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Communications in Information and Systems
Communications in Information and Systems
Wong, Wing Shing; Baillieul, John
The interaction of information and control has been a topic of interest to system
theorists that can be traced back at least to the 1950’s when the fields of communications, control,
and information theory were new but developing rapidly. Recent advances in our understanding of
this interplay have emerged from work on the dynamical effect of state quantization together with
results connecting communication channel data rates and system stability. Although this work has
generated considerable interest, it has been centrally concerned with the relationship between control
system performance and feedback information processing rates while ignoring the complexity (i.e. the
cost of information processing). The concepts of communication...
Verriest, Erik I.
The dynamics of hybrid systems with mode dynamics of different dimensions is
described. The first part gives some deterministic examples of such multi-mode multi-dimensional
$(M^3D)$ systems. The second part considers such models under sequential switching at random times.
More specifically, the backward Kolmogorov equation is derived, and Lie-algebraic methods are used
in the case where the modes are linear. For Poissonian switched equi-dimensional modes, the diffusion
limit and its implication in vibrational stability are studied. The motion of a pebble on an
elevator belt is given as an example.
Sanyal, Amit K.; Moseley, Christopher; Bloch, Anthony
Liberzon, Daniel
This paper discusses several recent results by the author and collaborators, which are
united by the common goal of making nonlinear control theory more robust to imperfect information.
These results are also united by common technical tools, centering around input-to-state stability
(ISS), small-gain theorems, Lyapunov functions, and hybrid systems. The goal of this paper is
to present an overview of these results which highlights their unifying features and which is more
accessible to a general audience than the original technical articles.
Khaneja, Navin
Control and manipulation of quantum mechanical systems using electromagnetic
fields is a widely studied subject in areas of physics and chemistry, including spectroscopy, atomic
molecular, and optical physics, and quantum chemistry. This article attempts to provide a glimpse
into the rich class of bilinear control systems that are ubiquitous in these problems. In this article,
we use control of spin systems in magnetic resonance as a model system to highlight characteristic
feature of problems in quantum control. Background information is provided to enable the reader
to appreciate new results and developments, where principled use of ideas from control theory have
provided new insights into finding optimal ways...
Scardovi, Luca; Leonard, Naomi; Sepulchre, Rodolphe
This paper proposes a methodology to stabilize relative equilibria in a model of
identical, steered particles moving in three-dimensional Euclidean space. Exploiting the Lie group
structure of the resulting dynamical system, the stabilization problem is reduced to a consensus
problem on the Lie algebra. The resulting equilibria correspond to parallel, circular and helical
formations. We first derive the stabilizing control laws in the presence of all-to-all communication.
Providing each agent with a consensus estimator, we then extend the results to a general setting that
allows for unidirectional and time-varying communication topologies.
Lee, Taeyoung; Leok, Melvin; McClamroch, N. Harris
This paper formulates optimal control problems for rigid bodies in a geometric manner
and it presents computational procedures based on this geometric formulation for numerically
solving these optimal control problems. The dynamics of each rigid body is viewed as evolving on a
configuration manifold that is a Lie group. Discrete-time dynamics of each rigid body are developed
that evolve on the configuration manifold according to a discrete version of Hamilton’s principle so
that the computations preserve geometric features of the dynamics and guarantee evolution on the
configuration manifold; these discrete-time dynamics are referred to as Lie group variational integrators.
Rigid body optimal control problems are formulated as...
Jayawardhana, Bayu; Logemann, Hartmut; Ryan, Eugene P.
An input-to-state stability theory, which subsumes results of circle criterion type, is
developed in the context of a class of infinite-dimensional systems. The generic system is of Lur’e
type: a feedback interconnection of a well-posed infinite-dimensional linear system and a nonlinearity.
The class of nonlinearities is subject to a (generalized) sector condition and contains, as particular
subclasses, both static nonlinearities and hysteresis operators of Preisach type.
Hirschorn, Ronald
The well known Brockett condition - a topological obstruction to the existence of
smooth stabilizing feedback laws - has engendered a large body of work on discontinuous feedback
stabilization. The purpose of this paper is to introduce a class of control-Lyapunov function from
which it is possible to specify a (possibly discontinuous) stabilizing feedback law. For control-affine
systems with unbounded controls Sontag has described a Lyapunov pair which gives rise to an explicit
stabilizing feedback law smooth away from the origin - Sontag’s “universal construction” of Artstein’s
Theorem. In this work we introduce the more general “lower bounded control-Lyapunov function”
and a “universal formula” for nonaffine systems....
