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IMA New Directions Short Course

Topics in Control Theory

Topics in Control Theory

May 27 - June 13, 2014

University of Minnesota, Twin Cities |

Control Theory is undergoing rapid development. The three-week short course will introduce the audience to three distinct areas in control. These topics are mathematical in nature and are appropriate for mathematicians interested in pursuing research in control theory. The lectures will be tutorial in nature but will touch on current research. The topics will be revisited in greater depth during the IMA 2015-2016 Annual Thematic Program in Control Theory and its Applications.

Week 1: (May 27-31, 2014) Optimization and control

Main lecturers: Pablo Parrilo, Massachusetts Institute of Technology and Ben Recht, University of Wisconsin, Madison

Week 2: (June 2-6, 2014) Distributed optimization and control

Main lecturers: Stephen Morse, Yale University and Angelia Nedich, University of Illinois

Week 3: (June 9-13, 2014) Optimal mass transport and distributed systems

Main lecturers: Allen Tannenbaum, Stony Brook University and Svetlozar Rachev, Stony Brook University

Participants must apply for at least two contiguous weeks of participation.

Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday Monday | Tuesday | Wednesday | Thursday | Friday | | |||
---|---|---|---|

Tuesday May 27, 2014 | |||

Week 1: Optimization and Control: a Convex Perspective | |||

8:00am-8:45am | Registration | Lind Hall 400 | |

8:45am-9:00am | Welcome to the IMA | Lind 305 | |

9:00am-10:30am | Introduction to dynamical systems. Linear dynamics, stability, Lyapunov functions, eigenvalue conditions. | Pablo Parrilo (Massachusetts Institute of Technology) | Lind 305 |

10:30am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Introduction to optimization. Quadratic forms. Gradient, Hessian. Convex sets and convex functions. Least squares. | Ben Recht (University of California, Berkeley) | Lind 305 |

12:30pm-2:00pm | Lunch | ||

2:00pm-3:30pm | Discussion | Pablo Parrilo (Massachusetts Institute of Technology)Ben Recht (University of California, Berkeley) | Lind 305 |

5:00pm-8:00pm | Group Dinner - Kafe 421 | ||

Wednesday May 28, 2014 | |||

8:30am-9:00am | Coffee | Lind Hall 400 | |

9:00am-10:30am | Lyapunov equations and inequalities. Duality in convex optimization and systems theory. Linear matrix inequalities (LMIs). S-Procedure and applications (ellipsoid containment, etc.). | Pablo Parrilo (Massachusetts Institute of Technology) | Lind 305 |

10:30am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Optimization methods: First order methods: basic gradient and extensions (accelerated, stochastic, subgradient, and projection). | Ben Recht (University of California, Berkeley) | Lind 305 |

12:30pm-2:00pm | Lunch | ||

2:00pm-3:30pm | Optimality, Duality, and Complementarity for Constrained Optimization | Stephen Wright (University of Wisconsin, Madison) | Lind 305 |

Thursday May 29, 2014 | |||

8:30am-9:00am | Coffee | Lind Hall 400 | |

9:00am-10:30am | Finding Lyapunov functions via convex optimization. Frequency domain descriptions. Kalman-Yakubovich-Popov lemma, Lyapunov proof of gradient methods. | Pablo Parrilo (Massachusetts Institute of Technology) | Lind 305 |

10:30am-10:40am | Group Photo | Lind 305 | |

10:40am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Polynomials and sum of squares (SOS). Nonconvex quadratic optimization and semidefinite relaxations. Generalizations via SOS. | Ben Recht (University of California, Berkeley) | Lind 305 |

12:30pm-2:00pm | Lunch | ||

2:00pm-3:30pm | Interior-Point and Augmented Lagrangian Algorithms for Optimization and Control | Stephen Wright (University of Wisconsin, Madison) | Lind 305 |

4:00pm-5:00pm | Homework Problems | Pablo Parrilo (Massachusetts Institute of Technology)Ben Recht (University of California, Berkeley) | |

Friday May 30, 2014 | |||

8:30am-9:00am | Coffee | Lind Hall 400 | |

9:00am-10:30am | System analysis via integral quadratic constraints (IQCs). Sector and Popov IQCs. Analysis of optimization methods. | Pablo Parrilo (Massachusetts Institute of Technology) | Lind 305 |

