Minimax Control of Linear Stochastic Systems with Noise Uncertainty

Douglas P. Looze; H. Vincent Poor; Kenneth S. Vastola; John C. Darragh

doi:10.1109/TAC.1983.1103353

Minimax Control of Linear Stochastic Systems with Noise Uncertainty

Douglas P. Looze, H. Vincent Poor, Kenneth S. Vastola, John C. Darragh

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

Abstract

The problem of linear-quadratic-Gaussian control of multivariable linear stochastic systems with uncertain second-order statistical properties is considered. Uncertainty is modeled by allowing process and observation noise spectral density matrices to vary' arbitrarily within given classes, and a minimax control formulation is applied to the quadratic objective functional. General theorems proving the existence and characterization of saddle-point solutions to this problem are presented, and the relationship of these results to earlier results on minimax state estimation are discussed. To illustrate the analytical results, the specific example of regulating a double-integrator plant is treated in detail.

Original language	English (US)
Pages (from-to)	882-888
Number of pages	7
Journal	IEEE Transactions on Automatic Control
Volume	28
Issue number	9
DOIs	https://doi.org/10.1109/TAC.1983.1103353
State	Published - Jan 1 1983
Externally published	Yes

All Science Journal Classification (ASJC) codes

Computer Science Applications
Control and Systems Engineering
Electrical and Electronic Engineering

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10.1109/TAC.1983.1103353

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abstract = "The problem of linear-quadratic-Gaussian control of multivariable linear stochastic systems with uncertain second-order statistical properties is considered. Uncertainty is modeled by allowing process and observation noise spectral density matrices to vary' arbitrarily within given classes, and a minimax control formulation is applied to the quadratic objective functional. General theorems proving the existence and characterization of saddle-point solutions to this problem are presented, and the relationship of these results to earlier results on minimax state estimation are discussed. To illustrate the analytical results, the specific example of regulating a double-integrator plant is treated in detail.",

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AU - Poor, H. Vincent

AU - Vastola, Kenneth S.

AU - Darragh, John C.

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Y1 - 1983/1/1

N2 - The problem of linear-quadratic-Gaussian control of multivariable linear stochastic systems with uncertain second-order statistical properties is considered. Uncertainty is modeled by allowing process and observation noise spectral density matrices to vary' arbitrarily within given classes, and a minimax control formulation is applied to the quadratic objective functional. General theorems proving the existence and characterization of saddle-point solutions to this problem are presented, and the relationship of these results to earlier results on minimax state estimation are discussed. To illustrate the analytical results, the specific example of regulating a double-integrator plant is treated in detail.

AB - The problem of linear-quadratic-Gaussian control of multivariable linear stochastic systems with uncertain second-order statistical properties is considered. Uncertainty is modeled by allowing process and observation noise spectral density matrices to vary' arbitrarily within given classes, and a minimax control formulation is applied to the quadratic objective functional. General theorems proving the existence and characterization of saddle-point solutions to this problem are presented, and the relationship of these results to earlier results on minimax state estimation are discussed. To illustrate the analytical results, the specific example of regulating a double-integrator plant is treated in detail.

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Minimax Control of Linear Stochastic Systems with Noise Uncertainty

Abstract

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