Finite word length stability issues in an l<sub>1</sub> framework

Whidborne, James F.; Istepanian, R.S.H.

doi:10.1080/002071700219876

Cited by 28 publications

(19 citation statements)

References 5 publications

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“…However, different realizations possess different degrees of stability robustness to FWL errors. An FWL design is to select optimal realizations for the given filter/control law by optimizing some FWL stability measures, such as the Frobenius-norm pole sensitivity measure υ f [4], the l 1 -based stability measure υ l [5], the 1-norm pole sensitivity measure υ 1 [6], [7], the stability radius measure υ r [8] and the pole sensitivity sum measure υ s [9]. In fact, the FWL stability measure υ proposed in [10] quantifies the FWL stability characteristics of a realization best.…”

Section: Introductionmentioning

confidence: 99%

Solving Finite Word Length Realization Problems in the Framework of Structured Singular Value

Chu

et al. 2006

2006 6th World Congress on Intelligent Control and Automation

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-Based on the structured singular value theory, a tractable stability measure is derived for controllers/filters with the finite word length implementation consideration. The optimal realizations of controllers/filters are defined as those that maximize this measure. A sophisticated optimization strategy is presented to provide an efficient method for solving this problem based on the linear matrix inequality, and a numerical example is given to illustrate the design procedure.

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Section: Introductionmentioning

confidence: 99%

Solving Finite Word Length Realization Problems in the Framework of Structured Singular Value

Chu

et al. 2006

2006 6th World Congress on Intelligent Control and Automation

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“…There are generally two types of FWL errors in the digital controller implementation. The first one is the rounding errors that occur in arithmetic operations [4], [5], and the second one is the controller parameter representation errors which have critical influence on closedloop stability [6], [7], [8], [9], [10], [11], [12]. Typically, these two types of errors are investigated separately for the reason of mathematical tractability.…”

Section: Introductionmentioning

confidence: 99%

“…This property can be utilized to select "optimal" realizations that optimize some FWL performance measures. Various FWL performance measures have been investigated, and these include the averaged roundoff noise gain [5], the complex stability radius measure [6], the transfer function sensitivity measure [7], the l 1 -based stability measure [8], the Frobenius-norm pole sensitivity measure [9], and the 1-norm pole sensitivity measure [10], [11]. In the direct strategy, controller design involves explicitly the considerations of FWL implementation.…”

Section: Introductionmentioning

confidence: 99%

A Search Algorithm for a Class of Optimal Finite-Precision Controller Realization Problems with Saddle Points

Wu¹,

Chen²,

Li³

et al. 2005

SIAM J. Control Optim.

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Abstract. With game theory, we review the optimal digital controller realization problems that maximize a finite word length (FWL) closed-loop stability measure. For a large class of these optimal FWL controller realization problems which have saddle points, a minimax-based search algorithm is derived for finding a global optimal solution. The algorithm consists of two stages. In the first stage, the closed form of a transformation set is constructed which contains global optimal solutions. In the second stage, a subgradient approach searches this transformation set to obtain a global optimal solution. This algorithm does not suffer from the usual drawbacks associated with using direct numerical optimization methods to tackle these FWL realization problems. Furthermore, for a small class of optimal FWL controller realization problems which have no saddle point, the proposed algorithm also provides useful information to help solve them.

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“…Due to the lack of analytical solutions to optimal FWL controller realization problems, numerical optimization methods have been adopted to search for optimal realizations [6]- [9]. A numerical optimization approach can be effective if the dimension of the problem is small.…”

Section: Introductionmentioning

confidence: 99%

“…where ¡ denotes the Frobenius norm, that is, for any complex-valued matrix Å, Å Õ ØÖ´Å À Åµ (6) with À denoting the conjugate transpose operator.…”

Section: Introductionmentioning

confidence: 99%

Global optimal realizations of finite precision digital controllers

Chen

Li³

et al.

Proceedings of the 41st IEEE Conference on Decision and Control, 2002.

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The paper analyzes global solutions to the optimal digital controller realization problem based on maximizing a finite word length (FWL) closed-loop stability measure. For each closed-loop eigenvalue, a single-pole FWL stability function is first introduced, and a single-pole FWL stability measure is then defined as the maximum of the corresponding single-pole stability function over all the controller realizations. It is shown that the minimum of the single-pole stability measures for all the closed-loop eigenvalues is an upper bound of the optimal value for the optimal realization problem. An analytical method to compute a single-pole stability measure is developed, and an expression for all the realizations which achieve a given single-pole measure is derived. When a realization, which is a solution of the minimum single-pole measure, further satisfies the condition that the values of all its single-pole stability functions are not less than the minimum single-pole measure, the minimum single-pole measure is the optimal value of the optimal realization problem and this realization is the solution for the optimal realization problem. An algorithm is presented to compute an optimal FWL controller realization. Unlike most of the existing methods relying on numerical optimization search algorithms, which can be computationally expensive and may easily be trapped at local optimal solutions, the proposed analytical approach guarantees to find a global optimal controller realization.

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Finite word length stability issues in an l₁ framework

Cited by 28 publications

References 5 publications

Solving Finite Word Length Realization Problems in the Framework of Structured Singular Value

Solving Finite Word Length Realization Problems in the Framework of Structured Singular Value

A Search Algorithm for a Class of Optimal Finite-Precision Controller Realization Problems with Saddle Points

Global optimal realizations of finite precision digital controllers

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Finite word length stability issues in an l1 framework

Cited by 28 publications

References 5 publications

Solving Finite Word Length Realization Problems in the Framework of Structured Singular Value

Solving Finite Word Length Realization Problems in the Framework of Structured Singular Value

A Search Algorithm for a Class of Optimal Finite-Precision Controller Realization Problems with Saddle Points

Global optimal realizations of finite precision digital controllers

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Finite word length stability issues in an l₁ framework