10:30am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Algorithms for SDP. Interior-point, bundle, and first order methods. | Ben Recht (University of California, Berkeley) | Lind 305 |

12:30pm-2:00pm | Lunch | ||

2:00pm-3:30pm | Stability Analysis with Dissipation Inequalities and Integral Quadratic Constraints | Peter Seiler (University of Minnesota Twin Cities) | Lind 305 |

Saturday May 31, 2014 | |||

8:30am-9:00am | Coffee | Lind Hall 400 | |

9:00am-10:30am | Synthesis: linear quadratic control (LQR), H2 and Hinf optimal control, extensions to nonlinear/decentralized. | Pablo Parrilo (Massachusetts Institute of Technology) | Lind 305 |

10:30am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Sparsity and rank: Applications to estimation, machine learning, and system identification. | Ben Recht (University of California, Berkeley) | Lind 305 |

12:30pm-2:00pm | Lunch | ||

2:00pm-3:30pm | Synthesis for Linear Parameter Varying Systems | Peter Seiler (University of Minnesota Twin Cities) | Lind 305 |

Monday June 02, 2014 | |||

Week 2: Control of Networked and Distributed Systems | |||

8:30am-9:00am | Coffee | Lind Hall 400 | |

9:00am-10:30am | Flocking and Consensus | A. Morse (Yale University) | Lind 305 |

10:30am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Flocking and Consensus | A. Morse (Yale University) | Lind 305 |

12:30pm-3:30pm | Lunch | ||

3:30pm-5:00pm | Distributed Coverage Optimization | Jorge Cortes (University of California, San Diego) | Lind 305 |

Tuesday June 03, 2014 | |||

8:30am-9:00am | Coffee | Lind Hall 400 | |

9:00am-10:30am | Distributed Optimization over Networks | Angelia Nedich (University of Illinois at Urbana-Champaign) | Lind 305 |

10:30am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Distributed Optimization Over Networks | Angelia Nedich (University of Illinois at Urbana-Champaign) | Lind 305 |

12:30pm-2:00pm | Lunch | ||

2:00pm-5:00pm | Discussion | A. Morse (Yale University)Angelia Nedich (University of Illinois at Urbana-Champaign) | Lind 305 |

Wednesday June 04, 2014 | |||

8:30am-9:00am | Coffee | Lind Hall 400 | |

9:00am-10:30am | Distributed Averaging and Gossiping | A. Morse (Yale University) | Lind 305 |

10:30am-10:40am | Group Photo | Lind 305 | |

10:40am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Distributed Averaging and Gossiping | A. Morse (Yale University) | Lind 305 |

12:30pm-2:00pm | Lunch | ||

2:00pm-5:00pm | Discussion | A. Morse (Yale University)Angelia Nedich (University of Illinois at Urbana-Champaign) | Lind 305 |

Thursday June 05, 2014 | |||

8:30am-9:00am | Coffee | Lind Hall 400 | |

9:00am-10:30am | Distributed Optimization over Networks | Angelia Nedich (University of Illinois at Urbana-Champaign) | Lind 305 |

10:30am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Distributed Optimization over Networks | Angelia Nedich (University of Illinois at Urbana-Champaign) | Lind 305 |

12:30pm-2:00pm | Lunch | ||

2:00pm-3:30pm | Convergence Rates in Distributed Consensus & Averaging | Alex Olshevsky (University of Illinois at Urbana-Champaign) | Lind 305 |

Friday June 06, 2014 | |||

8:30am-9:00am | Coffee | Lind Hall 400 | |

9:00am-10:30am | Distributed Optimization over Networks | Angelia Nedich (University of Illinois at Urbana-Champaign) | Lind 305 |

10:30am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Control of Rigid Formation | A. Morse (Yale University) | Lind 305 |

Monday June 09, 2014 | |||

Week 3: Optimal Mass Transport and Distributed Systems | |||

8:30am-9:00am | Coffee | Lind Hall 400 | |

9:00am-10:30am | Calculus of Variations | Allen Tannenbaum (State University of New York, Stony Brook (SUNY)) | Lind 305 |

10:30am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Monge-Kantorovich Mass Transference Problem, Minimal distances and minimal norms | Svetlozar (Zari) Rachev (State University of New York, Stony Brook (SUNY)) | Lind 305 |

