During each Annual Thematic Program, several seminars are offered. Talks will
include graduate-level lectures as well as seminars covering various topics
related to the theme.
Seminars for 2015-2016 will be held Thursdays from 11 a.m. to 12 p.m. in Lind Hall 305 unless otherwise noted.
Elements of Sliding Mode Control Theory
Antonella Ferrara, Università di Pavia
September 14, 2015 11:00 AM - 12:00 PM
Lind 305 [Map]Abstract
Sliding Mode Control is a nonlinear control method based on the use of a discontinuous control input which forces the controlled system to switch from one continuous structure to another, i.e. to evolve as a variable structure system. This structure variation makes the system state reach in a finite time a pre-specified subspace of the system state space, where the desired dynamical properties are assigned to the controlled system.
In the past years, an extensive literature has been devoted to the developments of Sliding Mode Control theory. This kind of methodology offers a number of benefits, the major of which is its robustness versus a significant class of uncertainties and disturbances. Yet, it presents a crucial drawback, the so-called chattering phenomenon, due to the high frequency switching of the control signal, which may disrupt or damage actuators, thus limiting its actual applicability. This drawback has been circumvented by recent theoretical developments oriented to increase the so-called order of the sliding mode, giving rise to Second Order and Higher Order Sliding Mode Control algorithms.
The three lectures based short course on Sliding Mode Control will cover the major theoretical aspects. It will start from the basic concepts (i.e. the definition and existence of a sliding mode, the solution in Filippov’s sense of the associated discontinuous differential equation, the invariance property versus matched uncertainties of the system in sliding mode), arriving to illustrate recent Higher Order Sliding Mode Control algorithms capable of solving, in a robust way, classical optimal control problems, such as the Fuller’s Problem.
Elements of Sliding Mode Control Theory
Antonella Ferrara, Università di Pavia
September 16, 2015 11:00 AM - 12:00 PM
Lind 305 [Map]Abstract
Sliding Mode Control is a nonlinear control method based on the use of a discontinuous control input which forces the controlled system to switch from one continuous structure to another, i.e. to evolve as a variable structure system. This structure variation makes the system state reach in a finite time a pre-specified subspace of the system state space, where the desired dynamical properties are assigned to the controlled system.
In the past years, an extensive literature has been devoted to the developments of Sliding Mode Control theory. This kind of methodology offers a number of benefits, the major of which is its robustness versus a significant class of uncertainties and disturbances. Yet, it presents a crucial drawback, the so-called chattering phenomenon, due to the high frequency switching of the control signal, which may disrupt or damage actuators, thus limiting its actual applicability. This drawback has been circumvented by recent theoretical developments oriented to increase the so-called order of the sliding mode, giving rise to Second Order and Higher Order Sliding Mode Control algorithms.
The three lectures based short course on Sliding Mode Control will cover the major theoretical aspects. It will start from the basic concepts (i.e. the definition and existence of a sliding mode, the solution in Filippov’s sense of the associated discontinuous differential equation, the invariance property versus matched uncertainties of the system in sliding mode), arriving to illustrate recent Higher Order Sliding Mode Control algorithms capable of solving, in a robust way, classical optimal control problems, such as the Fuller’s Problem.
Elements of Sliding Mode Control Theory
Antonella Ferrara, Università di Pavia
September 18, 2015 11:00 AM - 12:00 PM
Lind 305 [Map]Abstract
Sliding Mode Control is a nonlinear control method based on the use of a discontinuous control input which forces the controlled system to switch from one continuous structure to another, i.e. to evolve as a variable structure system. This structure variation makes the system state reach in a finite time a pre-specified subspace of the system state space, where the desired dynamical properties are assigned to the controlled system.
In the past years, an extensive literature has been devoted to the developments of Sliding Mode Control theory. This kind of methodology offers a number of benefits, the major of which is its robustness versus a significant class of uncertainties and disturbances. Yet, it presents a crucial drawback, the so-called chattering phenomenon, due to the high frequency switching of the control signal, which may disrupt or damage actuators, thus limiting its actual applicability. This drawback has been circumvented by recent theoretical developments oriented to increase the so-called order of the sliding mode, giving rise to Second Order and Higher Order Sliding Mode Control algorithms.
The three lectures based short course on Sliding Mode Control will cover the major theoretical aspects. It will start from the basic concepts (i.e. the definition and existence of a sliding mode, the solution in Filippov’s sense of the associated discontinuous differential equation, the invariance property versus matched uncertainties of the system in sliding mode), arriving to illustrate recent Higher Order Sliding Mode Control algorithms capable of solving, in a robust way, classical optimal control problems, such as the Fuller’s Problem.
