Robust controller design via linear programming

Ghulchak, Andrey; Rantzer, Anders

doi:10.1109/cdc.1999.830897

Cited by 6 publications

(8 citation statements)

References 7 publications

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“…Since the number of inequalities is still the continuum, we get a semi-infinite programming that can be solved in many ways. One is by taking a grid on the unit circle T (see discretization methods for semi-infinite programming in [10,23]), which has been realized and discussed in [8,9]. Another is to use a cutting plane algorithm and, in particular, the ACCP method [2,19] that usually performs better than the method of ellipsoids.…”

Section: Toward An Implementation Of the Primal-dual Methodmentioning

confidence: 99%

“…The gap between the true optimal value and its finite-dimensional counterpart can be arbitrarily large. To overcome this difficulty and to estimate the conservatism, convex duality has been widely used [3,4,8,11,12,16,17,24]. Once the dual problem is stated, a similar finite-dimensional scheme can be applied to obtain an opposite bound for the optimal value.…”

Section: Introductionmentioning

confidence: 99%

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Duality inH$^\infty$ Cone Optimization

Ghulchak

Rantzer²

2002

SIAM J. Control Optim.

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Positive real cones in the space H ∞ appear naturally in many optimization problems of control theory and signal processing. Although such problems can be solved by finite-dimensional approximations (e.g., Ritz projection), all such approximations are conservative, providing one-sided bounds for the optimal value. In order to obtain both upper and lower bounds of the optimal value, a dual problem approach is developed in this paper. A finite-dimensional approximation of the dual problem gives the opposite bound for the optimal value. Thus, by combining the primal and dual problems, a suboptimal solution to the original problem can be found with any required accuracy.

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Section: Toward An Implementation Of the Primal-dual Methodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Duality inH$^\infty$ Cone Optimization

Ghulchak

Rantzer²

2002

SIAM J. Control Optim.

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“…According to Figs. 7,8,(8) does not hold in the mid and high frequency range (at frequencies marks with stars). However, a closer look on the single contributions (Fig.…”

Section: Simulation Examplementioning

confidence: 99%

“…In [8], this problem is solved for a parametric uncertainty (i.e. T = 0) bounded in 1-norm and ∞-norm respectively using an FIR basis for α, β and the computational problem is recasted to a Linear Programming one.…”

Section: Remark 1 the Original Formulationmentioning

confidence: 99%

Robust Control of Identified Models with Mixed Parametric and Non-Parametric Uncertainties

Reinelt

Ljung

2003

European Journal of Control

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A framework for identification oriented robust controller design is developed. The model is identified from open-loop i/odata and contains parametric uncertainties as well as an additive and norm-bounded error. The set of all robustly stabilising controllers, that additionally guarantee robust performance is characterised by a system of second order cones, which can be efficiently solved by interior point algorithms.

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“…In this section, we use the duality result to obtain an upper bound. The next theorem is extracted from [10] and [11].…”

Section: A the Dual Problemmentioning

confidence: 99%