Piecewise-affine functions

92 Pages·2013·2.94 MB·English

Introduction PWAFunctions EvaluationAlgorithms Applications Conclusions
Piecewise-affine functions:
applications in circuit theory and control
Tomaso Poggi
Basque Center of Applied Mathematics
Bilbao
12/04/2013
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Introduction PWAFunctions EvaluationAlgorithms Applications Conclusions
Outline
1 Embedded systems
2 PWA functions
Definition
Classes and representation forms
3 Evaluation of PWA functions
4 Applications
Model Predictive Control
Virtual sensors (nonlinear state observers)
Others
5 Conclusions
Matlab software and toolboxes
Open issues
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Introduction PWAFunctions EvaluationAlgorithms Applications Conclusions
Outline
1 Embedded systems
2 PWA functions
Definition
Classes and representation forms
3 Evaluation of PWA functions
4 Applications
Model Predictive Control
Virtual sensors (nonlinear state observers)
Others
5 Conclusions
Matlab software and toolboxes
Open issues
2/46
Introduction PWAFunctions EvaluationAlgorithms Applications Conclusions
Outline
1 Embedded systems
2 PWA functions
Definition
Classes and representation forms
3 Evaluation of PWA functions
4 Applications
Model Predictive Control
Virtual sensors (nonlinear state observers)
Others
5 Conclusions
Matlab software and toolboxes
Open issues
2/46
Introduction PWAFunctions EvaluationAlgorithms Applications Conclusions
Outline
1 Embedded systems
2 PWA functions
Definition
Classes and representation forms
3 Evaluation of PWA functions
4 Applications
Model Predictive Control
Virtual sensors (nonlinear state observers)
Others
5 Conclusions
Matlab software and toolboxes
Open issues
2/46
Introduction PWAFunctions EvaluationAlgorithms Applications Conclusions
Outline
1 Embedded systems
2 PWA functions
Definition
Classes and representation forms
3 Evaluation of PWA functions
4 Applications
Model Predictive Control
Virtual sensors (nonlinear state observers)
Others
5 Conclusions
Matlab software and toolboxes
Open issues
2/46
Introduction PWAFunctions EvaluationAlgorithms Applications Conclusions
Embedded Systems
An embedded system is a computer system designed for executing
specific tasks within a larger system
We can find them in
Mobile phones, digital cameras, mp3 players, ...
Home appliances (microwave ovens, washing machines, ...)
Cars, planes, trains, ...
Embedded systems contain processing cores that are either
microprocessors or digital circuits
⇒ Digital Signal Processor (DSP)
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Introduction PWAFunctions EvaluationAlgorithms Applications Conclusions
Digital Signal Processor VS Personal Computer
Personal Computer Digital Signal Processor
General purpose Specific task
High power/frequency Low power/frequency
No deterministic execution time “Real Time”
Complex operations Simple operations
Available operations on DSP (Fixed point arithmetic)
Arithmetic: +, −, ×
Comparisons: =, >, <, ≥, ≤
Boolean: NOT, AND, OR, XOR
Memory
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Introduction PWAFunctions EvaluationAlgorithms Applications Conclusions
Algorithms for DSP
Requirements:
Fast execution
Limited resources
Low-level programming
Strategy
On-line execution
Off-line design
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Introduction PWAFunctions EvaluationAlgorithms Applications Conclusions
Algorithms for DSP
Requirements:
Fast execution
Limited resources
Low-level programming
Strategy
On-line execution ⇒ Maintain simplicity
Off-line design ⇒ All the hard math here
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