Physical Network System Dynamics
Abraham Jan (Arjan) van der Schaft, Rijksuniversiteit te Groningen
September 24, 2015 11:00 AM - 12:00 PM
Lind 305 [Map]Abstract
While complexity and large-scale systems have always been important themes in systems and control theory, the current flowering of network dynamics and control was not so easy to predict. Two main reasons for the enormous research activity are the ubiquity of large-scale networks in a large number of application areas (from power networks to systems biology) and the happy marriage between on the one hand systems and control theory and algebraic graph theory on the other. In this talk we will concentrate on network dynamics with a clear physical structure. Conservation laws and balance equations for physical network systems typically can be described with the aid of the incidence matrix of a directed graph, and associated Laplacian matrices. Several examples will be discussed, from mechanical systems to chemical reaction networks, and the common mathematical structure will be identified. Furthermore, it will be shown how this formulation leads to structure-preserving model reduction approaches. An attempt will be made to formulate open problems regarding scalability of analysis and control methodologies and connections to optimization.
Nonlinear Systems Toolbox
Arthur Krener, Naval Postgraduate School
October 5, 2015 11:00 AM - 12:00 PM
Lind 305 [Map]Nonlinear Systems Toolbox
Arthur Krener, Naval Postgraduate School
October 6, 2015 11:00 AM - 12:00 PM
Lind 305 [Map]Nonlinear Systems Toolbox
Arthur Krener, Naval Postgraduate School
October 7, 2015 11:00 AM - 12:00 PM
Lind 305 [Map]When MIMO Control Meets MIMO Communication
Li Qiu, Hong Kong University of Science and Technology
October 8, 2015 11:00 AM - 12:00 PM
Lind 305 [Map]Abstract
It is now well understood that there is a minimal requirement on the channel
quality in feedback stabilization via a communication channel. In the case of SISO plant and SISO channel. This minimal channel quality is given in terms of the degree of instability of the plant to be stabilized. For a MIMO system controlled via a MIMO communication channel, things are much less clear. In this talk, we will examine some known results and also speculate some possible directions. In the MIMO study, majorization theory plays an important role.
Mathematical Methods in the Control of Quantum Mechanical Systems
Domenico D'Alessandro, Iowa State University
October 15, 2015 11:00 AM - 12:00 PM
Lind 305 [Map]Abstract
In the last decades, advances in pulse shaping techniques have opened
up the possibility of manipulation of systems whose evolution follows
the laws of quantum mechanics. Moreover, novel applications, such as in
quantum information processing, have offered further motivation for
this study.
From a mathematical point of view, the field which is now known as'Quantum Control' is a combination of different mathematical techniques borrowed from a wide variety of mathematical areas. Different tools apply to different models which correspond to different approximations
of the physical system at hand. The simplest case is the one of a closed
system, i.e., a system non interacting with the environment in any way
other than through the external controls, controlled in open loop, and
whose state can be modeled as a vector in a finite dimensional Hilbert
space. In this case, the operator describing the evolution belongs to a
Lie group and the control system is determined by a family of right
invariant vector fields on such a Lie group. Techniques of geometric
control are therefore appropriate. As some of the above assumptions on
the physical model are relaxed, different tools have to be used. The
consideration of 'open' systems, which also allow for a continuous
measurement of the state and feedback, requires the introduction of
techniques of dynamical semigroups as well as stochastic calculus. The
study of infinite dimensional quantum control systems is often done
using tools of functional analysis and control of partial differential
equations.
This talk is a brief survey of the field from the point of view of the
mathematics that is used and needs to be developed. After introducing
basic notions of quantum mechanics and the relevant models used in applications I will indicate a number of open mathematical problems.
The Scope of Linear Matrix Inequality Techniques
J. William Helton, University of California, San Diego
November 5, 2015 11:00 AM - 12:00 PM
Lind 305 [Map]Abstract
One of the main developments in optimization over the last 20 years is
Semi-Definite Programming. It treats problems which can be expressed as a
Linear Matrix Inequality (LMI). Any such problem is necessarily convex,
so the determining the scope and range of applicability comes down to the
question:
How much more restricted are LMIs than Convex Matrix Inequalities?
The talk gives a survey of what is known on this issue and will be
accessible to about anybody.
There are several main branches of this pursuit.
First there are two fundamentally different classes of linear systems
problems. Ones whose statements do depend on the dimension of the
system "explicitly" and ones whose statements do not.
Dimension dependent systems problems lead to traditional
semialgebraic geometry problems, while dimension free systems
problems lead directly to problems in matrix unknowns and a new area
which might be called noncommutative semialgebraic geometry.
Most classic problems of control lead to noncommutative problems.
In this talk after laying out the distinctions above
we give results and conjectures on the answer to
the LMI vs convexity question.
Optimization in the Nervous System
Theoden Netoff, University of Minnesota, Twin Cities
November 11, 2015 1:00 PM - 2:00 PM
Lind 305 [Map]Abstract
Deep brain stimulation is a therapy where an electrode is placed in the
brain and periodic electrical pulses are delivered for treatment of
diseases such as Parkinson's Disease and Epilepsy. This therapy has
been quite successful in Parkinson's and moderately successful in
epilepsy. Despite the wide range of stimulation parameters that can be
used, only a small range is used by the clinician setting them. A
closed loop optimization algorithm optimizing stimulation parameters
based on physiological measures may deliver patient specific treatment
achieving higher efficacy with lower energy. I will discuss the
approaches my lab has taken for designing optimal stimulation from
physiological signals.
