Hybrid Systems: Model Identification and State Estimation Hamsa Balakrishnan, David Culler, Edward A. Lee, S. Shankar Sastry, Claire Tomlin (PI) University.

Slides:

Advertisements

Similar presentations

Pattern Recognition and Machine Learning

Advertisements

Linear Regression.

L1 sparse reconstruction of sharp point set surfaces

Biointelligence Laboratory, Seoul National University

Pattern Recognition and Machine Learning

4/15/2017 Using Gaussian Process Regression for Efficient Motion Planning in Environments with Deformable Objects Barbara Frank, Cyrill Stachniss, Nichola.

Basis Expansion and Regularization Presenter: Hongliang Fei Brian Quanz Brian Quanz Date: July 03, 2008.

Empirical Maximum Likelihood and Stochastic Process Lecture VIII.

Visual Recognition Tutorial

Chess Review November 21, 2005 Berkeley, CA Edited and presented by Optimal Control of Stochastic Hybrid Systems Robin Raffard EECS Berkeley.

EE 290A: Generalized Principal Component Analysis Lecture 6: Iterative Methods for Mixture-Model Segmentation Sastry & Yang © Spring, 2011EE 290A, University.

Hilbert Space Embeddings of Hidden Markov Models Le Song, Byron Boots, Sajid Siddiqi, Geoff Gordon and Alex Smola 1.

ActionWebs Hamsa Balakrishnan, David Culler, Edward A. Lee, S. Shankar Sastry, Claire Tomlin (PI) University of California at Berkeley July

Stochastic Collapsed Variational Bayesian Inference for Latent Dirichlet Allocation James Foulds 1, Levi Boyles 1, Christopher DuBois 2 Padhraic Smyth.

Lecture 29: Optimization and Neural Nets CS4670/5670: Computer Vision Kavita Bala Slides from Andrej Karpathy and Fei-Fei Li

1 Identification of Running Dynamics Perturbation response reveals control architecture.

Principal Component Analysis

Fusing Machine Learning & Control Theory With Applications to Smart Buildings & ActionWebs UC Berkeley ActionWebs Meeting November 03, 2010 By Jeremy Gillula.

1 AM3 Task 1.4 Stochastic Hybrid Models for Aerial and Ground Vehicles Sam Burden MAST Annual Review University of Pennsylvania March 8-9, 2010.

Regulatory Network (Part II) 11/05/07. Methods Linear –PCA (Raychaudhuri et al. 2000) –NIR (Gardner et al. 2003) Nonlinear –Bayesian network (Friedman.

Speaker Adaptation for Vowel Classification

FIN357 Li1 Binary Dependent Variables Chapter 12 P(y = 1|x) = G(  0 + x  )

Chess Review October 4, 2006 Alexandria, VA Edited and presented by Hybrid Systems: Theoretical Contributions Part I Shankar Sastry UC Berkeley.

Machine Learning CUNY Graduate Center Lecture 3: Linear Regression.

Chess Review November 21, 2005 Berkeley, CA Edited and presented by Advances in Hybrid System Theory: Overview Claire J. Tomlin UC Berkeley.

Multiobjective control: safety and efficiency Hamsa Balakrishnan, David Culler, Edward A. Lee, S. Shankar Sastry, Claire Tomlin (PI) University of California.

1 University of Freiburg Computer Networks and Telematics Prof. Christian Schindelhauer Wireless Sensor Networks 17th Lecture Christian Schindelhauer.

EE291E - UC BERKELEY EE291E: Hybrid Systems T. John Koo and S. Shankar Sastry Department of EECS University of California at Berkeley Spring 2002

1 Collision Avoidance Systems: Computing Controllers which Prevent Collisions By Adam Cataldo Advisor: Edward Lee Committee: Shankar Sastry, Pravin Varaiya,

Arizona State University DMML Kernel Methods – Gaussian Processes Presented by Shankar Bhargav.

ActionWebs Hamsa Balakrishnan, David Culler, Edward A. Lee, S. Shankar Sastry, Claire Tomlin (PI) University of California at Berkeley December

Machine Learning CUNY Graduate Center Lecture 3: Linear Regression.

Maryam Kamgarpour, Claire Tomlin, David Culler, Shankar Sastry, Edward Lee, Hamsa Balakrishnan University of California at Berkeley August Outreach.

Introduction to Machine Learning for Information Retrieval Xiaolong Wang.

Introduction to variable selection I Qi Yu. 2 Problems due to poor variable selection: Input dimension is too large; the curse of dimensionality problem.