12:30pm-2:00pm | Lunch | ||

2:00pm-3:00pm | Optimal Transportation and Applications to Economic Theory | Robert McCann (University of Toronto) | Lind 305 |

Tuesday June 10, 2014 | |||

8:30am-9:00am | Coffee | Lind Hall 400 | |

9:00am-10:30am | Partial Differential Equation Approach to Monge-Kantorovich | Allen Tannenbaum (State University of New York, Stony Brook (SUNY)) | Lind 305 |

10:30am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Generalized Kantorovich and Kantorovich-Rubinstein Functionals and K-minimal Metrics | Svetlozar (Zari) Rachev (State University of New York, Stony Brook (SUNY)) | Lind 305 |

12:30pm-2:00pm | Lunch | ||

2:00pm-3:00pm | Optimal Transportation and Applications to Economic Theory | Robert McCann (University of Toronto) | Lind 305 |

Wednesday June 11, 2014 | |||

8:30am-9:00am | Coffee | Lind Hall 400 | |

9:00am-10:30am | Approaches to Matricial Optimal Mass Transport (OMT) | Allen Tannenbaum (State University of New York, Stony Brook (SUNY)) | Lind 305 |

10:30am-10:40am | Group Photo | Lind 305 | |

10:40am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Glivenko-Cantelli Functional Limit Theorem and Bernstein-Kanttorovich Invariance Pronciple | Svetlozar (Zari) Rachev (State University of New York, Stony Brook (SUNY)) | Lind 305 |

12:30pm-2:00pm | Lunch | ||

2:00pm-3:30pm | Convergent Finite Difference Solvers for the Monge-Ampère Equation with Optimal Transportation Boundary Conditions | Adam Oberman (McGill University) | Lind 305 |

Thursday June 12, 2014 | |||

8:30am-9:00am | Coffee | Lind Hall 400 | |

9:00am-10:30am | Wasserstein Metric from Transport Theory and Riemannian Structure of Density Functions | Allen Tannenbaum (State University of New York, Stony Brook (SUNY)) | Lind 305 |

10:30am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Theory of Probability Metrics | Svetlozar (Zari) Rachev (State University of New York, Stony Brook (SUNY)) | Lind 305 |

12:30pm-2:00pm | Lunch | ||

2:00pm-3:30pm | Convergent Finite Difference Solvers for the Monge-Ampère Equation with Optimal Transportation Boundary Conditions | Adam Oberman (McGill University) | Lind 305 |

Friday June 13, 2014 | |||

8:30am-9:00am | Coffee | Lind Hall 400 | |

9:00am-10:30am | Applications to Medical Imaging and Theory of Shape | Allen Tannenbaum (State University of New York, Stony Brook (SUNY)) | Lind 305 |

10:30am-11:00am | Break | Lind Hall 400 | |

11:00am-12:30pm | Stability of Stochastic Systems | Svetlozar (Zari) Rachev (State University of New York, Stony Brook (SUNY)) | Lind 305 |

NAME | DEPARTMENT | AFFILIATION |
---|---|---|

Folashade Agusto | Mathematics and Statistics | Austin Peay State University |

Dimitrios Bermperidis | Department of Electrical and Computer Engineering | University of Minnesota Twin Cities |

Victoria Blumen | Department of Mathematics | University of Illinois at Urbana-Champaign |

Vladislav Bukshtynov | Energy Resources Engineering | Stanford University |

Yongxin Chen | Department of Electrical and Computer Engineering | University of Minnesota, Twin Cities |

Hyungjin Choi | Department of Computer Science and Engineering | University of Minnesota Twin Cities |

Juan Cockburn | Department of Computer Engineering | Rochester Institute of Technology |

Jorge Cortes | Department of Mechanical and Aerospace Engineering | University of California, San Diego |

Emiliano Dall'Anese | Department of Electrical Engineering | University of Minnesota Twin Cities |

Harshad Deshmane | Department of Electrical Engineering | University of Minnesota, Twin Cities |

Neil Dhingra | Department of Electrical Engineering | University of Minnesota, Twin Cities |

Sairaj Dhople | Department of Electrical and Computer Engineering | University of Minnesota Twin Cities |

Jin Dong | Department of Electrical Engineering and Computer Science | University of Tennessee |