In another application of control in the nervous system, I will discuss
how control is used in development. The nervous system must use closed
loop control during development to achieve the proper balance of
excitation and inhibition and network topological structures. I will
also briefly try to describe an open question of how neurons develop
complex networks with limited information about their neighbors.
Control and Inverse Problems for Partial Differential Equations on Graphs
Sergei Avdonin, University of Alaska
November 12, 2015 11:00 AM - 12:00 PM
Lind 305 [Map]Abstract
We consider control and inverse problems on metric graphs for several
types of PDEs including
the wave, heat and Schr\"odinger equations. We demonstrate that, for
graphs without cycles,
unknown coefficients of the equations together with the topology of the
graph and lengths of the edges
can be recovered from the dynamical Dirichlet-to-Neumann map associated
to the boundary vertices.
For general graphs with cycles additional observations at the internal
vertices are needed for stable identification.
The corresponding exact controllability results are also proved.
Variational Calculus, Sums of Squares and Moment Problems
Farhad Jafari, University of Wyoming
December 3, 2015 11:00 AM - 12:00 PM
Lind 305 [Map]Abstract
In this talk, we connect the general problem of variational calculus to
moment problems and describe how this reformulation may be used to approach the original problem. Some recent developments on moment problems will be described.
Non-smooth and Non-convex Optimization
Kazufumi Ito, North Carolina State University
December 10, 2015 11:00 AM - 12:00 PM
Lind 305 [Map]Abstract
A general class of non-smooth and non-convex optimization
problems is discussed. Such problems arise in imaging analysis, control
and inverse problems and calculus of variation and much more.
Our analysis focuses on the infinite dimensional case (PDE-constaint
problem and mass transport problem and so on). The Lagrange multiplier theory is developed. Based on the theory we
develop the semi-smooth Newton method in the form of
Primal-Dual Active set method. Examples are presented to demonstrate
the theory and our analysis.
Using Approximations in Controller Synthesis for Systems Modelled by Partial Differential Equations
Kirsten Morris, University of Waterloo
February 4, 2016 11:00 AM - 12:00 PM
Lind 305 [Map]Abstract
There are essentially two approaches to controller design for systems modeled by a partial differential equation: direct and indirect. In direct controller design, the original model is used design the controller. In indirect controller design, a finite-dimensional approximation of the system is obtained and controller design is based on this approximation. The chief drawback of direct controller design is that a representation of the solution suitable for calculation is required. For many practical examples, this is not possible and so indirect controller design is generally used in practice. The hope is that the controller designed using the finite-dimensional approximation has the desired effect on the original system. Unfortunately, this is not always the case. Conditions under which the indirect approach to controller design works have been obtained and are presented. The difference between approximation of parabolic and of hyperbolic equations is illustrated by several simple equations.
The performance of controlled partial differential equations depends on the location of controller hardware, the sensors and actuators. The best locations may be different from those chosen based on physical intuition. Furthermore, since it is often difficult to move hardware, and trial-and-error is laborious when there are multiple sensors and actuators, analysis is crucial. Approximations to the governing equations, often of very high order, are required and this complicates not only controller design but also optimization of the hardware locations. Care needs to be taken in formulating the joint optimization/ controller design problem in order to obtain correct results. Numerical issues will be briefly discussed.
Effect of Dynamic Network's Topology on Performance and Stability
Yoonsoo Kim, Gyeongsang National University
February 11, 2016 11:00 AM - 12:00 PM
Lind 305 [Map]Abstract
This talk is about the speaker's recent research work which offers ideas on how a network of dynamical systems is affected by its network topology from the performance and stability perspective. Unlike many existing works, the present talk focuses on the interplay between network topology and 'local dynamics'. More specifically, the present talk is mainly concerned with two issues. The first one is about finding the most important link(s) in the network which affects the network's H-infinity performance measure, and the second one is about designing the link weights that maximize the network's stability margin (MIMO gain and phase margins). A vehicle network for formation flight will be used to demonstrate the discussion on the two issues.
Some Remarks on Controllability and Time Optimal Control for Infinite Dimensional Dynamical Systems
Marius Tucsnak, Université de Lorraine
February 18, 2016 11:00 AM - 12:00 PM
Lind 305 [Map]Abstract
This talk aims to introduce, as elementary as possible, some classical or more recent results in infinite dimensional systems theory, with emphasis on controllability and time optimal control questions. After recalling the main controllability types and their characterization by duality, we provide an infinite dimensional version of the Hautus test, which we apply to Schrodinger type systems. The second part of the talk is devoted to time optimal control problems and more precisely to recently developed methods allowing to establish the ban-bag property of optimal controls.
Lecture
Scott Hansen, Iowa State University
February 25, 2016 11:00 AM - 12:00 PM
Lind 305 [Map]Abstract forthcoming.
Previous Annual Seminars