Gharesifard, Bahman; Lewis, Andrew D.; Mansouri, Abdol-Reza
We present a geometric formulation for the energy shaping problem. The central
objective is the initiation of a more systematic exploration of energy shaping with the aim of de-
termining whether a given system can be stabilized using energy shaping feedback. We investigate
the partial differential equations for the kinetic energy shaping problem using the formal theory of
partial differential equations. The main contribution is sufficient conditions for integrability of these
partial differential equations. We couple these results with the integrability results for potential
energy shaping. This gives some new avenues for answering key questions in energy shaping that
have not been addressed to this point.
Byrnes, Christopher I.
Yau, Stephen S. T.
It is well known that the filtering theory has important applications in both military
and commercial industries. The Kalman–Bucy filter has been used in many areas such as navigational
and guidance systems, radar tracking, solar mapping, and satellite orbit determination. However, the
Kalman–Bucy filter has limited applicability because of the linearity assumptions of the drift term
and observation term as well as the Gaussian assumption of the initial value. Therefore there has
been an intensive interest in solving the nonlinear filtering problem. The central problem of nonlinear
filtering theory is to solve the DMZ equation in real time and memoryless way. In this paper, we
shall describe...
Purkayastha, Punyaslok; Baras, John S.
We consider the routing problem in wireline, packet-switched communication networks. We cast our optimal routing
problem in a multicommodity network flow optimization framework. Our cost function is related to the congestion
in the network, and is a function of the flows on the links of the network. The optimization is over the set of flows
in the links corresponding to the various destinations of the incoming traffic. We separately address the
single commodity and the multicommodity versions of the routing problem. We consider the dual problems,
and using dual decomposition techniques, we provide primal-dual algorithms that converge to the optimal solutions
of the problems. Our algorithms,...
Hu, Jiaqiao; Fu, Michael C.; Marcus, Steven I.
We propose a randomized search method called Stochastic Model Reference Adaptive
Search (SMRAS) for solving stochastic optimization problems in situations where the objective
functions cannot be evaluated exactly, but can be estimated with some noise (or uncertainty), e.g.,
via simulation. The method generalizes the recently proposed Model Reference Adaptive Search
(MRAS) for deterministic optimization, which is motivated by the well-known Cross-Entropy (CE)
method. We prove global convergence of SMRAS in a general stochastic setting, and carry out
numerical studies to illustrate its performance. An emphasis of this paper is on the application
of SMRAS for solving static stochastic optimization problems; its various applications for solving
dynamic decision making...
Gerencsér, László; Kmecs, Ildikó; Torma, Balázs
Ekanayake, M. P. B.; He, B.; Huo, L.; Kaphle, K.; Martin, C.
The goal of this paper is to study the entire class of linear second order multi-point methods. We characterize,
as a three parameter family, those methods with good numerical
properties. We will examine the error analysis of the class of second order methods and will study
in some detail the statistics of switching between two methods. We characterize the average value
obtained by switching and construct the covariance matrix. Two examples are done in some detail.
Chiuso, Alessandro; Picci, Giorgio; Soatto, Stefano
In this paper we consider a simple estimation problem on the special orthogonal
group $SO(n)$ and indicate a possible way to construct approximate filters which is much in the same
spirit of the “wide sense” approach to linear filtering theory. Our interest is mainly motivated by
applications to computer vision.
Martin, P.; Egerstedt, M.
Robot navigation over large areas inevitably has to rely on maps of the environment.
The standard manner in which such maps are defined is through geometry, e.g. through traversability
grid maps or through a division of the environment into free-space and obstacle-space. In this paper,
we combine certain aspects of the geometric maps, through the notion of distinctive places, with a
topological description of how these places are related. What is novel is the idea that the adjacency
relation is defined by the existence of a control law that drives the robot between topologically
connected places. Moreover, these maps can be automatically constructed based on the...
Ebenbauer, Christian; Arsie, Alessandro
Dirr, G.; Helmke, U.
We investigate a generalization of Brockett’s celebrated double bracket flow that is
closely related to matrix Riccati differential equations. Using known results on the classification of
transitive Lie group actions on homogeneous spaces, necessary and sufficient conditions for accessibility
of the generalized double bracket flow on Grassmann manifolds are derived. This leads to
sufficient Lie–algebraic conditions for controllability of the generalized double bracket flow. Accessibility
on the Lagrangian Grassmann manifold is studied as well, with applications to matrix Riccati
differential equations from optimal control.