Joe A. Roman-Flores Supervisor: Dr. Paolo Rapisarda...
Transcript of Joe A. Roman-Flores Supervisor: Dr. Paolo Rapisarda...
![Page 1: Joe A. Roman-Flores Supervisor: Dr. Paolo Rapisarda ...ukacc.group.shef.ac.uk/wordpress/wp-content/... · Univ logo UKACC PhD Presentation Showcase Slide 2 Introduction Ø Identification](https://reader036.fdocuments.us/reader036/viewer/2022062508/60587aab8cd58d75961efacf/html5/thumbnails/1.jpg)
Univ logo
A Duality Approach to System Identification of LTV and NL Systems
Joe A. Roman-FloresSupervisor: Dr. Paolo Rapisarda
University of Southampton
UKACC PhD Presentation Showcase
![Page 2: Joe A. Roman-Flores Supervisor: Dr. Paolo Rapisarda ...ukacc.group.shef.ac.uk/wordpress/wp-content/... · Univ logo UKACC PhD Presentation Showcase Slide 2 Introduction Ø Identification](https://reader036.fdocuments.us/reader036/viewer/2022062508/60587aab8cd58d75961efacf/html5/thumbnails/2.jpg)
Univ logo UKACC PhD Presentation Showcase Slide 2
Introduction
Ø Identification theory for linear systems has strong basis and well-establish methodologies.
Ø Identification for nonlinear systems without prior information it is hard to achieve.
Ø Using duality approach allow us to obtain a state model from data, and the data will give us internal information about the system.
![Page 3: Joe A. Roman-Flores Supervisor: Dr. Paolo Rapisarda ...ukacc.group.shef.ac.uk/wordpress/wp-content/... · Univ logo UKACC PhD Presentation Showcase Slide 2 Introduction Ø Identification](https://reader036.fdocuments.us/reader036/viewer/2022062508/60587aab8cd58d75961efacf/html5/thumbnails/3.jpg)
Univ logo UKACC PhD Presentation Showcase Slide 3
Approach
Ø Based on input-output data (𝑢, 𝑦)we construct state trajectories 𝑥corresponding to it.
Ø Identify a state model from such input-state-output trajectories.
![Page 4: Joe A. Roman-Flores Supervisor: Dr. Paolo Rapisarda ...ukacc.group.shef.ac.uk/wordpress/wp-content/... · Univ logo UKACC PhD Presentation Showcase Slide 2 Introduction Ø Identification](https://reader036.fdocuments.us/reader036/viewer/2022062508/60587aab8cd58d75961efacf/html5/thumbnails/4.jpg)
Univ logo UKACC PhD Presentation Showcase Slide 4
Duality
Primal Dual
Ø The duality approach for identification exploits the duality relation between the external trajectories and the internal ones.
External : input-output 𝒖, 𝒚 &(𝒖+,𝒚′)
Internal : state 𝒙 &(𝒙+)
𝑑𝑑𝒕 𝒙 0 = 𝑨 0 𝒙 0 + 𝑩 0 𝒖 0𝒚 0 = 𝑪 0 𝒙 0
𝑑𝑑𝒕 𝒙
+ 0 = −𝑨 0 7𝒙+ 0 + 𝑪 0 7𝒖+ 0
𝒚+ 0 = 𝑩 0 7𝒙′ 0
LTV systems
![Page 5: Joe A. Roman-Flores Supervisor: Dr. Paolo Rapisarda ...ukacc.group.shef.ac.uk/wordpress/wp-content/... · Univ logo UKACC PhD Presentation Showcase Slide 2 Introduction Ø Identification](https://reader036.fdocuments.us/reader036/viewer/2022062508/60587aab8cd58d75961efacf/html5/thumbnails/5.jpg)
Univ logo UKACC PhD Presentation Showcase Slide 5
Identification procedure
Ø Procedure• Produce N experiments to get (𝑢, 𝑦)and (𝑢′, 𝑦′).• Using the duality relation obtain a matrix of data𝐸 𝑡 ∈ ℝ<×< representing the internal properties.
• Factorize the state from this matrix.• Obtain a set of equations to obtain a state model.
𝑢+7𝑦 − 𝑦+7𝑢 =𝑑𝑑𝑡 (𝑥
+7𝑄𝑥)
external internal
𝐸(𝑡)
![Page 6: Joe A. Roman-Flores Supervisor: Dr. Paolo Rapisarda ...ukacc.group.shef.ac.uk/wordpress/wp-content/... · Univ logo UKACC PhD Presentation Showcase Slide 2 Introduction Ø Identification](https://reader036.fdocuments.us/reader036/viewer/2022062508/60587aab8cd58d75961efacf/html5/thumbnails/6.jpg)
Univ logo UKACC PhD Presentation Showcase Slide 6
Identification procedureSelf-dual systems
Ø Matrix of data E(t) has special properties that allows to obtain information of the internal in a natural way.
• Easy factorization of the state.• State dimension from data.
Nonlinear systemsØ Identification using the variational system.
𝑢7𝑦− 𝑦7𝑢 =𝑑𝑑𝑡 (𝑥
7𝑄𝑥)
external internal
![Page 7: Joe A. Roman-Flores Supervisor: Dr. Paolo Rapisarda ...ukacc.group.shef.ac.uk/wordpress/wp-content/... · Univ logo UKACC PhD Presentation Showcase Slide 2 Introduction Ø Identification](https://reader036.fdocuments.us/reader036/viewer/2022062508/60587aab8cd58d75961efacf/html5/thumbnails/7.jpg)
Univ logo UKACC PhD Presentation Showcase Slide 7
Issues to overcome
Ø From numbers to functions.Ø Sufficiently informative data.Ø Factorization.
THANK YOU