Controller design to minimize a composite measure of the l1, H2 and l∞ norms

M. V. Salapaka; P. G. Voulgaris; M. Dahleh

Controller design to minimize a composite measure of the l1, H2 and l∞ norms

M. V. Salapaka, P. G. Voulgaris, M. Dahleh

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

In this paper duality theory is employed to show that the problem of minimizing a given linear combination of the l₁ norm, the square of the H₂ norm, and the l_∞ norm of the closed loop over all stabilizing controllers is equivalent to a finite dimensional convex optimization problem. It is shown that the dimension can be determined a priori. Relation to Pareto optimality is established and the continuity of the optimal solution with respect to changes in the coefficients of the linear combination is proven. The problem is studied for a single input single output, discrete time, linear time invariant system.

Original language	English (US)
Title of host publication	ASME Dynamic Systems and Control Division
Publisher	ASME
Pages	297-305
Number of pages	9
Volume	57-1
State	Published - Dec 1 1995
Event	Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition - San Francisco, CA, USA Duration: Nov 12 1995 → Nov 17 1995

Other

Other	Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition
City	San Francisco, CA, USA
Period	11/12/95 → 11/17/95

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title = "Controller design to minimize a composite measure of the l1, H2 and l∞ norms",

abstract = "In this paper duality theory is employed to show that the problem of minimizing a given linear combination of the l1 norm, the square of the H2 norm, and the l∞ norm of the closed loop over all stabilizing controllers is equivalent to a finite dimensional convex optimization problem. It is shown that the dimension can be determined a priori. Relation to Pareto optimality is established and the continuity of the optimal solution with respect to changes in the coefficients of the linear combination is proven. The problem is studied for a single input single output, discrete time, linear time invariant system.",

author = "Salapaka, {M. V.} and Voulgaris, {P. G.} and M. Dahleh",

year = "1995",

month = dec,

day = "1",

language = "English (US)",

volume = "57-1",

pages = "297--305",

booktitle = "ASME Dynamic Systems and Control Division",

publisher = "ASME",

note = "Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition ; Conference date: 12-11-1995 Through 17-11-1995",

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T1 - Controller design to minimize a composite measure of the l1, H2 and l∞ norms

AU - Salapaka, M. V.

AU - Voulgaris, P. G.

AU - Dahleh, M.

PY - 1995/12/1

Y1 - 1995/12/1

N2 - In this paper duality theory is employed to show that the problem of minimizing a given linear combination of the l1 norm, the square of the H2 norm, and the l∞ norm of the closed loop over all stabilizing controllers is equivalent to a finite dimensional convex optimization problem. It is shown that the dimension can be determined a priori. Relation to Pareto optimality is established and the continuity of the optimal solution with respect to changes in the coefficients of the linear combination is proven. The problem is studied for a single input single output, discrete time, linear time invariant system.

AB - In this paper duality theory is employed to show that the problem of minimizing a given linear combination of the l1 norm, the square of the H2 norm, and the l∞ norm of the closed loop over all stabilizing controllers is equivalent to a finite dimensional convex optimization problem. It is shown that the dimension can be determined a priori. Relation to Pareto optimality is established and the continuity of the optimal solution with respect to changes in the coefficients of the linear combination is proven. The problem is studied for a single input single output, discrete time, linear time invariant system.

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M3 - Conference contribution

AN - SCOPUS:17544396543

VL - 57-1

SP - 297

EP - 305

BT - ASME Dynamic Systems and Control Division

PB - ASME

T2 - Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition

Y2 - 12 November 1995 through 17 November 1995

ER -