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

http://maxplus.org guy.cohen@mail.enpc.fr

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 guy.cohen@mail.enpc.fr

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 guy.cohen@mail.enpc.fr

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 guy.cohen@mail.enpc.fr

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 guy.cohen@mail.enpc.fr

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