Download - Guy Cohen CERMICS-ENPC History & Motivations …cermics.enpc.fr/~cohen-g/documents/POSTA06/Base.pdfA Tour of Systems with the Max-Plus Flavor Guy Cohen CERMICS-ENPC [email protected]

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A Tour of Systems with the Max-Plus FlavorGuy Cohen CERMICS-ENPC

http://maxplus.org [email protected]

History & Motivations

System & Control Theory Geometry

Algebra

#[[γ, δ]]

• Almost half a century of algebra and about 25 years of (max,+) system & control theory

• Discrete event systems

• Other motivations

• Idempotent semimodules

• Skew projections and regular matrices

• Orthogonal projections and separation• Convexity

• Idempotent semirings

• Solving equations & residuation theory

• Counter and dater representations

• Control problems

A Tour of Systems with the Max-Plus FlavorGuy Cohen CERMICS-ENPC

http://maxplus.org [email protected]

History & Motivations

System & Control Theory Geometry

Algebra

#[[γ, δ]]

• Almost half a century of algebra and about 25 years of (max,+) system & control theory

• Discrete event systems

• Other motivations

• Idempotent semimodules

• Skew projections and regular matrices

• Orthogonal projections and separation• Convexity

• Idempotent semirings

• Solving equations & residuation theory

• Counter and dater representations

• Control problems

A Tour of Systems with the Max-Plus FlavorGuy Cohen CERMICS-ENPC

http://maxplus.org [email protected]

History & Motivations

System & Control Theory Geometry

Algebra

#[[γ, δ]]

• Almost half a century of algebra and about 25 years of (max,+) system & control theory

• Discrete event systems

• Other motivations

• Idempotent semimodules

• Skew projections and regular matrices

• Orthogonal projections and separation• Convexity

• Idempotent semirings

• Solving equations & residuation theory

• Counter and dater representations

• Control problems

A Tour of Systems with the Max-Plus FlavorGuy Cohen CERMICS-ENPC

http://maxplus.org [email protected]

History & Motivations

System & Control Theory Geometry

Algebra

#[[γ, δ]]

• Almost half a century of algebra and about 25 years of (max,+) system & control theory

• Discrete event systems

• Other motivations

• Idempotent semimodules

• Skew projections and regular matrices

• Orthogonal projections and separation• Convexity

• Idempotent semirings

• Solving equations & residuation theory

• Counter and dater representations

• Control problems

A Tour of Systems with the Max-Plus FlavorGuy Cohen CERMICS-ENPC

http://maxplus.org [email protected]

History & Motivations

System & Control Theory Geometry

Algebra

#[[γ, δ]]

• Almost half a century of algebra and about 25 years of (max,+) system & control theory

• Discrete event systems

• Other motivations

• Idempotent semimodules

• Skew projections and regular matrices

• Orthogonal projections and separation• Convexity

• Idempotent semirings

• Solving equations & residuation theory

• Counter and dater representations

• Control problems