Efi Foufoula-Georgiou | Department of Civil Engineering | University of Minnesota, Twin Cities |

Tryphon Georgiou | Department of Electrical Engineering | University of Minnesota, Twin Cities |

David Goluskin | Department of Mathematics | University of Michigan |

Qi Han | Department of Mathematical Sciences | Worcester Polytechnic Institute |

Sepideh Hassan Moghaddam | Department of Electrical Engineering | University of Minnesota, Twin Cities |

Weiwei Hu | Department of Mathematics | University of Southern California |

Olaniyi Iyiola | Department of Mathematics and Statistics | King Fahd University of Petroleum and Minerals |

Mihailo Jovanovic | Electrical and Computer Engineering | University of Minnesota, Twin Cities |

Vasileios Kekatos | Department of Electrical and Computer Engineering | University of Minnesota, Twin Cities |

Isabelle Kemajou-Brown | School of Mathematics | University of Minnesota, Twin Cities |

In-Jae Kim | Department of Mathematics and Statistics | Minnesota State University |

Donghoon Lee | Digital Technology Center | University of Minnesota Twin Cities |

Anders Lindquist | Royal Institute of Technology (KTH) | |

Jun Liu | Department of Mathematics | Southern Illinois University |

Wann-Jiun Ma | Department of Electrical Engineering | University of Notre Dame |

Jakub Marecek | Optimization of Nonlinear and Uncertain Systems | IBM Research Division |

Tyler Massaro | Department of Mathematics | University of Tennessee |

Robert McCann | Department of Mathematics | University of Toronto |

Christopher Miles | Department of Physics and Mathematics | University of Michigan |

Vassilios Morellas | Department of Computer Science and Engineering | University of Minnesota, Twin Cities |

A. Morse | Department of Electrical Engineering | Yale University |

Angelia Nedich | Department of Industrial and Enterprise Systems Engineering | University of Illinois at Urbana-Champaign |

Adam Oberman | McGill University | |

Alex Olshevsky | Department of Industrial & Enterprise Systems Engineering | University of Illinois at Urbana-Champaign |

Pablo Parrilo | Department of Electrical Engineering and Computer Science | Massachusetts Institute of Technology |

Svetlozar (Zari) Rachev | Department of Applied Mathematics and Statistics | State University of New York, Stony Brook (SUNY) |

Amin Rasekh | Civil Engineering | Texas A & M University |

Ben Recht | Department of Statistics | University of California, Berkeley |

Mauricio Rivas | Department of Mathematics | University of Houston |

Martin Schmoll | Department of Mathematical Sciences | Clemson University |

Peter Seiler | Aerospace Engineering and Mechanics | University of Minnesota Twin Cities |

Fatemeh Sheikholeslami | Digital Technology Center | University of Minnesota Twin Cities |

Arvind Singh | Department of Civil Engineering | University of Minnesota, Twin Cities |

Mohit Sinha | University of Minnesota Twin Cities | |

Andre Souza | Department of Mathematics | University of Michigan |

Panagiotis Stanitsas | Department of Computer Science and Engineering | University of Minnesota Twin Cities |

Andrew Steyer | Department of Mathematics | University of Kansas |

Zeinab Takbiri | Department of Civil Engineering | University of Minnesota, Twin Cities |

Saurav Talukdar | Department of Mechanical Engineering | University of Minnesota, Twin Cities |

Allen Tannenbaum | Department of Computational Science | State University of New York, Stony Brook (SUNY) |

William Toczyski | University of Minnesota, Twin Cities | |

Carlos Tolmasky | University of Minnesota Twin Cities | |

Panagiotis Traganitis | Department of Electrical and Computer Engineering | University of Minnesota Twin Cities |

Han Wang | Department of Mathematics | University of Illinois at Urbana-Champaign |

Zhu Wang | Institute for Mathematics and its Applications | University of Minnesota, Twin Cities |

Stephen Wright | Computer Sciences | University of Wisconsin, Madison |

Xiaofan Wu | Department of Electrical Engineering | University of Minnesota, Twin Cities |

Armin Zare | Department of Electrical and Computer Engineering | University of Minnesota, Twin Cities |

Dimitrios Zermas | Department of Computer Science and Engineering | University of Minnesota Twin Cities |

Jun Zhang | Department of Mathematics and Psychology | University of Michigan |

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