Geometric optimal control with applications

Monique Chyba, chyba@hawaii.edu
Gautier Picot, gpicot@hawaii.edu
Aaron Tamura Sato, aaronts@hawaii.edu
Steven Brelsford, stevenbrelsford@gmail.com
Department of Mathematics, University of Hawaii2565 McCarthy Mall, Honolulu, HI 96822, USA

Bernard Bonnard, bernard.bonnard@u-bourgogne.fr
Inria Sophia Antipolis and Institut de Mathematiques de Bourgogne,
9 avenue Savary, 21078 Dijon, France

 optimal control
Schedule
    ,
    DateTimeMaterialResources
    18 June 16:40-18:10
    Introduction
    M. Chyba, G. Picot
    		Presentation 1
    22 June 13:00-14:30
    Lecture: Lie brackets, Lie algebras, systems with piecewise constant controls
    M. Chyba
    		Chapter 1
    22 June 14:40-16:20
    Lecture: Frobenius and Nagano-Sussman theorem, Poisson stability
    M. Chyba
    		Chapter 2
    22 June 16:40-18:10
    Problems session, controllability
    G. Picot
    		 Controllability, Solutions
    24 June 16:40-18:10
    Chow's therem, enlargment techniques, introduction to calculus of variation
    M. Chyba
    		Chapter 2
    25 June 16:40-18:10
    Optimal control applied to space mechanics
    G. Picot, S. Brelsford
    		Presentation 2
    29 June 13:00-14:30
    Lecture: Introduction to Calculus of Variations, Euler-Lagrange Equations, Hamiltonian Equations and Hamilton-Jacobi-Bellman Equation
    M. Chyba
    		Chapter 3
    29 June 14:40-16:20
    Lecture: Second Order Conditions, The Accessory Problem and the Jacobi Equation, Scalar Riccati Equation
    M. Chyba
    		 Chapter 3
    29 June 16:40-18:10
    Problems session, Euler-Lagrange Eq.
    G. Picot
    		 Euler-Lagrange equations, Solutions
    01 July 16:40-18:10
    Lecture: Historical introduction, Pontryagin's Maximum Priciple and Weak Pontryagin's Maximum Priciple
    B. Bonnard
    		 Course notes, July 1st
    02 July 16:40-18:10
    Problems session, Weak Maximum Principle
    G. Picot
    		 Weak Maximum Principle, Solutions
    06 July 13:00-14:30
    Lecture: Application to Riemannian and Sub-Riemannian geometric-Classification Sub-Riemannian in dimension 3
    B. Bonnard
    		 Course notes, July 6th and Chapter 4
    06 July 14:40-16:20
    Lecture: Application to the swimming problem at low Reynolds number
    B. Bonnard
    		 The copepod swimmer
    06 July 16:40-18:10
    A hybrid control model of fractone-dependent morphogenesi (part 1)
    A. Tamura-Saro
    		Presentation 3
    08 July 16:40-18:10LectureWorking example: Nuclear Magnetic Resonance and Magnetic Resonance Imaging
    09 July 16:40-18:10
    A hybrid control model of fractone-dependent morphogenesis (part 2)
    A. Tamura-Saro
    		Presentation 4
    13 July 13:00-14:30
    Lecture
    B. Bonnard
    13 July 14:40-16:20
    Lecture
    B. Bonnard
    		Homework