Reading Ljung. \u00a0System Identification: theory for the user.<\/p>\n
1: Introduction.<\/p>\n
Goal: infer a model from observations. \u00a0“Model” refers to the set of relationships between variables in the system. \u00a0System identification involves analyzing input and output signals from the system.<\/p>\n
Example: assume a linear difference equation relates inputs to outputs. \u00a0Use least squares to find parameter values that minimize the least squares error. \u00a0This is partly an autoregression: a linear regression “where the regression vector contains old values of the variable to be explained”.<\/p>\n
Adding noise: assume the observed data are from a deterministic process with noise. \u00a0We’re interested in two expectation values: the parameters and the covariance of the parameter error.<\/p>\n
System identification involves: a data set, candidate models, and an assessment rule (see chapter 7). \u00a0Then use model validation to check whether the model is good enough. \u00a0This process ends up being iterative.<\/p>\n
2: Time invariant linear systems.<\/p>\n
Impulse response can be used to characterize the system. \u00a0If there’s an additive disturbance info is needed on that too (spectrum and pf).<\/p>\n
3: Simulation and prediction.<\/p>\n
4: Models of linear time-invariant systems.<\/p>\n
5: Models for time-varying and nonlinear systems.<\/p>\n
Linear time-varying models might be used when we linearize a nonlinear system about some trajectory.<\/p>\n
6: Nonparametric time and frequency domain methods.<\/p>\n
7: Parameter estimation methods.<\/p>\n
8: Convergence and consistency.<\/p>\n
9: Asymptotic distribution of parameter estimates.<\/p>\n
10: Computing the estimate.<\/p>\n
11: Recursive estimation methods.<\/p>\n
12: Options and objectives.<\/p>\n
<\/p>\n
13: Experiment Design.<\/p>\n
14: Preprocessing data.<\/p>\n
15: Choice of identification criterion.<\/p>\n
16: Model structure selection and model validation.<\/p>\n
17: System identification in practice.<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
Reading Ljung. \u00a0System Identification: theory for the user. 1: Introduction. Goal: infer a model from observations. \u00a0“Model” refers to the set of relationships between variables in the system. \u00a0System identification involves analyzing input and output signals from the system. Example: assume a linear difference equation relates inputs to outputs. \u00a0Use least squares to find parameter […]<\/p>\n","protected":false},"author":8032,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[1],"tags":[],"class_list":["post-220","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p7E5LF-3y","jetpack-related-posts":[{"id":217,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/09\/17\/notes-on-maybeck-stochastic-models-estimation-and-control\/","url_meta":{"origin":220,"position":0},"title":"Notes on Maybeck: Stochastic Models, Estimation, and Control","author":"siams","date":"17 September 2019","format":false,"excerpt":"Notes on Chapter 1 of Maybeck 1979,\u00a0Stochastic Models, Estimation, and Control. 1.1: why stochastic models, estimation, and control? A math model isn't perfect, and parameters are not known absolutely. \u00a0Sensors don't provide perfect data either. \u00a0Given uncertainties, you still want to be able to estimate quantities of interest and control\u2026","rel":"","context":"Similar post","block_context":{"text":"Similar post","link":""},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":186,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/07\/22\/notes-on-calculus-blue-volume-1-chapter-1\/","url_meta":{"origin":220,"position":1},"title":"Notes on “Calculus Blue” Volume 1, Chapter 1","author":"siams","date":"22 July 2019","format":false,"excerpt":"These notes are on the Calculus Blue videos by Ghrist on YouTube. \u00a0He emphasizes that the math will involve substantial (and worthwhile) work, which I really appreciate. 01 (0:51) \"Vectors & matrices: Intro\" \u00a0\"Your journey is not a short one\". \u00a0To learn \"calculus, the mathematics of the nonlinear\", prepare with\u2026","rel":"","context":"In "Math"","block_context":{"text":"Math","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/math\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":108,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/06\/10\/dynamical-systems-math-1b-differential-equations-background\/","url_meta":{"origin":220,"position":2},"title":"Dynamical systems: Math 1b differential equations background.","author":"siams","date":"10 June 2019","format":false,"excerpt":"I have been using the Strogatz textbook for teaching dynamical systems. \u00a0The course has multivariable calculus and linear algebra prerequisites. \u00a0Students might take the prerequisite courses different places. \u00a0For students who have taken Math 1b, AM\/Math 21a, Math 21b, there was 6-7 week of differential equations background (11 classes in\u2026","rel":"","context":"In "Dynamical Systems"","block_context":{"text":"Dynamical Systems","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/dynamical-systems\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":132,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/06\/12\/dynamical-systems-strogatz-chapter-5\/","url_meta":{"origin":220,"position":3},"title":"Dynamical Systems: Strogatz Chapter 5","author":"siams","date":"12 June 2019","format":false,"excerpt":"This chapter is mainly review of topics from prerequisite courses. \u00a0Steve does introduce the (Delta, tau)-plane for classifying fixed points of linear systems. \u00a0This chapter is a return to linear systems. There isn't a \"summary\" section in between Chapter 4 and Chapter 5. \u00a0That is probably a worthwhile spot to\u2026","rel":"","context":"In "Dynamical Systems"","block_context":{"text":"Dynamical Systems","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/dynamical-systems\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":112,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/06\/10\/dynamical-systems-math-21b-differential-equations-background\/","url_meta":{"origin":220,"position":4},"title":"Dynamical Systems: Math 21b differential equations background","author":"siams","date":"10 June 2019","format":false,"excerpt":"For students who have taken Math 1b, AM\/Math 21a, Math 21b, there was 6-7 week of differential equations background (11 classes in Math 1b + 9 classes in 21b). \u00a0See my prior post for the Math 1b diff eq content that is relevant to Dynamical Systems. Student diff eq background\u2026","rel":"","context":"In "Dynamical Systems"","block_context":{"text":"Dynamical Systems","link":"https:\/\/archive.blogs.harvard.edu\/siams\/category\/dynamical-systems\/"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":153,"url":"https:\/\/archive.blogs.harvard.edu\/siams\/2019\/06\/28\/blanchard-devaney-and-hall-3rd-edition-2006-differential-equations\/","url_meta":{"origin":220,"position":5},"title":"Blanchard, Devaney, and Hall 3rd edition (2006): Differential Equations. Sections 1.1-1.4, 1.8","author":"siams","date":"28 June 2019","format":false,"excerpt":"Chapter 1: First order differential equations. \u00a0They present a goal: predicting a future value of a quantity modeled by a differential equation. 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