Single Diophantine equation solution of the discrete-time polynomial H2 and H∞ control problems with a classical feedback structure

Haipeng Zhao; Joseph Bentsman

Single Diophantine equation solution of the discrete-time polynomial H₂ and H_∞ control problems with a classical feedback structure

Haipeng Zhao
, Joseph Bentsman

Research output: Contribution to journal › Conference article › peer-review

Abstract

The linear discrete-time polynomial optimal feedback control laws are typically obtained via simultaneous solution of two Diophantine equations. In the present work, a number-theory based technique is introduced that permits reduction of the polynomial controller synthesis procedures for the single-input-single-output (SISO) H₂ and H_∞ regulation and tracking control problems with a classical feedback structure and plants with arbitrary stability properties to solving a single Diophantine equation. The technique proposed is also used to reduce the solution of the multi-input-multi-output (MIMO) generalized H_∞ control problem.

Original language	English (US)
Pages (from-to)	676-681
Number of pages	6
Journal	Proceedings of the IEEE Conference on Decision and Control
Volume	1
State	Published - 2001
Externally published	Yes
Event	40th IEEE Conference on Decision and Control (CDC) - Orlando, FL, United States Duration: Dec 4 2001 → Dec 7 2001

ASJC Scopus subject areas

Control and Optimization
Control and Systems Engineering
Modeling and Simulation

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title = "Single Diophantine equation solution of the discrete-time polynomial H2 and H∞ control problems with a classical feedback structure",

abstract = "The linear discrete-time polynomial optimal feedback control laws are typically obtained via simultaneous solution of two Diophantine equations. In the present work, a number-theory based technique is introduced that permits reduction of the polynomial controller synthesis procedures for the single-input-single-output (SISO) H2 and H∞ regulation and tracking control problems with a classical feedback structure and plants with arbitrary stability properties to solving a single Diophantine equation. The technique proposed is also used to reduce the solution of the multi-input-multi-output (MIMO) generalized H∞ control problem.",

author = "Haipeng Zhao and Joseph Bentsman",

year = "2001",

language = "English (US)",

volume = "1",

pages = "676--681",

journal = "Proceedings of the IEEE Conference on Decision and Control",

issn = "0191-2216",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

note = "40th IEEE Conference on Decision and Control (CDC) ; Conference date: 04-12-2001 Through 07-12-2001",

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T1 - Single Diophantine equation solution of the discrete-time polynomial H2 and H∞ control problems with a classical feedback structure

AU - Zhao, Haipeng

AU - Bentsman, Joseph

PY - 2001

Y1 - 2001

N2 - The linear discrete-time polynomial optimal feedback control laws are typically obtained via simultaneous solution of two Diophantine equations. In the present work, a number-theory based technique is introduced that permits reduction of the polynomial controller synthesis procedures for the single-input-single-output (SISO) H2 and H∞ regulation and tracking control problems with a classical feedback structure and plants with arbitrary stability properties to solving a single Diophantine equation. The technique proposed is also used to reduce the solution of the multi-input-multi-output (MIMO) generalized H∞ control problem.

AB - The linear discrete-time polynomial optimal feedback control laws are typically obtained via simultaneous solution of two Diophantine equations. In the present work, a number-theory based technique is introduced that permits reduction of the polynomial controller synthesis procedures for the single-input-single-output (SISO) H2 and H∞ regulation and tracking control problems with a classical feedback structure and plants with arbitrary stability properties to solving a single Diophantine equation. The technique proposed is also used to reduce the solution of the multi-input-multi-output (MIMO) generalized H∞ control problem.

UR - https://www.scopus.com/pages/publications/0035712652

UR - https://www.scopus.com/pages/publications/0035712652#tab=citedBy

M3 - Conference article

AN - SCOPUS:0035712652

SN - 0191-2216

VL - 1

SP - 676

EP - 681

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

T2 - 40th IEEE Conference on Decision and Control (CDC)

Y2 - 4 December 2001 through 7 December 2001

ER -

Single Diophantine equation solution of the discrete-time polynomial H₂ and H_∞ control problems with a classical feedback structure

Abstract

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