many engineering fields such as transportation, communication, process engineering and more recently networked control systems. In recent years, time delay systems have attracted recurring interests from research community. Much of the research work has been focused on stability analysis and stabilization of time delay systems using the so-called Lyapunov-Krasovskii functionals and linear matrix inequality (LMI) approach. While the LMI approach does provide an efficient tool for handling systems with delays in state and/or inputs, the LMI based results are mostly only sufficient and only numerical solutions are available.For systems with known single input delay, there have been rather elegant analytical solutions to various problems such as optimal tracking, linear quadratic regulation and H ∞ control. We note that discrete-time systems with delays can usually be converted into delay free systems via system augmentation, however, the augmentation approach leads to much higher computational costs, especially for systems of higher state dimension and large delays. For continuous-time systems, time delay problems can in principle be treated by the infinite-dimensional system theory which, however, leads to solutions in terms of Riccati type partial differential equations or operator Riccati equations which are difficult to understand and compute. Some attempts have been made in recent years to derive explicit and efficient solutions for systems with input/output (i/o) delays. These include the study on the H ∞ control of systems with multiple input delays based on the stable eigenspace of a Hamlitonian matrix [46]. It is worth noting that checking the existence of the stable eigenspace and finding the minimal root of the transcendent equation required for the controller design may be computationally expensive. Another approach is to split a multiple delay problem into a nested sequence of elementary problems which are then solved based on J-spectral factorizations [62].In this monograph, our aim is to present simple analytical solutions to control and estimation problems for systems with multiple i/o delays via elementary tools such as projections. We propose a re-organized innovation analysis approach which allows us to convert many complicated delay problems into delay VI Preface free ones. In particular, for linear quadratic regulation of systems with multiple input delays, the approach enables us to establish a duality between the LQR problem and a smoothing problem for a delay free system. The duality contains the well known duality between the LQR of a delay free system and Kalman filtering as a special case and allows us to derive an analytical solution via simple projections. We also consider the dual problem, i.e. the Kalman filtering for systems with multiple delayed measurements. Again, the re-organized innovation analysis turns out to be a powerful tool in deriving an estimator. A separation principle will be established for the linear quadratic Gaussian control of sys...

show abstract

H/sub ∞/ prediction and smoothing for discrete-time systems: a J-spectral factorization approach

Cited by 15 publications

References 8 publications

Algebraic Riccati Equation and J-Spectral Factorization for Hinfty Smoothing and Deconvolution

Algebraic Riccati Equation and J-Spectral Factorization for Hinfty Smoothing and Deconvolution

Algebraic Riccati equation and J-spectral factorization for H<sub>∞</sub> smoothing and deconvolution

Control and Estimation of Systems with Input/Output Delays

Contact Info

Product

Resources

About

H/sub ∞/ prediction and smoothing for discrete-time systems: a J-spectral factorization approach

Cited by 15 publications

References 8 publications

Algebraic Riccati Equation and J-Spectral Factorization for Hinfty Smoothing and Deconvolution

Algebraic Riccati Equation and J-Spectral Factorization for Hinfty Smoothing and Deconvolution

Algebraic Riccati equation and J-spectral factorization for H<sub>&#x0221E;</sub> smoothing and deconvolution

Control and Estimation of Systems with Input/Output Delays

Contact Info

Product

Resources

About

Algebraic Riccati equation and J-spectral factorization for H<sub>∞</sub> smoothing and deconvolution