International Workshop on Hybrid Systems: Modeling, Simulation and
Optimization 
Invited Speakers 
Title: Timestepping
methods for large scale differential variational
inequalities (DVI) in nonsmooth dynamics
Authors:
Mihai Anitescu
Mathematics and Computer Science
Division, Argonne National Laboratory, USA
Abstract:
We discuss
recent advances in timestepping methods for solving
nonsmooth rigid body dynamics with contact and friction.
The advantage of such methods is that they do not have
to stop at every collision or stickslip event while
converging in a weak sense to the solution of the DVI.
We discuss
methods for solving the sub problems, which are
optimization problems with conic constraints, arising at
each time step. We particularly emphasize an algorithm,
recently developed with A. Tasora, that solves them in
their dual cone complementarity form with a Gauss Seidel
like iteration. We prove that the method is globally
convergent. Through numerical experiments, we
demonstrate that the method scales linearly with with an
increasing size of
the problem and show that it is very competitive for the
simulation of granular flow dynamics.

Title: Semismooth
Hybrid Automata
Authors: Paul
I. Barton, Mehmet Yunt
Chemical Engineering Department, Massachusetts Institute of
Technology, USA
Abstract:
The determination of optimal mode
sequences for hybrid systems with autonomous transitions is
examined. A class of hybrid systems that exhibit a locally Lipschitz
mapping between their parameters and their continuous states is
introduced. Lipschitzian optimization methods such as bundle methods
are explored for the solution of parametric optimization problems
that have this class of hybrid systems embedded. 
Title: MPEC
Strategies for Optimization of Chemical Process Dynamics
Authors: B.
T. Baumrucker,
Lorenz T. Biegler
Department of Chemical Engineering,
Carnegie Mellon University, USA
Abstract:
With the
development and widespread use of largescale nonlinear
programming (NLP) tools for process optimization, there has
been an
associated application of NLP formulations with
complementarity constraints in order to represent discrete
decisions. Also known as
Mathematical Programs with Equilibrium Constraints (MPECs),
these formulations can be used to model certain classes of
discrete events and can be more efficient than a mixed
integer formulation. In this talk, we consider MPEC
formulations and solution strategies for
chemical engineering applications, particularly for a
dynamic gas pipeline system. The results illustrate the
effectiveness of MPEC
strategies as well as some novel operating strategies for
pipeline networks.

Title: Constrained
and Distributed Hybrid Control
Authors: Francesco
Borrelli
Department of
Mechanical Engineering, University of California at
Berkeley, USA
Abstract:
Over the last few years
we have focused on the development of distributed controller
synthesis techniques for large scale hybrid systems with
constraints. There is a wealth of practical problems of this type.
However, at present systematic distributed control design for such
systems is still at its infancy.
In this seminar I will first summarize our theoretical efforts,
starting from constrained optimal control design for single systems.
Then, I will show how these results can be used in order to develop
a novel theory for distributed constrained optimal control for large
scale hybrid systems.
During the talk several applications will be used in order to
illustrate the benefits of the proposed approach.

Title: Reformulations,
Relaxations and Cutting Planes for Linear Generalized
Disjunctive Programming
Authors: Nicholas Sawaya, Ignacio
E. Grossmann
Department of
Chemical Engineering, Carnegie Mellon University, USA
Abstract:
Generalized
disjunctive programming (GDP) is an extension of the
wellknown disjunctive programming paradigm developed by
Balas. The GDP formulation involves Boolean and continuous
variables that are specified in algebraic constraints,
disjunctions and logic propositions, which is an alternative
representation to the traditional mixed integer programming
(MIP) formulation. Our research in this class of problems,
which has been motivated by its potential for improved
modeling and solution methods, has led to the development of
customized algorithms that exploit the underlying logical
structure of the problem in both the linear and nonlinear
cases. However, an outstanding question that has remained is
the exact relationship between GDP and disjunctive
programming. In this work, we establish for the linear case
new connections between disjunctive programming and
generalized disjunctive programming, which provide new
theoretical and computational insights that allow us to
exploit the rich theory developed Balas. In particular, we
propose a novel family of MIP reformulations corresponding
to the original GDP model that result in tighter relaxations
and stronger cutting planes than reported in previous work.
We illustrate this theory on the strippacking problem for
which computational results are presented. We also describe
the application of these ideas to the global optimization of
bilinear GDP problems.

Title: Iterative
Relaxation Abstraction for Verification and Design of Hybrid
Systems
Authors: Bruce
H. Krogh
Electrical and Computer Engineering, Carnegie Mellon
University, USA
Abstract:
Inspired by the
success of counterexample guided abstraction refinement (CEGAR)
techniques for verification of discrete systems, iterative
relaxation abstraction (IRA) combines the capabilities of
current tools for analysis of lowdimensional linear hybrid
automata (LHA) with the power of linear programming (LP) to
verify properties of models that cannot be handled by
traditional reachability analysis. On each iteration, a
lowdimensional abstraction is constructed using a subset of
the continuous variables from the original LHA. Hybrid
system reachability analysis generates a representation of
all possible paths to forbidden states in the relaxation
abstraction. Infeasibility analysis determines if a path
selected from this set represents a valid run of the LHA
using the constraints along the path from the original
highdimensional LHA. If the constraints along the path are
not feasible, LP techniques identify an irreducible
infeasible subset of constraints from which the set of
continuous variables is selected for the construction of the
next relaxation abstraction. IRA stops if no paths to bad
states remain or a legitimate violation of the reachability
specification is found. Following a review the use of LHA
to model hybrid systems with linear and nonlinear continuous
dynamics, the details of the IRA procedure for verification
will be described and illustrated with some examples.
Recent extensions of IRA for parameter optimization will
then be presented.

Title: Analysis
and numerical solution of hybrid differential algebraic
systems
Authors: Volker
Mehrmann
Institut für Mathematik, Technische Universität Berlin,
Germany
Abstract:
We discuss the
analysis and numerical solution of hybrid dynamical systems.
Our work is motivated by industrial applications arising in
the modeling and control of automatic gearboxes. We survey
the general theory of overand underdetermined systems of
nonlinear differential algebraic equations and show how this
general theory can be extended to hybrid systems. We discuss
the issues of consistent initialization after mode switching
as well sliding modes. We present several numerical examples
and indicate challenges and an outlook for future research.
This is joint
work, partially with Peter Hamann (Daimler AG) and Lena
Wunderlich (TU Berlin).

Title: Differential
Variational Inequalities and friends
Authors: David
Stewart
Department of Mathematics, University of Iowa
Abstract:
Differential
Variational Inequalities is a framework for a class of
hybrid systems that encompasses or relate to many
proposed problems (such as Linear Complementarity
Systems, Projected Dynamical Systems, Dynamic
Complementarity Problems, and Convolution
Complementarity Problems). Existence and uniqueness
results have been obtained which will be presented,
although there are still large gaps in our understanding
of some issues, particularly regarding uniqueness of
solutions. An important indicator of the difficulty of
these problems is the index, which will be described and
illustrated.

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