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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
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.
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.
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.