By Avinash Sridrahan, Scott Moeller and Bhaskar Krishnamachari.

Nonlinear Programming.  A nonlinear program (NLP) is similar to a linear program in that it is composed of an objective function, general constraints,

Data Mining Practical Machine Learning Tools and Techniques Chapter 4: Algorithms: The Basic Methods Section 4.6: Linear Models Rodney Nielsen Many of.

CS 782 – Machine Learning Lecture 4 Linear Models for Classification  Probabilistic generative models  Probabilistic discriminative models.

CS Statistical Machine learning Lecture 18 Yuan (Alan) Qi Purdue CS Oct

CS Statistical Machine learning Lecture 10 Yuan (Alan) Qi Purdue CS Sept

An Introduction to Support Vector Machines (M. Law)

Factor Analysis Psy 524 Ainsworth. Assumptions Assumes reliable correlations Highly affected by missing data, outlying cases and truncated data Data screening.

2.4 Nonnegative Matrix Factorization  NMF casts matrix factorization as a constrained optimization problem that seeks to factor the original matrix into.

ECE 8443 – Pattern Recognition ECE 8423 – Adaptive Signal Processing Objectives: ML and Simple Regression Bias of the ML Estimate Variance of the ML Estimate.

Javad Lavaei Department of Electrical Engineering Columbia University Joint work with Somayeh Sojoudi and Ramtin Madani An Efficient Computational Method.

EE4-62 MLCV Lecture Face Recognition – Subspace/Manifold Learning Tae-Kyun Kim 1 EE4-62 MLCV.

Biointelligence Laboratory, Seoul National University

Solve a system of linear equations By reducing a matrix Pamela Leutwyler.

Over-fitting and Regularization Chapter 4 textbook Lectures 11 and 12 on amlbook.com.

Logistic Regression Saed Sayad 1www.ismartsoft.com.

Review of statistical modeling and probability theory Alan Moses ML4bio.

CS Statistical Machine learning Lecture 7 Yuan (Alan) Qi Purdue CS Sept Acknowledgement: Sargur Srihari’s slides.

8.9: Finding Power Series Using Algebra or Calculus Many times a function does not have a simple way to rewrite as the sum of an infinite geometric series.

Deep Feedforward Networks

Boosting and Additive Trees (2)

René Vidal Time/Place: T-Th 4.30pm-6pm, Hodson 301

Segmentation of Dynamic Scenes from Image Intensities

Probabilistic Models for Linear Regression

Statistical Learning Dong Liu Dept. EEIS, USTC.

Estimates and 95% CIs of between- and within-pair variations for SS and OS twin pairs and achievement test scores in mathematics and reading assessed in.

Estimating Networks With Jumps

Linear regression Fitting a straight line to observations.

Nonlinear regression.

Biointelligence Laboratory, Seoul National University

5.2 Least-Squares Fit to a Straight Line

Logistic Regression Chapter 7.

Ch 3. Linear Models for Regression (2/2) Pattern Recognition and Machine Learning, C. M. Bishop, Previously summarized by Yung-Kyun Noh Updated.

Computer Animation Algorithms and Techniques

Kazuyuki Tanaka Graduate School of Information Sciences

Presentation transcript:

Hybrid Systems: Model Identification and State Estimation Hamsa Balakrishnan, David Culler, Edward A. Lee, S. Shankar Sastry, Claire Tomlin (PI) University of California at Berkeley December

Hybrid System Model Complex, multi-modal systems Can combine probabilistic, discrete techniques with control of continuous systems

Some results… Model ID: for stochastic linear hybrid systems, with mode switching governed by a Markovian switching matrix –Iteratively maximizing the likelihood of the discrete model and then finding the maximum likelihood continuous model [Balakrishnan et al, 2004] State estimation: –both discrete and continuous [Hwang, Balakrishnan et al, 2003] –asynchronous

Online System Identification

[Bickel and Li, 2007] Undersampling for high-dimensional systems Constrained dynamics Fast-slow dynamics Online System Identification

Look for a geometric structure for sparsity Local linear (hybrid) models are easy to manipulate Online System Identification

Local Linear Regression Solve for in for all Rewrite as: where

Difficulty in interpreting regression coefficients Gradient of function does not exist Online System Identification

Exterior derivative of function does exist Extension of gradients to manifolds Best local linear approximation of function on manifold Online System Identification

15 (Aswani et al., submitted 2009); (Bickel and Levina, 2008) Locally learn manifold Constrain regression vector to lie on the manifold by penalizing for deviations from manifold Where is chosen to penalize for lying off of the manifold New Estimation Approach